The Physics of Tennis

Everything a player does before contact (ground impulse, pelvis, trunk, shoulder, forearm, hand) is compressed without remainder into the racket's state at first contact: its velocity and angular velocity, its face orientation, the impact point on the string bed, and its inertia at that point. The impact lasts 3 to 5 ms (laboratory impact measurements, racket-parameter review S21). An impulse travels from the string bed to the hand in about 1.5 ms (S21, S22), so the hand does shape racket motion during contact, but that influence does not reach the ball's outgoing speed: zero versus maximal grip firmness on off-centre impacts produced no significant difference in post-impact ball velocity (S25, laboratory intervention, hand-held racket), and pre-impact grip force explains 25 to 36 percent of the variance in post-impact handle vibration while being unrelated to rebound speed or accuracy (S21, review of laboratory and simulation studies). Population: laboratory impacts and simulation, not matched to any player level; outcome: ball speed; evidence class: INTERVENTION on the rig, MODEL in simulation. The law follows from the impulse identities (S1): the ball's momentum and angular momentum change only through the force exchanged during contact, so a mechanical claim about a stroke is a claim about one of the contact-state variables or it is not a mechanical claim. A follow-through acts on the next contact state, never on the ball already in flight.

Linear and angular impulse: m(v+ - v-) = integral of F dt and dL = integral of r x F dt over the contact window (S1). The body is a coupled multi-segment system, M(q) q'' + C(q,q') + g(q) = tau + J^T F_ground (S2); the racket contact-point velocity is a geometric map v_C = J_C(q) q'. Once the ball is on the strings the only forces on it are the string-bed force and gravity, so the body's remaining influence is through how the racket itself responds (effective mass, compliance), and wave travel time to the hand (about 1.5 ms) against a 3 to 5 ms dwell lets the hand alter vibration, not the momentum already exchanged.

• S1OpenStax University Physics vol. 1, 9.2 Impulse and Collisionslinear and angular impulse identities; internal forces cancel in the whole-system momentum balance
• S2Koike & Harada 2013, JSME Symposium on Sports Engineering (dynamic contribution formulation)motion-dependent terms separated from joint torque; a kinematic contribution is not a causal one
• S21Allen et al. 2014 (Sheffield Hallam), review of tennis racket performance parametersimpact 3 to 5 ms; grip force unrelated to rebound speed; e_A about 0.4 at 280 N rising about 7 percent at 224 N; swingweight 0.030 to 0.035 kg m^2 band; 15 percent energy lost in the ball vs 2 to 4 percent in strings
• S22Cross, The sweet spots of a tennis racquetCOR about 0.86 at the node, 0.54 at the tip, 0.71 at the throat; effective mass M_e = M/(1 + M b^2/I_cm)
• S25Elliott 1982, grip firmness and post-impact ball velocity (off-centre impacts)zero vs maximal grip firmness: no significant difference in post-impact ball velocity

For the component normal to the string plane, v_out = e_A v_in + (1 + e_A) V_r, where e_A is the apparent coefficient of restitution at the impact point (S21, S23, S24). Hand-held, mid-string, at 280 N string tension, e_A is about 0.40, rising about 7 percent to 0.43 when tension drops 20 percent to 224 N (S21, laboratory measurement); so one extra m/s of racket speed is worth about 1.4 m/s of ball speed and one extra m/s of incoming ball speed about 0.4 m/s, a 3.5 to 1 ratio that is a model consequence of e_A about 0.4, not a measured stroke. e_A is set by the racket's effective mass at the impact point, M_e = M/(1 + M b^2/I_cm), smallest at the tip and largest at the throat (S22, S3): the coefficient of restitution of a freely suspended racket peaks at about 0.86 at the vibration node near the string centre and falls to about 0.54 at the tip and 0.71 at the throat (S22), and the hand-held perpendicular speed ratio varies from about 0.1 to 0.5 by impact point against about 0.85 with the head clamped (S24, S23). An impact-point error of about one head radius therefore costs about 37 percent of the restitution term, the largest single loss measured anywhere in the system; no body-segment timing error has been shown to cost that order (S22, S21). Clamped-head string and spin tests overstate normal rebound by roughly a factor of two and must be rescaled before being applied to a stroke (S23, S24, S6). About 15 percent or more of the kinetic energy is lost inside the ball and only 2 to 4 percent in the strings (S21). Population: rig and hand-held laboratory impacts; outcome: ball speed; evidence class: INTERVENTION on the rig and MODEL.

One-dimensional momentum balance with a restitution condition: v_n+ = (1 + e_n) M_eff U_n/(M_eff + m) + (m - e_n M_eff) v_n-/(M_eff + m). For a freely recoiling rigid racket 1/M_eff = 1/M_r + (r x n)^T I_r^-1 (r x n), so an off-centre impulse spends part of the collision in racket rotation (S3, S22). The ball is the main energy sink (S21, S23), which is why court or racket restitution changes move ball speed less than racket speed does.

• S3Cross & Bower, Effects of swing-weight on swing speed and racket powerV = C/I0^0.27 in maximal-effort rod swings by four male students; mass vs swingweight separated; effective-mass model
• S6Cross & Lindsey, TWU spin experimentincoming conditions affect rebound spin more than small string-property changes; hand-held tests do not reproduce clamped results
• S21Allen et al. 2014 (Sheffield Hallam), review of tennis racket performance parametersimpact 3 to 5 ms; grip force unrelated to rebound speed; e_A about 0.4 at 280 N rising about 7 percent at 224 N; swingweight 0.030 to 0.035 kg m^2 band; 15 percent energy lost in the ball vs 2 to 4 percent in strings
• S22Cross, The sweet spots of a tennis racquetCOR about 0.86 at the node, 0.54 at the tip, 0.71 at the throat; effective mass M_e = M/(1 + M b^2/I_cm)
• S23Cross, Effects of string tension and ball dynamicsclamped vs hand-held restitution; incoming-speed dependence; ball as the main energy sink
• S24Cross & Lindsey, TWU racquet power (effective mass and ACOR by impact point)hand-held perpendicular speed ratio 0.1 to 0.5 by impact point vs about 0.85 clamped

In maximal-effort swings of weighted rods by four male students, swing speed decreased with swingweight as V = C/I0^n with n = 0.27 for I0 above 0.03 kg m^2, while swing speed stayed approximately constant as mass increased at fixed swingweight (S3, within-person INTERVENTION on the implement, n = 4, non-tennis strokes). Remarkably similar exponents were obtained for softball bats (0.25) and golf clubs (0.26) (S3, S21), so the exponent describes the human rotational actuator across implements rather than any racket. Combining V(I0) with e_A(I0, r) gives an interior optimum, which the racket-parameter review places at swingweights of about 0.030 to 0.035 kg m^2 for ball speed and accuracy (S21, MODEL plus review). The constant C is an individual property and is not measured in any tennis population here. Population: four male students swinging rods, bats and clubs; outcome: implement speed; the transfer to a tennis stroke by an adult club player is an inference.

A rotational actuator with a torque-velocity limit drives an implement of moment of inertia I0 about a pivot near the hands; the achievable angular velocity falls as inertia rises, and the empirical power law with n about 0.25 to 0.27 is the fitted shape of that limit. Ball speed then rises with I0 through effective mass (S22) but falls with I0 through V, giving the interior optimum.

• S3Cross & Bower, Effects of swing-weight on swing speed and racket powerV = C/I0^0.27 in maximal-effort rod swings by four male students; mass vs swingweight separated; effective-mass model
• S21Allen et al. 2014 (Sheffield Hallam), review of tennis racket performance parametersimpact 3 to 5 ms; grip force unrelated to rebound speed; e_A about 0.4 at 280 N rising about 7 percent at 224 N; swingweight 0.030 to 0.035 kg m^2 band; 15 percent energy lost in the ball vs 2 to 4 percent in strings
• S22Cross, The sweet spots of a tennis racquetCOR about 0.86 at the node, 0.54 at the tip, 0.71 at the throat; effective mass M_e = M/(1 + M b^2/I_cm)

Spin is a tangential collision outcome. During an oblique impact the ball first slides on the strings while friction spins it up, then grips; rolling commenced near the mid-point of impact in Cross's measurements, and before separation the gripped contact releases and the friction force reverses, so the ball leaves with less spin than it carried mid-impact (S4, S5, laboratory oblique impacts, clamped and hand-held). The tangential restitution e_T depends much more strongly on incident spin than on incident angle (S4, S5): a ball incident with enough topspin can leave with more parallel speed and more spin than one incident with backspin, so the incoming ball's spin is a first-order input to the outgoing spin. The string bed supplies an independent increment through lateral main-string movement and return, which needs low string-on-string friction and adequate ball-on-string traction: cutting cross strings from 19 to 13 raised rebound topspin from 117 to 170 rad/s at fixed incoming kinematics while outbound speed stayed independent of pattern (S19, rig INTERVENTION), and ITF clamped-racket tests at 25 m/s, 40 degrees to the normal with 4000 rpm incoming backspin returned 1100 to 1900 rpm across string types, a 70 percent spread at identical kinematics (S21). On a clamped racket, string tension, frame stiffness and impact velocity all changed post-impact angular velocity (S20); on a hand-held racket incoming conditions moved spin more than small string-property changes (S6). In 13 male collegiate players hitting topspin forehands off shoulder-high feeds, racket face angle and vertical racket velocity predicted ball spin within the task, while racket-path angle alone was not a significant predictor (S10, CORRELATIONAL, laboratory). Population: rig impacts and collegiate men; outcome: ball spin; evidence class: INTERVENTION on rigs, CORRELATIONAL for the players.

Angular impulse dL = -R n x J_t for a centred sphere; the tangential impulse is bounded by friction |F_t| <= mu F_n during sliding and by the rolling condition at grip, so spin is capped near omega <= v_t/R at the transition. Tangential elastic storage in the string bed (e_x > 0) adds angular impulse during the restitution phase when main strings slide laterally and return (S5, S19); grip-release reversal subtracts it. Equal path angles therefore give different spin when face angle, incoming spin, impact point or string response differ.

• S4Cross, Oblique impact of a tennis ball on the strings of a tennis racketball slides, grips, then releases during one impact; court grip above about 20 degrees incidence; horizontal speed roughly halves after a gripping zero-spin bounce
• S5Cross, Enhancing the bounce of a ball (tangential elastic storage, inter-string friction)tangential energy storage and return in the string bed; additional spin requires e_x > 0; low inter-string friction
• S6Cross & Lindsey, TWU spin experimentincoming conditions affect rebound spin more than small string-property changes; hand-held tests do not reproduce clamped results
• S10Kwon et al. 2017, racquet kinematics and topspin angular velocity13 male collegiate players: face angle and vertical racket velocity predicted topspin; path angle alone not significant
• S19Washida, Elliott & Allen 2014, Procedia Engineering 72:557-562, main string movement and ball spinfewer cross strings: larger main-string deflection, higher rebound spin, lower horizontal rebound speed
• S20Bower & Sinclair 2007, Sports Engineering 10:111-122, racket stiffness, string tension and impact velocity effects on ball angular velocityclamped racket: tension, stiffness and impact velocity all affected post-impact angular velocity
• S21Allen et al. 2014 (Sheffield Hallam), review of tennis racket performance parametersimpact 3 to 5 ms; grip force unrelated to rebound speed; e_A about 0.4 at 280 N rising about 7 percent at 224 N; swingweight 0.030 to 0.035 kg m^2 band; 15 percent energy lost in the ball vs 2 to 4 percent in strings

After separation the ball obeys m dv/dt = m g - (1/2) rho A C_D |w| w + (1/2) rho A C_L |w|^2 l, with Magnus force along omega x w (S13, MODEL). Drag on a tennis ball at 30 m/s exceeds the ball's weight (S13), so no tennis trajectory is a vacuum parabola. Wind-tunnel measurements of new balls give C_D about 0.6 to 0.7 over Reynolds numbers 167,000 to 284,000 with no drag crisis because the felt trips the boundary layer (S31, laboratory measurement), while free-flight measurements give C_D 0.507 +/- 0.024, independent of speed and spin, with significant lift at near-zero spin from surface asymmetry and shot-to-shot variation in both coefficients (S30, field measurement). Two laws follow. There is a lift floor: a ball with near-zero spin still deviates, so spin governs flight only above that floor. And every spin value inferred from a tracked trajectory inherits the C_D disagreement of about 0.5 against 0.6, roughly 18 percent: a 2023 comparison found a trajectory model estimated spin with bias +/- SD of 2.92 +/- 222.76 rpm against Hawk-Eye's -100.01 +/- 542.44 rpm, an RMSE 327.63 rpm lower, and neither method estimated spin consistently above 4500 rpm (S29, MODEL vs tracking, professional serves). The 2026 decomposition of 8,654 serves from the 2022 Australian Open fit trajectories with median residuals of 4.8 mm before the bounce and 2.4 mm after, with spin inferred through an assumed constant drag coefficient per trajectory and a specified lift-spin relation (S12, MODEL, touring professionals, men and women). Nap height changes drag enough to move a typical serve about 40 cm at the receiver's baseline (S31, S13). Population: laboratory balls and professional match tracking; outcome: ball flight and inferred spin.

Drag and lift scale with rho A |w|^2; the felt fixes a turbulent boundary layer so the drag coefficient does not fall at a critical speed as it does for smooth spheres; the Magnus force is perpendicular to velocity along the spin-velocity cross product, so topspin adds a downward component, backspin an upward one, and a vertical spin axis curves flight sideways. Inferring spin from curvature requires assuming C_D and the C_L to spin relation, so the two coefficients' uncertainty propagates into every tracked spin figure.

• S12Eassom, Robertson & Reid 2026, Sports Engineering, tennis ball trajectory decomposition from tracking data8,654 serves, 2022 Australian Open: median fit residuals 4.8 mm before and 2.4 mm after bounce; spin inferred via aerodynamic model
• S13Cross & Lindsey, TWU aerodynamics of a tennis balldrag at 30 m/s exceeds the ball's weight; Magnus force direction; dependence on Reynolds number and spin parameter
• S29Trajectory-model versus Hawk-Eye spin estimation (Int. J. Performance Analysis in Sport, 2023)model bias +/- SD 2.92 +/- 222.76 rpm vs Hawk-Eye -100.01 +/- 542.44 rpm; RMSE 327.63 rpm lower; neither valid above 4500 rpm
• S30Cross & Lindsey, Measurements of drag and lift on tennis balls in flightfree-flight C_D 0.507 +/- 0.024, independent of speed and spin; lift present at near-zero spin; shot-to-shot variation
• S31Mehta & Pallis, The aerodynamics of a tennis ball (wind tunnel)C_D about 0.6 to 0.7 for new balls over Re 167,000 to 284,000; no drag crisis; nap condition shifts drag

At the court the normal impulse sets the rebound's vertical speed through the ball's restitution, and the tangential friction impulse couples horizontal speed and spin: delta v_x = J_x/m and delta omega = -R J_x/I_b (S1, S18, MODEL). The ITF 2026 Technical Booklet defines Court Pace Rating as CPR = 100(1 - mu) + 150(0.81 - e_T), measured with a spin-free ball at about 30 m/s and 16 degrees, with sliding assumed throughout contact (S14); courts are classed by sliding friction (COF above 0.71 high, below 0.55 low) and by restitution (COR above 0.85 high, below 0.78 low), and for the standard test the ball slides throughout only if mu is below 0.77 (S26, laboratory and field measurements). Sliding friction is not a constant: COF is roughly constant below about 15 degrees incidence and falls as the angle rises (S26). A ball incident without spin at more than about 20 degrees usually grips the court, after which its horizontal speed is roughly halved regardless of incidence angle (S4). The horizontal coefficient of restitution of a tennis ball, measured by video for zero-spin incidence at various angles on several surfaces, ranged from -0.51 to +0.24 with incident angle and friction, and under some conditions the ball spun faster than the rolling limit because ball or surface stored tangential elastic energy (S18, laboratory INTERVENTION). So the court is not a passive brake: both impact surfaces in tennis can return tangential energy. When R omega exceeds v_x at contact, friction acts forward and converts spin into forward speed; an increase in post-bounce rpm never means the court created energy. Bounce height depends on incoming vertical speed and normal restitution, not on topspin alone, and pressurized balls lose about 20 percent of restitution when punctured (S21, S23). Population: laboratory ball-surface impacts and ITF court tests; outcome: rebound speed, angle and spin.

Oblique impact on a surface: normal restitution v_z+ = -e v_z-; tangential impulse changes translation and rotation in fixed ratio through the ball's moment of inertia; the bottom-point slip u_x = v_x - R omega decides whether friction slows or speeds the ball; tangential compliance (e_x > 0) allows spin beyond the rolling limit. Pure rotation about the vertical axis produces no sideways slip at a point contact, so a 'sidespin' that curves flight need not kick sideways on the bounce.

• S1OpenStax University Physics vol. 1, 9.2 Impulse and Collisionslinear and angular impulse identities; internal forces cancel in the whole-system momentum balance
• S4Cross, Oblique impact of a tennis ball on the strings of a tennis racketball slides, grips, then releases during one impact; court grip above about 20 degrees incidence; horizontal speed roughly halves after a gripping zero-spin bounce
• S14ITF 2026 Technical Booklet (court pace rating)CPR = 100(1 - mu) + 150(0.81 - e_T); test at about 30 m/s and 16 degrees; sliding assumed throughout
• S18Cross 2002, Am. J. Phys., horizontal coefficient of restitution for a superball and a tennis balltennis-ball horizontal COR from -0.51 to +0.24 with incident angle and sliding friction; spin above the rolling limit via tangential elastic storage
• S21Allen et al. 2014 (Sheffield Hallam), review of tennis racket performance parametersimpact 3 to 5 ms; grip force unrelated to rebound speed; e_A about 0.4 at 280 N rising about 7 percent at 224 N; swingweight 0.030 to 0.035 kg m^2 band; 15 percent energy lost in the ball vs 2 to 4 percent in strings
• S23Cross, Effects of string tension and ball dynamicsclamped vs hand-held restitution; incoming-speed dependence; ball as the main energy sink
• S26Cross, Measurements of the speed and bounce of tennis courtsITF classes by COF and COR; Pace = 100(1 - mu) when sliding throughout; mu < 0.77 slides throughout the standard test; COF falls above about 15 degrees incidence

Across the opened stroke studies, no single joint or timing deviation is established as the dominant cause of lost racket speed, ball speed or spin across stroke families and skill levels; a dominant error can be named only after the output, stroke, incoming ball, impact point, equipment and measurement model are fixed (S2, S9, S15, S27, S28). Segment 'contribution' percentages are kinematic projections of a velocity field onto racket-head velocity, not energy or impulse shares: in 11 players' power serves, internal rotation contributed 54.2 percent, hand flexion 31.0 percent, horizontal flexion 12.9 percent, shoulder linear velocity 9.7 percent and forearm extension -14.4 percent of forward racket velocity (S27, CORRELATIONAL kinematics), and the method's authors state the contribution depends on both the segment's angular velocity and the racket's instantaneous position relative to its axis, with pronation fastest at impact (24 rad/s) yet ranked fourth at 4 m/s (S28); in elite forehands measured by IMU, upper-arm horizontal flexion accounted for about 45 to 48 percent, forearm extension 17 to 21 percent and internal rotation 14 to 16 percent of modeled anteroposterior racket velocity (S16). Percentages that exceed 100 percent with a negative member cannot be additive sources. Across skill, six ATP professionals against seven high-performance players showed later peak pelvis (-0.075 +/- 0.008 vs -0.093 +/- 0.012 s before impact) and trunk angular velocity (-0.057 +/- 0.004 vs -0.075 +/- 0.011 s; p < 0.01) with a tendency to higher racket speed (33.1 +/- 2.4 vs 31.1 +/- 1.9 m/s; p < 0.05) and similar peak angular velocities (S9, CORRELATIONAL, 400 Hz, fastest successful shots selected). In 36 competitive servers the time between peak vertical and peak anteroposterior ground force (r = -0.519) and between peak anteroposterior force and impact (r = -0.522) were the best predictors of maximal racket velocity, while mean and peak vertical ground force and its rate of development did not correlate (S15, CORRELATIONAL, two force plates); in nine players three peak ground-force components jointly explained 37 percent of ball-speed variance at prescribed effort levels, which is a share of variance, not of energy (S8); a greater knee-flexion group gained +130.3 deg/s knee extension and +3.33 km/h (about 0.93 m/s, about 3 percent) of racket velocity (S32). None of these is a perturbation study: no study constrained a segment and measured the racket-speed consequence, so causal contribution remains an inference from coordination. Population: touring and competitive men, elite forehands, 400 to 480 Hz laboratory capture; outcome: racket-head and ball speed; evidence class: CORRELATIONAL throughout.

Racket contact-point velocity is v_C = J_C(q) q', a sum of angular-velocity vectors with configuration-dependent lever arms, so a joint can create racket speed early in the swing without a large instantaneous geometric share at contact, and vice versa (S2). The question 'what caused the loss' requires a counterfactual map from torque history to the contact state, which only an intervention or a validated forward-dynamics model supplies; peak-order timing identifies neither.

• S2Koike & Harada 2013, JSME Symposium on Sports Engineering (dynamic contribution formulation)motion-dependent terms separated from joint torque; a kinematic contribution is not a causal one
• S8Shimokawa et al. 2020, ground reaction forces and forehand ball speed9 players; three peak GRF components jointly explained 37 percent of ball-speed variance
• S9Landlinger et al. 2010, JSSM 9:643-651, forehand of different skill levels6 ATP professionals vs 7 high-performance players, 400 Hz: pelvis and trunk peak timing differ, racket speed 33.1 vs 31.1 m/s
• S15Fourel et al. 2024, J Strength Cond Res 38(9):1667-1674, force-time curve variables and serve performance36 competitive players, two force plates: GRF timing intervals r = -0.519 and -0.522 best predictors of racket velocity; peak vertical GRF not correlated
• S16Pedro et al. 2022, Sensors 22:1283, IMU upper-limb joint contribution to racket head speed (elite forehand)upper-arm horizontal flexion about 45 to 48 percent, forearm extension 17 to 21, internal rotation 14 to 16 percent of modeled anteroposterior racket velocity
• S27Elliott, Marshall & Noffal 1995, contributions of upper-limb segment rotations in the power serve11 players: internal rotation 54.2 percent, hand flexion 31.0, horizontal flexion 12.9, shoulder linear 9.7, forearm extension -14.4 percent of racket velocity
• S28Sprigings et al. 1994, three-dimensional kinematic method for arm segment rotations and racquet-head speedcontribution depends on segment angular velocity and racquet position; internal rotation 8 m/s greatest, pronation 24 rad/s but fourth at 4 m/s
• S32Knee flexion and serve racket velocity (PMC 2024)greater knee-flexion group: +130.3 deg/s knee extension speed and +3.33 km/h racket velocity
• S33Iino & Kojima, kinematics of table tennis topspin forehands by performance leveladvanced players: larger lower-trunk rotation contribution and steeper racket acceleration, racket speed at impact not different (named limit: table tennis)

Serves, drives, slices, volleys and drop shots differ in the incoming ball state, contact height, reachable racket configurations and the three-dimensional spin axis they set, not in the physics that maps the contact state to the ball (S1, S4, S7). In seven male players serving with marked balls at 500 Hz, mean forward ball speeds were about 51, 46 and 40 m/s for flat, slice and kick serves with spins of about 1240, 2300 and 3400 rpm, no flat serve was spin-free and the spin axes differed (S7, CORRELATIONAL, descriptive; the attached markers modified the measured ball). In 37 experienced and recreational adults, a commercial handle sensor reported topspin forehands at about 111 against 94 km/h and 2130 against 1590 rpm by group, with the instrumented rackets weighing about 376 g and spin inferred from handle motion rather than observed ball rotation (S11, CORRELATIONAL, device-inferred). A blocked return or volley can take most of its outgoing speed from the incoming ball, so a short racket motion is not a small ball impulse; a drop shot lowers outgoing speed by lowering relative normal speed or letting the racket recoil, with spin and direction remaining separate quantities (S1, S4, S24, MODEL deductions). The coverage gap is itself a finding: the opened joint-level studies measure touring professionals, competitive and collegiate men and elite forehands or serves; slice backhands, one- and two-handed backhand drives, volleys, drop shots, overheads, kick-serve spin-axis mechanics, women in contribution studies and adult recreational players are effectively unstudied at the segment level (S9, S10, S16, S27), and the professional tracking set covers flight, not body mechanics (S12). So any finding from a professional or collegiate population is a finding about that population until a source shows it transfers. Claimed PROBABLE because the stroke-family measurements rest on one small serve study and one device-inferred adult study.

The same impulse map (normal channel for speed, tangential channel for spin and launch direction) applies to every stroke; what changes is the input state: incoming velocity and spin, contact height, available swing path and time, and the achievable face orientation. Two hands on the handle add a force couple and a closed-loop constraint, slice reverses the tangential impulse sign, and a toss removes most incoming horizontal momentum.

• S1OpenStax University Physics vol. 1, 9.2 Impulse and Collisionslinear and angular impulse identities; internal forces cancel in the whole-system momentum balance
• S4Cross, Oblique impact of a tennis ball on the strings of a tennis racketball slides, grips, then releases during one impact; court grip above about 20 degrees incidence; horizontal speed roughly halves after a gripping zero-spin bounce
• S7Sakurai et al. 2007, ISB congress, ball spin in flat, slice and kick serves7 male players, 500 Hz: forward speeds about 51/46/40 m/s and spins about 1240/2300/3400 rpm; no flat serve spin-free
• S9Landlinger et al. 2010, JSSM 9:643-651, forehand of different skill levels6 ATP professionals vs 7 high-performance players, 400 Hz: pelvis and trunk peak timing differ, racket speed 33.1 vs 31.1 m/s
• S10Kwon et al. 2017, racquet kinematics and topspin angular velocity13 male collegiate players: face angle and vertical racket velocity predicted topspin; path angle alone not significant
• S11Rigozzi et al. 2023, Sensors 23:5146, flat vs topspin forehands in experienced and recreational adults37 adults, handle sensor: about 111 vs 94 km/h and 2130 vs 1590 rpm; sensor-inferred spin, 376 g instrumented rackets
• S12Eassom, Robertson & Reid 2026, Sports Engineering, tennis ball trajectory decomposition from tracking data8,654 serves, 2022 Australian Open: median fit residuals 4.8 mm before and 2.4 mm after bounce; spin inferred via aerodynamic model
• S16Pedro et al. 2022, Sensors 22:1283, IMU upper-limb joint contribution to racket head speed (elite forehand)upper-arm horizontal flexion about 45 to 48 percent, forearm extension 17 to 21, internal rotation 14 to 16 percent of modeled anteroposterior racket velocity
• S24Cross & Lindsey, TWU racquet power (effective mass and ACOR by impact point)hand-held perpendicular speed ratio 0.1 to 0.5 by impact point vs about 0.85 clamped
• S27Elliott, Marshall & Noffal 1995, contributions of upper-limb segment rotations in the power serve11 players: internal rotation 54.2 percent, hand flexion 31.0, horizontal flexion 12.9, shoulder linear 9.7, forearm extension -14.4 percent of racket velocity

In adults changing a motor pattern, three outcomes must be measured separately because each can move without the others: (1) acquisition, the movement and result produced during a practice session with the coach, the cue and the feed present; (2) retention, the same movement produced after a delay of at least 24 hours and ideally a week or more, with no reminder, no video and no coach; (3) transfer, the retained movement produced under representative conditions, a live opponent, variable balls, time pressure and a score. Observation: in Soderstrom and Bjork's 2015 review of the laboratory and classroom literature (CORRELATIONAL and INTERVENTION studies across adults), considerable learning occurred without performance gains during practice and substantial practice gains failed to appear at delayed tests; in Shea and Morgan 1979 (72 college students, INTERVENTION, 10-minute and 10-day retention) the group that looked better during acquisition retained and transferred worse. Observation in tennis: Buszard, Reid, Krause, Kovalchik and Farrow 2017 (INTERVENTION, 16 skilled youth tennis players, 10 serve-practice sessions, tests one week before and one week after) found no practice-performance difference between groups, yet the moderate-interference group improved serve displacement from the T only in the match-play transfer test and the low-interference group improved only in the closed skill test. Inference: a closed test and a match test estimate different quantities, so a stroke judged on one has not been judged on the other. Boundary: the dissociation is documented in laboratory adults, college students and skilled juniors; the Buszard effect sizes are from 16 juniors and are the only tennis-specific measurement opened; no leg opened a delayed, uncued, representative test of a prescribed stroke change in experienced adult club players.

Learning is a change in the stored capability to produce a movement; performance is the movement produced now under present support. Present support (a cue, a feed, a coach, a predictable ball) raises performance without changing the stored capability, and the stored capability can rise while effortful practice lowers today's performance. A measurement taken while the support is present estimates the sum of capability and support and cannot separate them; a delayed uncued test removes the support term; a representative test adds the match's own perturbations. The three estimands differ in what is held constant, so one number cannot stand for another.

• S1Soderstrom & Bjork 2015, Learning Versus Performance: An Integrative Review (Perspectives on Psychological Science)performance during practice is an unreliable index of learning; learning is inferred only from delayed retention and transfer
• S24Shea & Morgan 1979, Contextual interference effects on the acquisition, retention, and transfer of a motor skill (Journal of Experimental Psychology: Human Learning and Memory)72 college students, three tasks: blocked practice looked better during acquisition; random practice retained better at 10 minutes and 10 days under changed conditions and transferred better
• S2Buszard, Reid, Krause, Kovalchik & Farrow 2017, Quantifying Contextual Interference and Its Effect on Skill Transfer in Skilled Youth Tennis Players (Frontiers in Psychology 8:1931)16 skilled youth tennis players, 10 serve sessions: moderate CI improved match-play transfer but not the closed skill test; low CI the reverse; no practice-performance difference
• S26Winstein & Schmidt 1990, Reduced frequency of knowledge of results enhances motor skill learning (Journal of Experimental Psychology: Learning, Memory, and Cognition)reduced or faded knowledge of results improved delayed retention relative to feedback after every trial although frequent feedback helped during practice
• S25Savion-Lemieux & Penhune 2005, The effects of practice and delay on motor skill learning and retention (Experimental Brain Research 161:423)amount of practice per se did not change 4-week retention of a timed motor sequence; distribution of practice over several days did

In adults who adapt a movement and then train an opposing one, the first pattern is not erased. Observation (INTERVENTION with MODEL fit, healthy young adults in laboratory reaching tasks): Smith, Ghazizadeh and Shadmehr 2006 showed that after adaptation followed by counter-adaptation, clamping errors produced spontaneous recovery, a rebound toward the first pattern, which a two-process model reproduces: a fast process that responds strongly to error but decays quickly and a slow process that responds weakly but retains; the slow process is also initially biased against the second adaptation (anterograde interference). Kitago, Ryan, Mazzoni, Krakauer and Haith 2013 (INTERVENTION, adults, visuomotor rotation) compared washout by error clamp, by removing feedback, by removing the perturbation and by passage of time: time alone produced partial and inconsistent unlearning, every method left savings on re-exposure, and the authors describe unlearning as reversion to habit without forgetting. Szegedi-Hallgató et al 2017 (INTERVENTION, adults, a changed statistical regularity) found proactive interference from the old regularity, consolidation-dependent gains for the new one, and both old and new knowledge accessible afterwards. Avraham et al 2021 (INTERVENTION, adults) found that faster relearning is carried by explicit re-aiming while implicit adaptation is attenuated, so faster reacquisition is not a sign the old memory is gone. Inference: a tennis stroke hit for years is a slow-process memory; its behavioral disappearance in practice is evidence about present expression, never about storage. Boundary: every measurement is from laboratory adaptation and sequence tasks over minutes to days in young adults; the extension to a years-old stroke in an adult club player is a mechanism inference the legs agree on and no tennis study tests.

Motor memory is multi-rate. The fast component carries most of the behavior early in a change and decays within minutes to days without error feedback; the slow component carries the long-practiced pattern, changes little per trial, and retains across months. Training a new pattern drives the fast component and only slowly moves the slow one, so when the fast component decays or is stripped of feedback the slow component's output, the old stroke, is what remains. Savings and spontaneous recovery are the two signatures a pure overwriting system cannot produce and a multi-rate system must.

• S3Smith, Ghazizadeh & Shadmehr 2006, Interacting Adaptive Processes with Different Timescales Underlie Short-Term Motor Learning (PLoS Biology)a fast error-sensitive poorly-retaining process plus a slow error-insensitive well-retaining process predict savings, spontaneous recovery and anterograde interference
• S4Kitago, Ryan, Mazzoni, Krakauer & Haith 2013, Unlearning versus savings in visuomotor adaptation (Frontiers in Human Neuroscience)unlearning behaves as reversion to habit rather than forgetting; time alone gives partial inconsistent unlearning; savings persist after every washout method
• S5Szegedi-Hallgató et al 2017, Explicit instructions and consolidation promote rewiring of automatic behaviors in the human mind (Scientific Reports)rewiring a learned regularity shows proactive interference from the old one, consolidation-dependent gains for the new one, and both remain accessible
• S6Avraham, Morehead, Kim & Ivry 2021, Reexposure to a sensorimotor perturbation produces opposite effects on explicit and implicit learning processes (PLoS Biology)savings on re-exposure is carried by explicit re-aiming while implicit adaptation is attenuated; faster relearning is not evidence of erasure
• S8Lee & Schweighofer 2009, Dual Adaptation Supports a Parallel Architecture of Motor Memory (Journal of Neuroscience)two opposing adaptations are retained together when slow states are indexed by contextual cues; a single two-state memory cannot hold both

When an adult holds two motor patterns for the same task, the pattern expressed on a given trial is selected by contextual cues present at retrieval. Observation (INTERVENTION with MODEL fit, healthy adults in reaching tasks): Lee and Schweighofer 2009 showed that two opposing adaptations are retained together only when slow memory states are indexed by contextual cues, which a single two-state memory cannot do; Heald, Lengyel and Wolpert 2021 showed across sensorimotor experiments that much apparent learning and forgetting is a change in which existing memory is expressed, driven by inferred context, rather than a change in the memory itself. Proteau, Marteniuk and Lévesque 1992 (INTERVENTION, adults, aiming) found learning specific to the sensory information available in practice, with performance falling when a practiced information source was withdrawn even after extended practice. Observation in tennis (INTERVENTION, 16 skilled youth players): in Buszard et al 2017 the serve improvement appeared in the test whose conditions matched the practice conditions, closed for low-interference practice and match-play for moderate-interference practice. Inference: a stroke rebuilt against a basket feed, a flat trajectory, a coach's voice and no score is indexed to that cue set; a match presents a different cue set in which the old stroke holds the index, so transfer failure is a retrieval failure and more repetitions in the practice context deepen the practice index. Boundary: the mechanism is measured in laboratory adults and modeled; the tennis observation is one study of 16 juniors on the serve; no leg opened a study that recorded which stroke pattern an experienced adult produced across practice and match within the same period.

Memory retrieval is a selection problem. The nervous system holds several candidate motor memories for one action and infers from present cues, ball flight, opponent position, score, fatigue, the coach's presence, which context it is in and so which memory to express. Repetition strengthens a memory and strengthens its binding to the cues present when it was practiced; it does not rebind it to cues that were absent. A match supplies cues bound for years to the old stroke, so the old stroke wins selection there until the new stroke has been practiced under those cues.

• S8Lee & Schweighofer 2009, Dual Adaptation Supports a Parallel Architecture of Motor Memory (Journal of Neuroscience)two opposing adaptations are retained together when slow states are indexed by contextual cues; a single two-state memory cannot hold both
• S7Heald, Lengyel & Wolpert 2021, Contextual inference underlies the learning of sensorimotor repertoires (Nature)behavior change can be a change in which existing motor memory is expressed, selected by inferred context, rather than a change in the memory itself
• S9Proteau, Marteniuk & Lévesque 1992, A Sensorimotor Basis for Motor Learning: Evidence Indicating Specificity of Practice (Quarterly Journal of Experimental Psychology)learning is specific to the sensory information available during practice; removing a practiced information source degrades performance even after extended practice
• S2Buszard, Reid, Krause, Kovalchik & Farrow 2017, Quantifying Contextual Interference and Its Effect on Skill Transfer in Skilled Youth Tennis Players (Frontiers in Psychology 8:1931)16 skilled youth tennis players, 10 serve sessions: moderate CI improved match-play transfer but not the closed skill test; low CI the reverse; no practice-performance difference
• S5Szegedi-Hallgató et al 2017, Explicit instructions and consolidation promote rewiring of automatic behaviors in the human mind (Scientific Reports)rewiring a learned regularity shows proactive interference from the old one, consolidation-dependent gains for the new one, and both remain accessible

Observation (INTERVENTION, 42 adults): Sperl, Gergeleit and Cañal-Bruland 2021 exchanged two letters on a familiar keyboard mapping; speed fell and errors rose immediately, participants who performed better on the old mapping were disrupted more on the new one, and measures of response inhibition predicted parts of the disruption. Observation (CORRELATIONAL case series, three elite golfers): Carson and Collins 2015 tracked established-technique changes with kinematics, intra-individual variability and rated mental effort; the authors' generalization across levels is that the more experienced and overlearned the execution, the more difficult it is to change, and their 2011 framework applies the same refinement procedures to a recreational adult golfer on the basis of movement automaticity rather than skill level. Inference: an adult who has hit one forehand for years is proficient at that forehand and a novice at selecting against it; the experienced player's advantage in the old pattern is a liability in the change, paid through inhibition. Boundary: the direct measurement is a keyboard task in 42 adults over one session; the sport evidence is a three-case series in elite golfers; no leg opened a study scaling change cost against years of tennis practice.

An automated pattern is retrieved with little attention and strong cue binding. Producing a different pattern to the same cue requires suppressing the automatic retrieval before the new pattern can be issued, so the change runs through the inhibition system on every trial until the new binding dominates. The stronger and faster the old retrieval, the more inhibition each trial costs and the more often inhibition fails under load, which is why proficiency in the old pattern predicts larger disruption during the change.

• S10Sperl, Gergeleit & Cañal-Bruland 2021, On the role of different subdimensions of inhibition for successful motor skill change (Human Movement Science)42 adults, a swapped keyboard mapping: better performance on the old mapping predicted larger disruption on the new one; response-inhibition measures predicted the disruption
• S12Carson & Collins 2015, Tracking Technical Refinement in Elite Performers: The Good, the Better, and the Ugly (International Journal of Golf Science)three elite golfers changing an established technique: kinematic change and reduced conscious control came apart; one achieved the change without reduced mental effort, one both, one neither; the more overlearned the execution, the harder the change
• S11Carson & Collins 2011, Refining and regaining skills in fixation/diversification stage performers: the Five-A Model (International Review of Sport and Exercise Psychology)technical refinement in already-automated performers is a different problem from acquisition; the model proposes Analysis, Awareness, Adjustment, Re-automation, Assurance; testing against implicit motor learning is still required

To change an automated movement an adult must attend to it explicitly; explicit control is the control mode that breaks under pressure, so a changed stroke is pressure-fragile by construction until it is re-automated. Observation: Masters and Maxwell 2008 (review of INTERVENTION studies) describe reinvestment, in which anxiety leads a performer to control a movement with explicit rules, consuming working memory and disrupting automatic execution. Liao and Masters 2001 (INTERVENTION, table tennis novices) found analogy learners accumulated fewer explicit rules and were less impaired by a secondary task; Lam, Maxwell and Masters 2009 (INTERVENTION, novices) found the explicit group fell on a pressured transfer test while the analogy group did not. Cabral, Wilson and Miller 2022 (meta-analysis of 10 INTERVENTION studies, median 9 participants per group) found implicit learners performed better under high than low pressure, Hedges g_av -1.17 (95 percent CI -1.61 to -0.74), while comparison groups did not differ, and flagged publication bias and underpowering. Bounds: Kal et al 2018 (systematic review) found most implicit-versus-explicit comparisons showed no automaticity difference on low-quality evidence; Koedijker, Oudejans and Beek 2008 (INTERVENTION, 10,000 forehands over six weekly sessions) found the rule gap narrowed from 1,400 to 10,000 repetitions and no retention difference; Collins, MacPherson, Bobrownicki and Carson 2023 argue explicit awareness has a role in refining an established skill; Wulf and Su 2007 (INTERVENTION, expert golfers) found the control condition performed like internal focus while external focus still improved accuracy. Carson and Collins 2015 (three elite golfers) found kinematic change and reduced mental effort came apart, one golfer changing the movement without reducing conscious control. Inference: the debt is real and is paid down by re-automation; its size, not the instruction style alone, sets the stroke's fragility. Boundary: the pressure evidence is from novices in small samples; the refinement evidence is three cases; the pressure increment itself is the skill under pressure vector's.

Automatic execution runs outside working memory; a changed component is assembled under working-memory control until its new binding is strong enough to run without it. Pressure draws attention inward and loads working memory, so a component that still depends on working memory loses its controller exactly when the match raises the stakes, while a fully automated component is unaffected. The fragility is a property of how much of the stroke still runs explicitly, which is why reducing declarative content and re-automating both reduce it.

• S13Masters & Maxwell 2008, The theory of reinvestment (International Review of Sport and Exercise Psychology)under pressure a performer reinvests explicit rule-based control in a movement, which consumes working memory and disrupts automatic execution
• S14Liao & Masters 2001, Analogy learning: a means to implicit motor learning (Journal of Sports Sciences)table tennis novices learning the forehand topspin by analogy accumulated fewer explicit rules than an explicit group and were less impaired by a concurrent secondary task
• S15Lam, Maxwell & Masters 2009, Analogy Learning and the Performance of Motor Skills under Pressure (Journal of Sport and Exercise Psychology)the explicit group's performance fell on a pressured transfer test relative to retention while the analogy group's did not; analogy learners reported less access to movement rules
• S16Cabral, Wilson & Miller 2022, The Effect of Implicit Learning on Motor Performance Under Psychological Pressure: A Systematic Review and Meta-Analysis (Sport, Exercise, and Performance Psychology)10 studies, median 9 participants per group: implicit learners performed better under high than low pressure (Hedges g_av -1.17, 95 percent CI -1.61 to -0.74) while comparison groups did not differ; publication bias and underpowering flagged
• S17Kal, Prosée, Winters & van der Kamp 2018, Does implicit motor learning lead to greater automatization of motor skills compared to explicit motor learning? A systematic review (PLOS ONE)most implicit-versus-explicit comparisons found no difference in automaticity; the evidence base was judged low quality with unclear risk of bias
• S30Koedijker, Oudejans & Beek 2008, Table tennis performance following explicit and analogy learning over 10,000 repetitions (International Journal of Sport Psychology)over 10,000 forehands across six weekly sessions explicit learners reported more rules than analogy learners, the gap narrowed from 1,400 to 10,000 repetitions, and the groups did not differ at retention
• S18Collins, MacPherson, Bobrownicki & Carson 2023, An Explicit Look at Implicit Learning: an Interrogative Review for Sport Coaching Research and Practice (Sports Coaching Review)the coaching-science case that implicit-learning superiority is overstated and that explicit awareness has a role in refining an established skill
• S19Wulf & Su 2007, An External Focus of Attention Enhances Golf Shot Accuracy in Beginners and Experts (Research Quarterly for Exercise and Sport)in expert golfers the control condition performed about the same as internal focus; external focus still improved accuracy in practice and retention
• S12Carson & Collins 2015, Tracking Technical Refinement in Elite Performers: The Good, the Better, and the Ugly (International Journal of Golf Science)three elite golfers changing an established technique: kinematic change and reduced conscious control came apart; one achieved the change without reduced mental effort, one both, one neither; the more overlearned the execution, the harder the change

Observation (meta-analyses of INTERVENTION studies): Brady 2004 pooled 139 effect sizes from 61 studies, mean effect .38 for random over blocked practice, .57 in basic research against .19 in applied research, .50 in adults against .10 in younger learners, no difference between retention and transfer outcomes, and mean study power .43. Czyż, Wójcik and Solarská 2024 pooled 34 studies on transfer: SMD 0.55 overall favoring random practice, 0.54 in adults, 1.28 in older adults, 0.12 in young participants, and smaller and nonsignificant in applied settings. Czyż et al 2024 pooled 54 studies on delayed retention: a medium benefit overall, almost negligible in applied settings, large in older adults, medium in adults, negligible and nonsignificant in young participants. Observation in skilled sport: Hall, Domingues and Cavazos 1994 (INTERVENTION, 30 college batters, six weeks, same extra dose) found random ordering of pitch types beat blocked ordering on both test formats; Buszard et al 2017 (INTERVENTION, 16 skilled youth tennis players) found moderate interference improved match-play serve transfer where low interference did not. Observation on spacing: Savion-Lemieux and Penhune 2005 (INTERVENTION, adults, timed motor sequence) found 4-week retention depended on distribution across days, not on one, three or six blocks of practice. Inference: the direction is robust and favors adults, the magnitude in applied sport is small, and session count across days governs weeks-long retention more than repetitions within a day. Boundary: every tennis-specific number is from 16 juniors on the serve; the adult effect sizes are from laboratory tasks; the applied estimates are near zero with wide uncertainty.

Interleaving forces the learner to reconstruct the movement plan on each trial instead of repeating a plan held in working memory, so each trial exercises retrieval, the operation a delayed test and a match demand; blocked repetition exercises execution of an already-loaded plan, which inflates acquisition and leaves retrieval untrained. Spacing across days lets consolidation run between exposures so each new day's retrieval starts from the consolidated state. In applied settings the task is already variable and noisy, which shrinks the added effect of a schedule.

• S20Brady 2004, Contextual interference: a meta-analytic study (Perceptual and Motor Skills)139 effect sizes from 61 studies: mean effect .38; basic research .57 versus applied .19; adults .50 versus younger learners .10; retention and transfer not different; mean study power .43
• S21Czyż, Wójcik & Solarská 2024, The effect of contextual interference on transfer in motor learning: a systematic review and meta-analysis (Frontiers in Psychology)34 studies in the quantitative analysis: overall transfer effect SMD 0.55 favoring random practice; medium in adults (0.54), large in older adults (1.28), negligible in young participants (0.12); smaller and nonsignificant in applied settings
• S22Czyż et al 2024, High contextual interference improves retention in motor learning: systematic review and meta-analysis (Scientific Reports)54 studies, delayed-retention results only: medium benefit of high CI overall; almost negligible in applied settings; large in older adults, medium in adults, negligible and nonsignificant in young participants
• S23Hall, Domingues & Cavazos 1994, Contextual Interference Effects with Skilled Baseball Players (Perceptual and Motor Skills)30 skilled college batters, six weeks, same extra dose: random ordering of pitch types beat blocked ordering on both random and blocked post-tests
• S24Shea & Morgan 1979, Contextual interference effects on the acquisition, retention, and transfer of a motor skill (Journal of Experimental Psychology: Human Learning and Memory)72 college students, three tasks: blocked practice looked better during acquisition; random practice retained better at 10 minutes and 10 days under changed conditions and transferred better
• S2Buszard, Reid, Krause, Kovalchik & Farrow 2017, Quantifying Contextual Interference and Its Effect on Skill Transfer in Skilled Youth Tennis Players (Frontiers in Psychology 8:1931)16 skilled youth tennis players, 10 serve sessions: moderate CI improved match-play transfer but not the closed skill test; low CI the reverse; no practice-performance difference
• S25Savion-Lemieux & Penhune 2005, The effects of practice and delay on motor skill learning and retention (Experimental Brain Research 161:423)amount of practice per se did not change 4-week retention of a timed motor sequence; distribution of practice over several days did

Observation: Winstein and Schmidt 1990 (INTERVENTION, adults) found that reducing or fading knowledge of results improved delayed retention although frequent feedback helped during practice, the finding behind the guidance hypothesis. Wulf, Chiviacowsky, Schiller and Ávila 2010 (INTERVENTION, adults) found feedback after every trial beat feedback after a third of trials on transfer when the feedback directed attention externally, so the content of feedback reversed the frequency result. McKay, Hussien, Carter, Yantha and Ste-Marie (2021 preprint, meta-analysis of 61 papers, k = 75, N = 2,228) found no significant effect of reduced feedback frequency at acquisition, immediate or delayed retention, substantial heterogeneity and a Z-curve indicating a severely underpowered literature. Proteau, Marteniuk and Lévesque 1992 (INTERVENTION, adults) found performance fell when a practiced information source was withdrawn even after extended practice. Inference: the general law survives, performance produced with a coach's cue, a video, a swing thought or a predictable feed does not license inference about performance without them, because it follows from the three-test law and cue-indexed retrieval; the specific quantitative prescription to reduce feedback frequency does not survive the pooled evidence. Boundary: all measurements are laboratory adults on simple tasks; no leg opened a feedback-schedule study in stroke change for experienced tennis players.

Augmented feedback and cues enter the control loop as an external error signal; while present they correct the next attempt without the learner's own error detection running. When the stroke is produced with that signal present, the learner's capability without it is unmeasured. Whether a given frequency builds dependence or builds learning depends on what information the feedback carries and where it points attention, which is why frequency alone has no pooled effect while content does.

• S26Winstein & Schmidt 1990, Reduced frequency of knowledge of results enhances motor skill learning (Journal of Experimental Psychology: Learning, Memory, and Cognition)reduced or faded knowledge of results improved delayed retention relative to feedback after every trial although frequent feedback helped during practice
• S27Wulf, Chiviacowsky, Schiller & Ávila 2010, Frequent External-Focus Feedback Enhances Motor Learning (Frontiers in Psychology)feedback after every trial beat feedback after a third of trials on transfer when the feedback directed attention externally; the content of feedback changes the frequency result
• S28McKay, Hussien, Carter, Yantha & Ste-Marie 2021 preprint, Meta-analysis of reduced relative feedback frequency effect on motor learning and performance (PsyArXiv)61 papers, k = 75, N = 2,228: no significant effect of reduced feedback frequency at acquisition, immediate or delayed retention; substantial heterogeneity; Z-curve shows the literature severely underpowered
• S9Proteau, Marteniuk & Lévesque 1992, A Sensorimotor Basis for Motor Learning: Evidence Indicating Specificity of Practice (Quarterly Journal of Experimental Psychology)learning is specific to the sensory information available during practice; removing a practiced information source degrades performance even after extended practice
• S1Soderstrom & Bjork 2015, Learning Versus Performance: An Integrative Review (Perspectives on Psychological Science)performance during practice is an unreliable index of learning; learning is inferred only from delayed retention and transfer

Observation: the on-target literature on changing an established technique in automated performers is thin. Carson and Collins 2011 define their object as refinement, a small tweak or polish rather than a completely new movement, and state that testing their model against implicit motor learning and existing coaching approaches is still required; Carson and Collins 2015 is a three-golfer case series; Hanin, Korjus, Jouste and Baxter 2002, the Old Way/New Way contrast method the Gemini leg relies on, is two Olympic-athlete case studies; Milanese et al 2016 (INTERVENTION, 34 golfers, one-week retention) and Gray 2018 (INTERVENTION, experienced batters, six weeks) correct or shift a single identified feature and report no competition transfer. No leg opened a study that assigned experienced adults to a large versus a small technique change with matched dose, delayed uncued retention and representative transfer, and all four legs said so. Inference from the granted mechanisms: the non-erasure law (A2) means a larger change recruits more anterograde interference; the entrenchment law (A4, S10) means cost scales with the automaticity of what is replaced; the explicit-control debt law (A5) means a larger change installs more declarative rules and so more pressure liability. The opposite inference, that a small change is absorbed into the old attractor and a large change escapes it, is argued by the Gemini leg from dynamical-systems reasoning and the two case studies, and is not refuted by any opened measurement. Decision principle, not a measured effect: change the smallest set of control variables whose contact-mechanics consequence is large, test retention and transfer, and widen scope only when the narrower change fails those tests or when the old pattern is mechanically unable to produce the target ball. Boundary: this is a SIGNAL axiom; the scope comparison is unmeasured in any population and the case evidence is n = 3 and n = 2.

The size of a technique change sets how much of the coordination must be re-bound to new cues, how much automatic retrieval must be inhibited per trial and how many declarative rules carry the assembly. Each of those costs is measured to rise with the quantity changed, so on the measured mechanisms expected cost is increasing in scope. The counter-mechanism, that similar patterns compete for one cue set and a dissimilar pattern earns its own context, is a modeling argument about cue separation that would reduce retrieval competition at the price of the other three costs; which dominates has not been measured.

• S11Carson & Collins 2011, Refining and regaining skills in fixation/diversification stage performers: the Five-A Model (International Review of Sport and Exercise Psychology)technical refinement in already-automated performers is a different problem from acquisition; the model proposes Analysis, Awareness, Adjustment, Re-automation, Assurance; testing against implicit motor learning is still required
• S12Carson & Collins 2015, Tracking Technical Refinement in Elite Performers: The Good, the Better, and the Ugly (International Journal of Golf Science)three elite golfers changing an established technique: kinematic change and reduced conscious control came apart; one achieved the change without reduced mental effort, one both, one neither; the more overlearned the execution, the harder the change
• S29Hanin, Korjus, Jouste & Baxter 2002, Rapid Technique Correction Using Old Way/New Way: Two Case Studies with Olympic Athletes (The Sport Psychologist)two Olympic-athlete case studies of deliberate old-pattern versus new-pattern contrast practice; the evidence class for the wedge method is case report
• S31Milanese et al 2016, Correction of a Technical Error in the Golf Swing: Error Amplification Versus Direct Instruction (Journal of Motor Behavior)34 golfers randomized to error amplification, direct instruction or control; a single technical fault corrected with motion capture and a one-week retention test; full-text effect sizes unverified by any leg
• S32Gray 2018, Comparing cueing and constraints interventions for increasing launch angle in baseball batting (Sport, Exercise, and Performance Psychology)experienced batters, six weeks: an individually adjusted barrier constraint beat internal and external cueing on bat-path and ball outcomes; delayed retention and competition transfer not verified from the abstract
• S10Sperl, Gergeleit & Cañal-Bruland 2021, On the role of different subdimensions of inhibition for successful motor skill change (Human Movement Science)42 adults, a swapped keyboard mapping: better performance on the old mapping predicted larger disruption on the new one; response-inhibition measures predicted the disruption

For any reply a tennis receiver might choose, the commitment time plus the remaining motor work must not exceed the interception time of that reply; the interception time and the motor work both depend on which reply is chosen, so there is no single ball deadline, and taking the ball early, blocking, retreating and a full swing each carry a different deadline. The chain that fills the interval (pickup, prediction, choice, initiation, movement) is bookkeeping, not five serial stages: prediction runs while the opponent prepares, general preparation precedes directional commitment, and ball flight can still revise an unfolding response. In measured play the first racket movement of 10 skilled receivers came 129 ms after contact against a live hitter and 179 ms against a cloaked ball machine at matched flight times (S3, within-person, skilled college-level players), and a ground-stroke receiver denied the first third of ball flight started the forward swing earlier and lengthened it rather than failing (S31, within-person, 113 km/h feeds). Scope: an analytical constraint plus two within-person measurements on skilled players; the exact milliseconds are those studies', not constants.

Interception requires the racket at a point in space at the moment the ball reaches it; the ball's flight is fixed by the opponent's contact, drag, bounce and distance, while the receiver's remaining displacement, body organisation and racket path depend on where and how the receiver chooses to meet it. Finite acceleration makes remaining motor work a time cost, so earlier commitment, better starting position and a simpler reply are interchangeable ways to satisfy one inequality; a visible first step measures the sum of several overlapping processes, not a completed internal decision.

• S1Triolet, Benguigui, Le Runigo & Williams 2013, Quantifying the nature of anticipation in professional tennis, J Sports Sci 31(8)Professional-match video coding: reaction-to-anticipation transition 140 to 160 ms after contact; anticipation in 6.14 to 13.42 percent of coded situations, almost only when tactically disadvantaged; accuracy non-monotonic, rising again for responses earlier than about 120 ms before contact
• S2HAL open-archive record of Triolet et al. 2013Same record as S1, the open-archive copy the exa leg opened
• S3Shim, Carlton, Chow & Chae 2005, J Motor Behavior 37(2)13 skilled vs 12 novice players: four-alternative anticipation 63.1 vs 43.7 percent (chance 25); skilled players not more accurate than novices with point-light displays; 10 experts initiated racket movement 129 ms after contact against a live hitter vs 179 ms against a cloaked ball machine
• S4Shim et al. 2005 abstract record (exa library)Abstract of S3: skilled more accurate with live and video but not point-light displays; faster reaction latencies against a live opponent
• S31The kinematics of the return of serve in tennis: the role of anticipatory information (The Sport Journal)Mean ball speed 113 km/h, delivery time 1.1 s: median initial movement 0.38 s against a ball machine vs 0.41 s against a real server; occluding the first third of ball flight brought the forward swing earlier and lengthened it; no server-kinematic timing use up to 125 km/h

In video coding of professional tennis matches, the transition between reaction (100 percent correct placement of the response) and anticipation (less than 100 percent) sat 140 to 160 ms after the opponent's contact, anticipatory responses made up 6.14 to 13.42 percent of coded situations (denominator: coded rally situations in professional matches; design: observational video coding; population: touring professionals), and they appeared almost exclusively when the responder was tactically disadvantaged (S1, S2, published 2013). Accuracy did not fall monotonically as responses came earlier: it rose again for responses initiated more than about 120 ms before contact, which the authors attribute to situations carrying unusually strong contextual information (S1). Scope: an observational benchmark from professional matches on more than one surface; the percentages are proportions of coded situations, not of points, and the 140 to 160 ms boundary is an operational definition of this coding, not a physiological constant.

Waiting for post-contact ball flight yields near-certain direction information, so a receiver with time to spare chooses that regime; when the opponent's shot removes that time (a tactically unfavourable situation), the receiver is pushed into committing on pre-contact information, which is probabilistic and therefore sub-100 percent accurate. Very early commitments occur only where the situation itself has nearly one viable opponent reply, so the prior is strong and accuracy recovers; the mid-window, where kinematic evidence tempts commitment but is still ambiguous, is where errors concentrate.

• S1Triolet, Benguigui, Le Runigo & Williams 2013, Quantifying the nature of anticipation in professional tennis, J Sports Sci 31(8)Professional-match video coding: reaction-to-anticipation transition 140 to 160 ms after contact; anticipation in 6.14 to 13.42 percent of coded situations, almost only when tactically disadvantaged; accuracy non-monotonic, rising again for responses earlier than about 120 ms before contact
• S2HAL open-archive record of Triolet et al. 2013Same record as S1, the open-archive copy the exa leg opened

A receiver's prediction of the opponent's shot combines contextual priors (court positions, rally state, known tendencies) with kinematic likelihoods from the opponent's unfolding body and racket motion, weighted by the reliability of each channel at that instant: priors dominate early in the stroke and whenever kinematics are ambiguous, kinematics dominate in the final window before contact (S27, review of within-person manipulation studies). Measured signatures: telling players a disguise was unlikely or likely shifted classification of ambiguous movements across 25, 50 and 75 percent conditions (S27); with stroke kinematics held constant, skilled players' judgements followed the opponent's court position more than less-skilled players' did, and both groups were above chance with postural information removed (S28, cross-sectional); adding movement cues to a context-only animation raised experts from 50.0 to 68.45 percent while novices stayed near 38 percent (S8, cross-sectional, experts and novices); in stochastic masking of ground strokes, information that supported correct direction judgements accrued mainly in the last 0.083 s before contact in 34 skilled non-elite players (ITN 1.6 to 2.8), with only a suggestive torso signal (S17). Scope: laboratory video and animation tasks in skilled and novice adults; the weighting is a model that fits these manipulations, and no study here measured it on court.

Two information sources about one future event are combined most accurately when each is weighted by its inverse variance; early in a stroke the body has not yet differentiated between shots, so the kinematic likelihood is flat and the prior carries the estimate, while in the final 80 to 100 ms the arm and racket commit and the likelihood sharpens. Skill is calibration of the weights, not possession of one channel: novices can use salient context but cannot extract the late kinematic signal (S8, S30), and experts lean less on tendencies as kinematics become reliable.

• S8Murphy, Jackson & Williams 2019, informational constraints, option generation and anticipationExperts rose from 50.0 to 68.45 percent when movement cues were added to context-only animation; novices stayed about 38 percent; participants generated 1.74 options per trial with video vs 1.96 with animation
• S17Mann, Buscombe et al. 2019, Front Psychol (published 2019-08-27), information accrual before racket-ball contact by stochastic masking34 skilled non-elite players (ITN 1.6 to 2.8): information for ground-stroke direction accrued mainly in a window reaching back about 0.083 s before contact; spatial result only suggestive of the torso; mean 63.2 percent correct
• S27Gredin, Bishop, Williams & Broadbent 2020 review, Int Rev Sport Exerc Psychol, the use of contextual priors and kinematic information in anticipationReliability-weighted integration of priors and kinematics: priors weigh more early and when kinematics are ambiguous, kinematics late; stated disguise probability shifted classification of ambiguous movements (25 vs 50 vs 75 percent)
• S28Contextual cue utilization in visual anticipation in tennis: the opponent's on-court positionWith stroke kinematics held constant, skilled players' judgements were more influenced by the opponent's court position than less-skilled players'; both groups above chance with postural information removed
• S30Pilot study on dynamic-contextual and kinematic information in tennis anticipation, Movement & Sport Sciences 2022Experts and novices both used dynamic context (court positions); only experts anticipated from low context and only experts improved when late kinematic information was added

The anticipation advantage of skilled players over less-skilled players is located in the shot-specific information carried by the opponent's movement, not in looking behaviour: skilled players responded about 137 ms earlier with different gaze organisation but no difference in fixation number or mean duration (S5, cross-sectional); replacing arm-racket dynamics with those of the opposite shot cost skilled players accuracy and was the largest decrement, while less-skilled players were hurt only by that swap (S6); removing the ball toss dropped skilled players to chance in a serve stimulus set (S7); and skilled players were not more accurate than novices on point-light displays in one coupled task (S3), so an advantage that survives texture removal in some studies did not in this one. Because the content is emitted by the sender, the sender can cut it: disguise removed the expert advantage at 40 ms before contact and pushed novices below chance on disguised shots occluded at contact (S25, cross-sectional, experts vs novices), and anxiety increased directional errors most in the context-only condition (S26). Scope: laboratory video manipulations in skilled and novice adults; gaze measures are allocation data and cannot by themselves show extraction.

Information about shot direction exists only where the opponent's movement differs between shots; eye position sets what is sampled, but peripheral and parafoveal vision carry biological motion, so fixation location is neither necessary nor sufficient for extraction. A manipulation that changes the content while leaving the display region visible (swapping dynamics) isolates content from looking; removing a region confounds content with attention. A deceiving opponent emits false content, so a model that credits the content is driven below chance, which is the fingerprint distinguishing deception from mere noise.

• S3Shim, Carlton, Chow & Chae 2005, J Motor Behavior 37(2)13 skilled vs 12 novice players: four-alternative anticipation 63.1 vs 43.7 percent (chance 25); skilled players not more accurate than novices with point-light displays; 10 experts initiated racket movement 129 ms after contact against a live hitter vs 179 ms against a cloaked ball machine
• S4Shim et al. 2005 abstract record (exa library)Abstract of S3: skilled more accurate with live and video but not point-light displays; faster reaction latencies against a live opponent
• S5Williams, Ward, Knowles & Smeeton 2002, J Exp Psychol Applied 8(4)Skilled players responded about 137 ms earlier; fixation number and mean duration did not differ; 45 min video plus 45 min on-court training in recreational adults moved field onset 2195.8 to 2001.0 ms, about 186 ms earlier than pooled placebo and control, d = 1.03, no accuracy difference
• S6Williams, Huys, Canal-Bruland & Hagemann 2009, swapping movement dynamics in tennis anticipationSkilled players lost accuracy when proximal or arm-racket dynamics were replaced by the opposite shot's dynamics; less-skilled players lost accuracy only for the arm-racket swap
• S7Jackson & Mogan 2007, spatial occlusion of tennis servesRemoving the ball toss or arm-racket region impaired skilled players' direction judgements; with the toss removed skilled performance fell to chance in this stimulus set
• S25Jackson, Warren & Abernethy 2006, the effect of disguise on anticipationExperts more accurate overall (p < .001); disguise reduced accuracy (p = .001) and removed the expert advantage at 40 ms before contact; novices below chance on disguised shots occluded at contact
• S26Cocks, Jackson, Bishop & Williams 2016, Cognition and Emotion, anxiety, anticipation and contextual informationSkilled players higher in accuracy and processing efficiency; high anxiety lowered processing efficiency with no accuracy change; directional errors under anxiety largest in the context-only condition

A receiver can respond earlier by committing on less evidence (moving along a speed-accuracy frontier, with more errors at fixed evidence quality) or by obtaining more discriminative evidence sooner (moving the frontier); mean response time therefore does not measure processing speed, and training that lowers caution is not the same as training that improves information use (S12, diffusion-model account). Measured: in a one-session occlusion protocol with 39 male expert players (mean age 28.1), response time fell in every group, 734.82 to 463.59 ms in the same-opponent group, 584.42 to 431.24 ms in the varied-opponent group and 687.34 to 589.36 ms in the control group, with no group-by-test interaction, while only the same-opponent group gained accuracy (about 55 to 65 percent), so the shared latency drop is task familiarisation and the differential effect is prediction quality (S9, S10, randomized, published 2025-01-07). In recreational adults, 90 minutes of training moved field response onset about 186 ms earlier (d = 1.03) with no accuracy change, a package effect that does not isolate encoding or choice (S5, randomized with placebo and control). In match coding, accuracy was non-monotonic in time-to-contact (S1). Scope: laboratory and field-feed designs in expert and recreational adults; the model is general decision theory, the tennis measurements are these studies'.

In an evidence-accumulation process, accuracy and mean decision time both rise with the ratio of threshold to noise: at fixed drift and noise, raising the dimensionless threshold from 0.5 to 1 moves idealized accuracy from about 73 to 88 percent while mean decision time grows about 3.3-fold (an illustrative calculation, not a tennis estimate). Raising drift (better evidence sooner) shortens time and raises accuracy together. An observed latency change is therefore a projection of two parameters onto one axis, and only matched-accuracy latency or matched-occlusion accuracy comparisons separate them.

• S1Triolet, Benguigui, Le Runigo & Williams 2013, Quantifying the nature of anticipation in professional tennis, J Sports Sci 31(8)Professional-match video coding: reaction-to-anticipation transition 140 to 160 ms after contact; anticipation in 6.14 to 13.42 percent of coded situations, almost only when tactically disadvantaged; accuracy non-monotonic, rising again for responses earlier than about 120 ms before contact
• S5Williams, Ward, Knowles & Smeeton 2002, J Exp Psychol Applied 8(4)Skilled players responded about 137 ms earlier; fixation number and mean duration did not differ; 45 min video plus 45 min on-court training in recreational adults moved field onset 2195.8 to 2001.0 ms, about 186 ms earlier than pooled placebo and control, d = 1.03, no accuracy difference
• S9Triolet & Benguigui 2025, Anticipation training for expert tennis players when facing a specific player, Front Psychol 15:1508627 (published 2025-01-07)39 male expert players (mean age 28.1), three groups of 13, clips occluded 340 ms before contact, 72 training trials in one ~1 h session; only the same-opponent group raised accuracy (about 55 to 65 percent); response time fell in every group (734.82 to 463.59, 584.42 to 431.24, control 687.34 to 589.36 ms) with no group-by-test interaction; retention and court transfer not tested
• S10PMC copy of Triolet & Benguigui 2025Same record as S9, opened 2026-10-04 and read for the group-level numbers
• S12Ratcliff, Thapar & McKoon 2006, aging and practice in masked perceptual tasks (diffusion model)College-age and 60 to 75 year old adults: practice improved evidence quality and changed decision criteria; older adults approached younger accuracy after four sessions; nondecision time stayed somewhat slower

In adults, the prediction components of anticipation move under controlled training: 72 feedback trials on one opponent's serves, occluded 340 ms before contact, raised accuracy only in the same-opponent group of expert players (about 55 to 65 percent; varied-opponent and control groups unchanged), in a single session, with retention and court transfer untested (S9, S10, randomized, 39 experts, published 2025-01-07); 38 adults without substantial tennis experience (mean age 19.5) rose from 59.1 to 74.3 percent when trained with the arm-racket region visible and transferred the gain to untrained regions, while the group trained with that region hidden stayed at 62.5 to 62.3 percent (S11, randomized to display condition, laboratory stick figures, 2013); 21 intermediate players (about 20.8 years) trained on rally-ordered clips reached a field decision time of 275 ms (SD 31) against 305 ms (SD 46) for quasi-random clips after three 24-trial sessions, with accuracy at ceiling above 90 percent in both (S16, 2017); random practice beat blocked practice on 7-day laboratory retention and on field decision time (S14, S15, 2015); a 3-week occlusion programme improved high-performance players more than beginners among 32 participants (S29, abstract-level, 2025). Scope: adult experts, intermediates and novices in laboratory and field-feed tasks; none of these measured match outcomes.

Learning a shot-specific mapping requires that the training display preserve discoverable, reliable information (the arm-racket region) and that feedback link the display to the outcome; a display stripped of the informative region yields no learning (S11). Opponent-specific exposure sharpens the prior for that opponent (S9) without changing generic speed. A rally-ordered sequence restores the contextual prior that isolated clips remove, so the learned skill includes the early channel and transfers to a field decision measured before the ball is struck (S16); random ordering forces reconstruction of the discrimination on each trial, which costs acquisition and buys retention (S14).

• S9Triolet & Benguigui 2025, Anticipation training for expert tennis players when facing a specific player, Front Psychol 15:1508627 (published 2025-01-07)39 male expert players (mean age 28.1), three groups of 13, clips occluded 340 ms before contact, 72 training trials in one ~1 h session; only the same-opponent group raised accuracy (about 55 to 65 percent); response time fell in every group (734.82 to 463.59, 584.42 to 431.24, control 687.34 to 589.36 ms) with no group-by-test interaction; retention and court transfer not tested
• S10PMC copy of Triolet & Benguigui 2025Same record as S9, opened 2026-10-04 and read for the group-level numbers
• S11Smeeton, Huys & Jacobs 2013, PLoS ONE (published 2013-11-11), learning informative movement from stick figuresExperiment 3: 38 adults (mean age 19.5) without substantial tennis experience; the group trained with the arm-racket region visible rose 59.1 to 74.3 percent and transferred to untrained regions; the group trained with it hidden stayed 62.5 to 62.3 percent; on-court transfer not tested
• S14Broadbent, Causer, Ford & Williams 2015, contextual interference in perceptual-cognitive skills training (Brunel repository)Random vs blocked video practice of tennis anticipation: random group higher accuracy on a 7-day retention test and lower decision times in a field-based transfer protocol
• S15Broadbent et al. 2015 full text (Brighton repository)Same record as S14, the full-text copy the exa leg opened
• S16Broadbent, Ford, O'Hara, Williams & Causer 2017, PLoS ONE (published 2017-03-29), sequential structure of practice21 intermediate players (mean age about 20.8), 3 sessions of 24 trials: the sequential group's field decision time 275 ms (SD 31) vs 305 ms (SD 46) for the non-sequential group, p = .05; accuracy above 90 percent in both (ceiling); laboratory retention 79 vs 64 percent in the sequential condition
• S29Carboch, Mrazova & Brenton 2025, Int J Sports Sci Coaching, perceptual-cognitive training on serve-return anticipation32 participants split by level into intervention and control; 3-week video occlusion training; high-performance players gained more anticipation performance than beginners; abstract-level, results table not opened

Video-based temporal occlusion training improves anticipation with a large pooled effect, d = 1.21 [0.83, 1.59] across 12 intervention studies, 25 effect sizes and N = 248 from novices to national or international level, and the field-transfer effect, d = 0.85 [0.40, 1.30], did not differ significantly from the video-transfer effect, d = 1.26 [0.80, 1.72], p = 0.211, with publication bias inconclusive on so few studies (S19, meta-analysis, published 2024-08-05, multiple sports). In team sports the discount is explicit: task-specific response-accuracy ES 1.51 [0.98, 2.05] (n = 381) against on-court transfer ES 0.65 [0.15, 1.16] (n = 247); transfer measured by verbal response ES 0.41 [0.07, 0.75] against sport-specific action ES 0.87 [-0.22, 1.96]; adults ES 0.63 [0.29, 0.98] (S20, S21, 22 studies, published 2024-10-09, not tennis). The canonical tennis implicit-training result dissolved on re-analysis: groups differed before training and the placebo group that only watched matches improved most across the four occlusion points up to impact (S22, S23). Scope: pooled sport populations; the tennis-specific transfer estimate is one component of S19, and the team-sport discount is carried as a bound on, not a measurement of, tennis.

A video task with a verbal or button response trains and tests a perceptual judgement uncoupled from the movement it must drive; on court the judgement must be expressed through a timed interception under a shorter effective deadline, so part of the laboratory gain is specific to the uncoupled response and does not survive the coupling. Passive observation of matches also carries information, which is why a placebo that watches tennis can improve and why an active control is required to attribute a gain to the training content.

• S19Muller, Morris-Binelli, Hambrick & Macnamara 2024, Sports Medicine (published 2024-08-05), temporal occlusion training meta-analysis12 intervention studies, 25 effect sizes, N = 248 from novices to national or international level: d = 1.21 [0.83, 1.59]; video transfer d = 1.26 [0.80, 1.72] vs field transfer d = 0.85 [0.40, 1.30], difference p = 0.211; publication bias inconclusive
• S20Zhu et al. 2024, Behavioral Sciences 14:919 (published 2024-10-09), perceptual-cognitive training in team sports meta-analysis22 studies, 45 effect sizes: task-specific response accuracy ES 1.51 [0.98, 2.05] (n = 381) vs on-court transfer ES 0.65 [0.15, 1.16] (n = 247); verbal-response transfer ES 0.41 [0.07, 0.75] vs sport-specific action ES 0.87 [-0.22, 1.96]; adults ES 0.63 [0.29, 0.98]; soccer, rugby and other team sports, not tennis
• S21PubMed record of Zhu et al. 2024Same record as S20
• S22Jackson 2003, re-analysis of Farrow & Abernethy 2002 (J Sports Sci)Pre-intervention group differences; the explicit group did improve; the placebo (match-watching) group showed the largest mean improvement across the four occlusion points up to impact
• S23PubMed record of the Farrow & Abernethy 2002 re-analysisSame record as S22

Two adult quantities behave differently under training. The irreducible looking-to-doing latency of a practised real-time task slowed from age 24 [95 percent CI 20, 29] in 3,305 StarCraft 2 players aged 16 to 44, a 39-year-old typical player being about 150 ms slower per cycle than a 24-year-old, with no evidence that expertise attenuated the decline (S24, cross-sectional, correlational, published 2014-04-09, a video game and not tennis). Meanwhile the decision parameters moved with practice in 60 to 75 year olds: evidence quality improved and criteria changed over four sessions of masked perceptual tasks until accuracy approached that of college-age adults, while nondecision time stayed somewhat slower (S12, within-person practice, non-tennis). In tennis, experts intercepting a simulated ball deviated 400 ms before contact were more accurate because their visuo-motor delay in adapting the movement was shorter, and that delay predicted accuracy and national ranking (S18, cross-sectional, 2010), which locates an expertise marker in coupling rather than in a reflex. Eight weeks of plyometrics in 30 male collegiate players improved hexagon-test time 6.2 and 9.2 percent and jump power, with no measure of cue use (S13, randomized, published 2026-06-17). Scope: the floor estimate is from a non-tennis population and transfers to tennis only as a bound; the plasticity estimates are laboratory; no adult intervention on movement time or coupling in tennis was opened.

Sensory noise and conduction set a nondecision time that practice does not shorten and age lengthens, so gains in an adult come from enlarging the window the floor sits in: better priors and cue extraction move the onset of usable evidence earlier, a calibrated criterion removes conservatism, and shorter information-movement coupling lets late ball-flight information still steer the stroke. Physical training changes the motor side of the deadline inequality (movement time) independently of any perceptual change.

• S12Ratcliff, Thapar & McKoon 2006, aging and practice in masked perceptual tasks (diffusion model)College-age and 60 to 75 year old adults: practice improved evidence quality and changed decision criteria; older adults approached younger accuracy after four sessions; nondecision time stayed somewhat slower
• S13Pang & Li 2026, Front Physiol (published 2026-06-17), plyometric training in collegiate tennis players30 male collegiate players randomized to two plyometric groups or control for eight weeks: hexagon-test time improved 6.2 and 9.2 percent, jump power improved, T-test not different between groups; no measure of cue use or choice
• S18Le Runigo, Benguigui & Bardy 2010, Visuo-motor delay, information-movement coupling, and expertise in ball sportsTennis experts intercepted a simulated ball deviated 400 ms before contact more accurately than non-experts, explained by a shorter visuo-motor delay; delay predicted accuracy, and accuracy predicted national ranking
• S24Thompson, Blair & Henrey 2014, PLoS ONE (published 2014-04-09), over the hill at 24: cognitive-motor decline in StarCraft 23,305 players aged 16 to 44: looking-doing latency slows from age 24 [20, 29]; a 39-year-old about 150 ms slower than a 24-year-old; no evidence that expertise attenuates the decline; a real-time strategy game, not tennis

A pressured shot is a launch distribution with a mean (where the player aims and how much risk the choice carries) and a spread (how reliably the body produces that intent), and pressure can move either, in either direction. Touring professionals, seven Grand Slams 2006 to 2007, stroke-by-stroke (S6): men's odds of a winner were about 28 log points lower and of an unforced error 33 log points lower in the top importance quartile than the bottom, a move of the aim toward safety with the ball still in play. Thirty novices at a prescribed table-tennis target (S17): stakes shortened the swing, lowered forward-swing and ball speed and shifted the landing (p<.008) with grip force unchanged, a change of execution with the choice fixed by the task. Touring professionals, more than 650,000 Grand Slam points 2016 to 2019 (S16): a 1-to-5 pressure index raised the probability of a double fault or unforced error (p<.001) and a prior-point error raised it again (OR 1.2, 95% CI 1.17 to 1.23). The S6 and S16 patterns are reconciled only by measuring choice and execution separately. Boundary: professionals (S6, S16, correlational), novices (S17, within-person manipulation), laboratory adults (S11); no row measures an adult club player's shot choice under match pressure.

The outgoing ball is fixed by the collision at contact (impulse, racket orientation, timing), so a shot is a distribution over launch conditions mapped through flight to a landing distribution; its mean is the policy and its covariance is the execution. Any scalar outcome (a point won, an error counted) sums over both and cannot recover either; two shots with the same error rate can have opposite aim shifts. Pressure acts through attention on both the planning of the aim and the online control of the swing (S11), so the two can move in opposite directions in the same player.

• S6Paserman 2010, Gender differences in performance in competitive environments? Evidence from professional tennis players (working paper, January 2010)Seven Grand Slams 2006 to 2007, stroke-by-stroke; men's odds of a winner about 28 log points and of an unforced error 33 log points lower in the top importance quartile than the bottom; women 19 to 44 and 14 to 29 log points lower; professionals play a more conservative, less aggressive strategy as importance rises
• S17Sekiya and Tanaka 2018, Movement modifications related to psychological pressure in a table tennis forehand task (Perceptual and Motor Skills; Semantic Scholar record)30 novices after 135 practice trials; under money and score-cancellation pressure backswing and forward swing shortened, forward-swing and ball speed fell (p<.008), contact shifted forward, landing shifted left (p<.007), grip force unchanged; anxiety and heart rate rose p<.025
• S16Harris, Vine, Eysenck and Wilson 2021, Psychological pressure and compounded errors during elite-level tennis (Psychology of Sport and Exercise; Semantic Scholar record)More than 650,000 points across 12 Grand Slams 2016 to 2019; a 1-to-5 pressure index raised the probability of a double fault or unforced error (ps<.001); a prior-point error OR 1.2 [1.17, 1.23]; multiplicative; winning players as susceptible to pressure and prior errors as losing players
• S11DeCaro, Thomas, Albert and Beilock 2011, Choking under pressure: multiple routes to skill failure (JEP: General; Europe PMC record)Outcome-contingent pressure (distraction) hurt rule-based category learning; monitoring by others hurt information-integration learning; interventions designed by pressure type (Exp 3); monitoring effect replicated in a serial reaction time task (Exp 4)

When 12 skilled (BTMR 10.2 to 8.1, 10.5 years of play) and 12 less-skilled male players anticipated opponents' shots under low and high anxiety (S4; manipulation confirmed, confidence 5.40 vs 6.13, p<.001), response accuracy did not change (F(1,22)=0.06, ηp²=.00) while processing efficiency, accuracy divided by rated mental effort, fell (F(1,22)=20.11, p<.001, ηp²=.48); the only accuracy loss was in the condition carrying context alone and only for the skilled group (Anxiety x Skill on directional errors F(1,22)=5.11, p<.05): anxiety taxed the top-down use of context, not speed. In a scenario task (S12; two experiments of 120, 40 per group, ages 17 to 20, Chinese National Level 1 and 2 players and university students) experts chose in 21,082 ± 514 ms against 25,867 ± 1,034 ms for skilled and 33,925 ± 2,548 ms for novices, with skilled players turning extremely conservative under time pressure and experts choosing by the competitive state: a difference in deliberate preference measured in tens of seconds in adolescents, not an on-court reaction time. Touring professionals (S16): pressure raised counted errors and winners were as susceptible as losers. Boundary: skilled club and university players (S4, within-person), adolescents and students (S12, cross-sectional stated preferences), professionals (S16, correlational); no opened study measures on-court decision time under match pressure in adults.

Anxiety shifts attentional control toward the stimulus-driven system and recruits compensatory effort, so the resources spent per unit of performance rise before the performance itself falls (the efficiency-before-effectiveness signature). Context use is a top-down process and is the first to lose quality, while the reading of postural cues, a bottom-up process, is spared. A player therefore pays for an unchanged outcome with effort and worse use of the point's history, which is why outcome-only designs miss the first and largest pressure effect.

• S4Cocks, Jackson, Bishop and Williams 2016, Anxiety, anticipation and contextual information: a test of attentional control theory (Cognition and Emotion)12 skilled vs 12 less-skilled male players; under high anxiety response accuracy unchanged F(1,22)=0.06 while processing efficiency fell F(1,22)=20.11, p<.001, ηp²=.48; skilled players' directional errors rose only in the context-only condition (Anxiety x Skill F(1,22)=5.11, p<.05)
• S12Shangguan and Zha 2025, The impact of framing effects, competitive state, and time pressure on risk-taking decisions in tennis players of different skill levels (Frontiers in Psychology, 2025-11-04)Two experiments of 120 (40 expert, 40 skilled, 40 novice; ages 17 to 20); scenario decision time novice 33,925 ms, skilled 25,867 ms, expert 21,082 ms; under high time pressure skilled players turned extremely conservative, experts chose by competitive state
• S16Harris, Vine, Eysenck and Wilson 2021, Psychological pressure and compounded errors during elite-level tennis (Psychology of Sport and Exercise; Semantic Scholar record)More than 650,000 points across 12 Grand Slams 2016 to 2019; a 1-to-5 pressure index raised the probability of a double fault or unforced error (ps<.001); a prior-point error OR 1.2 [1.17, 1.23]; multiplicative; winning players as susceptible to pressure and prior errors as losing players

Outcome-contingent pressure (stakes) pulls attention into worry and hurts processes that need working memory; being watched (monitoring) pulls attention onto the steps of an automated skill and hurts proceduralized execution. In S11 each route hurt a different category-learning task, interventions designed by route removed the choke (Exp 3), and the monitoring route replicated in a serial reaction time task (Exp 4). In proceduralized putting (S18) self-consciousness training eliminated the choke and dual-task training did not. In 53 semi-professional tennis players (29.9 ± 9.0 y, 21.5 y of play) hitting second serves under expert evaluation (S3), anxiety lowered accuracy (B=-.24, p=.04) and the entire effect ran through self-reported distraction (indirect effect 95% CI .04 to .30) with skill-focus carrying nothing (-.02 to .05): in an experienced adult's serve under evaluation the distraction route dominated. A match applies stakes and an audience at once, so a serve is exposed on both routes, and which bites depends on the learning stage (a stroke still run on explicit rules sits on the monitoring route). Boundary: adult semi-professionals (S3, between-person with mediation), laboratory adults (S11), novice and expert golfers (S18); no tennis mediation test in juniors or club adults was opened.

Skilled action is controlled by two attentional systems; pressure biases the allocation. Stakes load working memory with outcome worry and starve attention-demanding processes (choice, context use); observation raises self-focus and re-engages step-by-step control of a skill that runs best without it, which raises movement variability. Which route damages a given stroke depends on where that stroke's control is stored: a long-automated serve is exposed to monitoring, a rebuilt stroke still carried on rules is exposed to both, and an evaluated adult serve in S3 lost through distraction.

• S11DeCaro, Thomas, Albert and Beilock 2011, Choking under pressure: multiple routes to skill failure (JEP: General; Europe PMC record)Outcome-contingent pressure (distraction) hurt rule-based category learning; monitoring by others hurt information-integration learning; interventions designed by pressure type (Exp 3); monitoring effect replicated in a serial reaction time task (Exp 4)
• S18Beilock and Carr 2001, On the fragility of skilled performance: what governs choking under pressure? (JEP: General; Europe PMC record)Putting choked under pressure, alphabet arithmetic did not; in putting, self-consciousness training eliminated the choke while dual-task training did not, supporting explicit-monitoring theories for proceduralized skills
• S3Englert and Oudejans 2014, Is choking under pressure a consequence of skill-focus or increased distractibility? Results from a tennis serve task (Psychology 5:1035-1043)53 semi-professional players (anxiety n=25, neutral n=28), 29.9 y; anxiety lowered second-serve accuracy B=-.24, p=.04; effect fully mediated by self-reported distraction (indirect 95% CI .04 to .30), skill-focus did not mediate (-.02 to .05)

In 50 expert golfers across three pressure levels (S10) rising pressure increased anxiety, effort and heart rate and increased putting accuracy while grip force fell, with effort and heart rate partially mediating the gain. In 40 skilled college tennis players (S2) a coach-evaluation and money manipulation raised ball speed (p<.001) and racket speed (p=.013) in both groups and neither group's serve score fell (interaction p=.287); the authors wrote that 'pressure manipulation must be reconsidered' because no choke was induced. In 20 highly skilled juniors (S1) the same class of manipulation lowered the right-hand control group's accuracy (Phase x Group p=.003), so induction worked there. The law: a pressure effect is a within-player contrast whose sign is not fixed, and a protective claim is defined only where the control arm measurably lost accuracy. Boundary: expert golfers (S10, within-person), skilled college players and juniors (S1, S2, randomized two-group); none of these measured shot choice.

Arousal and effort are inputs to motor control as well as costs: raised effort and heart rate can tighten the temporal envelope of a well-learned skill and improve its outcome, and reduced grip force under pressure runs against the folk picture of tightening up. Because the sign of the pressure effect depends on the skill's control storage, the manipulation's strength and the performer, a pressure manipulation must be checked on the outcome before any intervention effect can be read as protection; a null in the control arm leaves the protective contrast undefined.

• S10Cooke, Kavussanu, McIntyre, Boardley and Ring 2011, Effects of competitive pressure on expert performance: underlying psychological, physiological, and kinematic mechanisms (Psychophysiology; Europe PMC record)50 expert golfers, three pressure levels; pressure increased putting accuracy, anxiety, effort and heart rate and decreased grip force; effort and heart rate partially mediated the improvement
• S2Mizuno and Masaki 2024, Effects of left-hand contraction on tennis serve performance (Frontiers in Psychology)40 skilled college players 20.0 y; neither group deteriorated under pressure (total-score interaction p=.287); max-score count rose in the contraction group p=.021; ball speed up p<.001 and racket speed up p=.013 in both groups; authors say no choking was induced
• S1Beckmann, Fimpel and Wergin 2021, Preventing a loss of accuracy of the tennis serve under pressure (PLOS ONE)20 right-handed male juniors 17 to 18 y; left-hand dynamic handgrip held serve accuracy while the right-hand group fell under pressure, Phase x Group F(1,18)=11.88, p=.003; only valid serves analysed, velocity unmeasured; anxiety rose p<.001 in both groups

Practising under pressure raises later performance under pressure by g=0.67 (95% CI 0.43 to 1.12) after one outlier is removed, across 14 studies and 394 participants from novices to elite athletes and police (S9), with benefit on open and closed tasks and no clear moderator. Quiet-eye training in 22 elite golfers (S20, RCT 11/11) held the final fixation at 2,794 ms versus 1,405 ms under pressure, holed 60 percent versus 36 percent (p<.005), explained 43 percent of performance-error variance and cut 1.92 putts per competitive round while controls did not change. Ten days of adaptive working-memory training in recreational adult club players (S14; 30 recruited, 25 analysed, ages about 32 to 35) raised volley accuracy under pressure (Condition x Group p=.044, ηp²=.165; trained 2.67 to 3.44, controls 2.56 to 2.65) and moved the quiet-eye offset later (p=.006), while controls never deteriorated. Left-hand contraction held serve accuracy in 20 juniors (S1, p=.003) but gave no score interaction in 40 college players (S2, p=.287), and across ten studies the pooled g=0.59 (0.14 to 1.03) shrinks under trim-and-fill (S19). In every tennis trial the target was prescribed, so the effects are on execution and no opened trial measured shot choice or decision time. Boundary: the populations above; no trial in adult club players beyond S14, none with a match transfer test.

Each remedy changes one part of the control system: pressure practice makes the pressure state familiar so attentional control is less disturbed by it; a long final fixation keeps attention on the external target and stabilizes the temporal envelope of the stroke; working-memory training raises the capacity that outcome worry would otherwise consume; a left-hand contraction is proposed to damp verbal-analytic control. Because each acts on execution within a given task, its effect is local to that task, population and manipulation check, and transfers to shot selection only by assumption.

• S9Low, Sandercock, Freeman, Winter, Butt and Maynard 2021, Pressure training for performance domains: a meta-analysis (Sport, Exercise, and Performance Psychology 10(1))14 studies (10 sport, 4 law enforcement), n=394; after one outlier removed g=0.67, 95% CI [0.43, 1.12], I²=17.1%; benefit for novice and experienced on open and closed tasks; no clear moderators
• S20Vine, Moore and Wilson 2011, Quiet eye training facilitates competitive putting performance in elite golfers (Frontiers in Psychology)22 elite male golfers (handicap 2.78), RCT 11/11; under pressure QE-trained held QE 2,794 ms vs 1,405 ms, holed 60 percent vs 36 percent (t(20)=3.75, p<.005); QE duration explained 43 percent of performance-error variance; 1.92 fewer putts per competitive round, controls unchanged
• S14Ducrocq, Wilson, Vine and Derakshan, Adaptive working memory training reduces the negative impact of anxiety on competitive motor performance (JSEP; accepted manuscript PDF)30 recreational club players recruited (ages about 32 to 35 y), 25 analysed; 10 days adaptive dual n-back vs 1-back control; volley accuracy Condition x Group F(1,23)=4.535, p=.044, ηp²=.165, trained group 2.67 to 3.44, controls 2.56 to 2.65 (no deterioration); QE offset interaction p=.006; QE duration interaction null
• S1Beckmann, Fimpel and Wergin 2021, Preventing a loss of accuracy of the tennis serve under pressure (PLOS ONE)20 right-handed male juniors 17 to 18 y; left-hand dynamic handgrip held serve accuracy while the right-hand group fell under pressure, Phase x Group F(1,18)=11.88, p=.003; only valid serves analysed, velocity unmeasured; anxiety rose p<.001 in both groups
• S2Mizuno and Masaki 2024, Effects of left-hand contraction on tennis serve performance (Frontiers in Psychology)40 skilled college players 20.0 y; neither group deteriorated under pressure (total-score interaction p=.287); max-score count rose in the contraction group p=.021; ball speed up p<.001 and racket speed up p=.013 in both groups; authors say no choking was induced
• S19Luan, Wang, Keil, Ehrlenspiel and Mirifar 2024, A systematic meta-analysis of the effectiveness of (left) hand contractions on motor performance (Sport, Exercise, and Performance Psychology; Europe PMC record)10 studies; pooled g=0.59, 95% CI [0.14, 1.03]; trim-and-fill correction: the effect may not be as robust as it first appeared; study quality limits the evidence

A 30-minute Stroop task with no physical load lowered groundstroke targeting in 66 male players aged 24.3 ± 2.5 against both a placebo and a control condition (p<.001, η²=.20) while raising Stroop time and errors (p=.001, η²=.20), in a randomized placebo-controlled crossover (S13). Physical fatigue at 90 percent of peak heart rate cut groundstroke accuracy from 24.81 to 14.81 percent in 13 experts (LTA 6.2) and from 16.62 to 8.38 percent in 17 non-experts (LTA 10.2), moderate fatigue at 70 percent changed nothing, and the fatigue x expertise interaction was not significant (S5): experts kept a higher level and lost as much. Pressure draws on the same attentional account and the same execution, so a third-set pressure point sits on a baseline already lowered by an unknown amount; a pressure finding from fresh players transfers to a fatigued player only with the fatigue state measured. Boundary: adult male players (S13, within-person), college-age experts and non-experts (S5, within-person); no study crosses pressure with fatigue in tennis.

Attentional control is a shared, depletable resource: a sustained cognitive load lowers it without touching the muscles, and high-intensity physical work lowers stroke accuracy through neuromuscular and perceptual decrement. Because pressure's first effect is also on attentional control (efficiency before effectiveness), an unstated fatigue state confounds the pressure contrast: the same manipulation produces a different loss on a depleted baseline, and expertise does not shield the baseline from physical fatigue.

• S13Öztürker and Erman 2025, Impact of mental fatigue on tennis players' attention and groundstroke performance (Frontiers in Psychology, 2025-05-02)66 male players 24.3 y, randomized placebo-controlled crossover; a 30-minute Stroop task raised Stroop time and errors (p=.001, η²=.20) and lowered groundstroke targeting against control and placebo (p<.001, η²=.20)
• S5Lyons, Al-Nakeeb, Hankey and Nevill 2013, The effect of moderate and high-intensity fatigue on groundstroke accuracy in expert and non-expert tennis players (JSSM 12:298-308)13 experts and 17 non-experts; groundstroke accuracy at rest/moderate/high fatigue experts 24.81/25.00/14.81 percent, non-experts 16.62/16.18/8.38 percent; no fatigue x expertise interaction (p>.05)

Across 16 studies of 1,794 players aged 12 to 32 (600 elite, 1,194 sub-elite; S7), elite players exceed sub-elite on lower-extremity power (SMD 0.53), endurance (0.59), agility (0.54), speed (0.35) and most of all stroke velocity (SMD 1.00, large): at the good-to-elite boundary the physical difference is real and the biggest single effect is in the ball the stroke produces. Experts also pick up cues more accurately and faster (S8, 42 studies, 388 effect sizes), so a cognitive and a physical gap coexist in the same co-selected bodies. Laboratory perceptual-cognitive training gains transfer to the court at ES 0.65 (0.15 to 1.16) against 1.51 (0.98 to 2.05) in the laboratory (S15, 22 studies, team sports), so the field 'decision' construct already carries movement and execution. Under match pressure, winning professionals were as susceptible to pressure and prior errors as losing ones across 650,000 points (S16), the opposite of a gap carried by pressure resistance at that level. Attributing a level difference to decision speed under pressure would require a condition x level interaction on a choice measure, mediation through it, and physical equivalence shown at a stated precision; no opened source supplies any of the three. An NTRP computer rating adjusts on match outcomes against expected outcomes and 'not how well someone can hit their strokes or play points in a lesson' (S21), so a rating difference cannot name the component that moved. Boundary: elite vs sub-elite 12 to 32 y (S7, cross-sectional), expert vs novice across sports (S8), elite team-sport athletes (S15), touring professionals (S16), USTA league adults (S21); the elite-to-world-class boundary and the adult club boundary are untested in opened rows.

A level is an outcome of co-selected, mutually compensating attributes: earlier recognition buys time, leg power buys reach and racket speed, accepted margin buys safety, and the same shot outcome can be purchased with any of them inside one ballistic budget. A comparison of levels therefore estimates a partial derivative in a system where the inputs covary and are jointly selected; without exogenous variation in one input, or a condition x level interaction with mediation, the attribution is not identified, and a rating that aggregates match outcomes against expectation removes the component information entirely.

• S7Lambrich and Muehlbauer 2022, Physical fitness and stroke performance in healthy tennis players with different competition levels: a systematic review and meta-analysis (PLOS ONE)16 studies, 1,794 players (600 elite, 1,194 sub-elite), 12 to 32 y; SMD favouring elite: lower-extremity power 0.53, endurance 0.59, agility 0.54, speed 0.35, stroke velocity 1.00
• S8Mann, Williams, Ward and Janelle 2007, Perceptual-cognitive expertise in sport: a meta-analysis (JSEP 29:457-478; Europe PMC record)42 studies, 388 effect sizes (point-biserial); experts better than non-experts on response accuracy and response time, with fewer, longer fixations and longer quiet eye; paradigm and modality moderate the effect
• S15Zhu, Zheng, Liu, Guo and Cao 2024, Effects of perceptual-cognitive training on anticipation and decision-making skills in team sports: a systematic review and meta-analysis (Behavioral Sciences)22 studies, 45 effect sizes, elite team-sport athletes; task-specific accuracy ES 1.51 [0.98, 2.05] vs on-court transfer accuracy ES 0.65 [0.15, 1.16]; task response time ES -0.91 [-1.45, -0.38] vs on-court -0.44 [-0.81, -0.06]
• S16Harris, Vine, Eysenck and Wilson 2021, Psychological pressure and compounded errors during elite-level tennis (Psychology of Sport and Exercise; Semantic Scholar record)More than 650,000 points across 12 Grand Slams 2016 to 2019; a 1-to-5 pressure index raised the probability of a double fault or unforced error (ps<.001); a prior-point error OR 1.2 [1.17, 1.23]; multiplicative; winning players as susceptible to pressure and prior errors as losing players
• S21USTA, NTRP ratings FAQA computer rating compares the actual match outcome with the expected outcome from the players' dynamic ratings and adjusts up or down; ratings are based on matches, not how well someone can hit their strokes or play points in a lesson