High-resolution tactile observation makes hidden racket-control mechanisms learnable

Sensing, reconstruction and functional validation

• Reconstruction validated contact mechanics, with pose-estimation errors of 0.0453 in normalized grip position and 4.01° in angle; the model showed stronger grip stabilization during posture holding and stronger drive activity during dynamic strokes.The response-weighted median distance from tactile-active nodes to the handle surface was 0.652R, where R is the handle inradius.Source: Sensing, reconstruction and functional… · p. 2

Greater skill specificity and earlier preparation with expertise

• Experts showed greater skill-specific control: drive–grip angle range widened from 42.6° in Low players to 56.0° in Experts, and skill identity explained 17.89% versus 3.25% of recruitment-timing variance.Spatial force patterns were also more distinct across skills in Advanced and Expert players, including when the number of learned patterns was held fixed.Source: Greater skill specificity and earlier… · p. 2, Figure 3 · p. 5
• Experts shifted control earlier: force redistribution advanced from 19.0 ms after impact in Low players to 8.6 ms, while model-estimated perception-to-control interval fell from 39.3 ms to 37.9 ms.Regional recruitment peaks did not consistently advance and remained predominantly post-impact, indicating a selective rather than uniform shift toward anticipation.Source: Greater skill specificity and earlier… · pp. 2, 4, Figure 3 · p. 5

Expertise refines local forces and regional coordination

• Expert modulation was more focal and distal, with residual magnitude and spatial coverage at 27% and 65% of Low-group values; geometric torque cancellation per unit residual reached 34%.In Experts, residual activity concentrated near the fingertips rather than extending across the palm and finger bases.Source: Expertise refines local forces and… · p. 5, Figure 4 · p. 6
• Spatiotemporal coordination followed an acquire–refine pattern: Advanced players coordinated more regions over longer sequences, while Experts showed fewer regions and shorter, more coherent sequences.The pattern appeared in 9/10 regional partitions and 10/10 five-skill-averaged sequence-duration estimates; chain-level torque consistency and step-to-step alignment were also higher in Advanced and Expert players than Low players.Source: Expertise refines local forces and… · pp. 5–7, Figure 4 · p. 6
• Halving sensor count retained 57.4% of contact-region boundaries, while reducing acquisition from 100 to 50 Hz retained 93.2–95.2% of repeatable timing relationships and 30 Hz retained 54.6–64.3%.Learning functional regions from tactile evidence also revealed that regional sequences were longest in Advanced players across all five skills, a pattern obscured by anatomical boundaries or fixed region counts.Source: Expertise refines local forces and… · p. 7

Mechanism-guided practice improves skill and control coordination

• Learners gained 0.72 expert-rated skill levels with mechanism guidance versus 0.05 with level-only feedback, a 0.67-level between-group difference (95% CI 0.39–0.98; P = 0.0014).The randomized groups each included 12 learners and practised for 10 minutes across five skills.Source: Mechanism-guided practice improves… · p. 7, Figure 5 · p. 8
• Among six guided learners followed across three sessions, improvement accumulated to 1.23 levels (95% CI 0.76–1.68), with partial between-session decline; exploratory analyses also showed shifts toward earlier drive regulation and greater skill specificity.The study’s cross-sectional acquire–refine pattern requires longitudinal validation, and generalization beyond racket control remains untested.Source: Mechanism-guided practice improves… · p. 7, Discussion · p. 9

Control-organization layer

• The control layer separated tactile-history representations for object-driving torque and motion from grip-based stabilization of the predicted velocity increment.The drive branch predicted a torque proxy and velocity increment; the grip branch produced a gate that attenuated that increment along each axis.Source: Control-organization layer · p. 10

Spatiotemporal-realization layer

• Contact-based regions defined the spatial units for timing analysis, while a directed tree summarized their recruitment order and torque consistency assessed sequence coherence.Region count indexed spatial extent, sequence duration indexed temporal span, and torque consistency used equal-magnitude regional torque proxies.Source: Spatiotemporal-realization layer · p. 11

Mechanism-guided skill learning

• Personalized guidance compared each learner’s contact pattern and regional timing with an Expert-group reference, then prioritized the largest spatial and timing discrepancies.The interface paired contact and timing instructions with tactile maps, timing visualizations, synchronized video, and motion suggestions derived from tactile–motion coordination.Source: Mechanism-guided skill learning · pp. 11–12
• A randomized study assigned 24 learners to mechanism-guided or proficiency-level-only feedback, matched practice at 10 minutes, and assessed blinded expert-rated skill-level change across five skills.Each group included four beginners, four intermediate players, and four advanced players; the primary outcome averaged expert ratings across skills before and after training.Source: Mechanism-guided skill learning · p. 12

Statistical analysis

• Participant-level or participant-clustered analyses addressed repeated strokes and skills, with multiple-comparison corrections applied to specified trend, sensor, regional, and temporal tests.Guidance-group rating changes were compared using a two-sided Welch test, with participant-bootstrap confidence intervals and a baseline-adjusted HC3 analysis.Source: Statistical analysis · p. 12

• The supplementary information is available, and correspondence and material requests should be directed to L.C.Source: Additional information · p. 14
• The supplementary-information title identifies the paper as “High-resolution tactile observation makes hidden racket-control mechanisms.”Source: Additional information · p. 15
• The listed authors are Haoyang Tian, Zhengwei Li, Houcheng Li, Xu Yang, Peigeng Gu, Xinyue Wang, Tairan Zhu, Shuo Jiang and Long Cheng.Source: Additional information · p. 15

• The glove records normal contact signals and hand motion synchronously at 100 Hz across 864 nodes.The arrays cover fingertips, phalanges, thumb and palm while leaving finger gaps and bending regions flexible.Source: Supplementary Note 1: Tactile–inertial… · p. 16
• Eight arrays comprise four 96-node non-thumb finger arrays, one 96-node thumb array and three 128-node palm arrays.Flexible array tails connect to a dorsal acquisition board and six-axis IMU.Source: Supplementary Note 1: Tactile–inertial… · p. 16, Figure 1 · p. 16

Supplementary Note 2: Wearable spatiotemporal sensing capacity

• The comparison uses node count and system-level acquisition rate; individual-element response times are kept separate.The table lists reported values and marks system-level rates that were not explicitly reported.Source: Supplementary Note 2: Wearable… · p. 16, Table 1 · p. 17, Figure 2 · p. 17
• 86,400 sensing-node frames s−1 from 864 nodes at 100 Hz exceeds the reported throughput of several representative tactile systems.The comparison includes an 18-node, 500-Hz system, a 548-node, approximately 7.3-Hz glove and an up-to-1,152-node, 13-Hz glove.Source: Supplementary Note 2: Wearable… · p. 16, Figure 2 · p. 17

Supplementary Note 3: Calibration platform and sensor characterization

• Across ten sites, the loading-slope coefficient of variation was 7.77%.Across 0–3 N, median cycle-wise R2 was 0.968 for loading and 0.962 for unloading.Source: Supplementary Note 3: Calibration… · p. 17
• The calibration apparatus pairs motor-driven loading and unloading with reference-force measurements to generate synchronized calibration records.Source: Figure 3 · p. 18

Supplementary Note 4: Racket-control tasks

• The five tasks varied grasp, force direction and racket-face control, including four near-net spin strokes and a backhand rear-court transition.The four spin strokes used brief racket-face adjustments around shuttle contact; the transition used a different grip and force direction.Source: Supplementary Note 4: Racket-control… · p. 18

Supplementary Note 5: Reconstructing hand–racket contact mechanics

• With complete tactile input, reconstructed active contact had a median node-to-surface distance of 0.652R; omitted-region nodes had a median distance of 1.100R.Here R is the fixed handle inradius.Source: Supplementary Note 5: Reconstructing… · pp. 18–19, Table 2 · p. 19

Supplementary Note 6: Functional validation of drive–grip representations

• Drive-latent RMS magnitude was 11.20 during dynamic strokes and 7.64 during posture holding, while mean grip gate shifted from 0.726 to 0.876.The drive-to-total latent-norm ratio was 0.529 versus 0.232, respectively.Source: Supplementary Note 6: Functional… · p. 20

Supplementary Note 7: Fixed-rank sensitivity of skill-specific spatial force patterns

• Across all 21 rank–initialization settings, Advanced and Expert players showed greater between-skill spatial force-basis distances than Low players.The further Advanced-to-Expert increase was consistent at ranks 5, 6 and 8, but varied at other ranks.Source: Supplementary Note 7: Fixed-rank… · p. 21, Table 3 · p. 21

Supplementary Note 8: Spatial and temporal organization of regional coordination

• Under a common selection rule, High-proficiency maps contained 22–24 regions across five seeds, compared with 15–16 for Low maps.These regions represent groups of co-active sensors, not independent physiological control units.Source: Supplementary Note 8: Spatial and… · p. 21
• Adaptive maps recovered an Advanced sequence-duration peak across all five skills, with a mean peak margin of +11.06 ms.The reference partitions contained 16, 20 and 17 regions in Low, Advanced and Expert; the acquire–refine pattern appeared in 9/10 additional initializations.Source: Supplementary Note 8: Spatial and… · pp. 22–23
• Mechanical-coherence directions persisted across several map controls, but none of the three reported endpoints passed Holm correction.The adaptive, proficiency-specific representation yielded the strongest and most consistent acquire–refine pattern; shared and anatomical representations generally weakened it.Source: Supplementary Note 8: Spatial and… · pp. 24–25
• Whole-hand contact redistribution advanced from 19.0 ms after impact in Low players to 8.6 ms in Experts, while local recruitment peaks remained post-impact.Median local peak times were 45.6, 38.0 and 55.6 ms after impact for Low, Advanced and Expert players.Source: Supplementary Note 8: Spatial and… · pp. 25–26

Sensitivity of temporal weighting

• Expert-minus-Low expected-lag contrasts were negative in all eight fitting refits, ranging from -3.58 to -1.86 ms.The direction also persisted in 9/9 representation-size fits and 9/9 matched-sampling fits.Source: Supplementary Note 9: Model temporal… · p. 26
• Across 26 conditions, Expert model profiles placed more weight on recent tactile history than Low profiles; 21 contrasts had 95% confidence intervals below zero.Individual temporal weights reduced validation prediction loss relative to uniform weights by 0.0395 [0.0320, 0.0475], shared global weights by 0.0039 [0.0028, 0.0050], and shuffled profiles by 0.0008 [0.0004, 0.0013].Source: Supplementary Note 9: Model temporal… · p. 26

Interpretation and scope

• The estimated interval describes the decoder’s use of tactile history, not a physiological delay measurement.Source: Supplementary Note 9: Model temporal… · p. 27

Sensitivity of temporal weighting

• Exploratory tests at 25, 20, 12.5 and 10 Hz did not resolve a further change, as all five paired-change 95% intervals included zero.These tests concern model history weighting.Source: Supplementary Note 9: Model temporal… · p. 27

Regional allocation

• Adaptive maps retained eight palm subregions, whereas the anatomical map represented the palm as one region.The learned 15-region maps retained seven or eight palm subregions.Source: Supplementary Note 10: Data-derived… · p. 27

Held-out representation comparison

• Adaptive maps reduced waveform error by 4.34% relative to anatomical regions, while learned 15-region maps reduced it by 2.10%.Adaptive maps also reduced palm activity-time dispersion by 8.47% and increased force-direction coherence by 19.10 percentage points relative to anatomical regions.Source: Supplementary Note 10: Data-derived… · p. 27, Table 8 · p. 28

Reversed-split sensitivity

• In the reversed split, adaptive maps reduced waveform error by 5.03% and activity-time dispersion by 8.44%, and increased force-direction coherence by 17.50 percentage points relative to anatomical regions.All three comparisons had PHolm = 3.4 × 10−4.Source: Supplementary Note 10: Data-derived… · p. 28

Supplementary Note 11: Spatial sampling of local contact structure

• At 432 nodes, boundary recall was 0.574 and small-region preservation was 0.945; at 108 nodes, these fell to 0.123 and 0.348.The analysis evaluated held-out co-activation modularity, boundary recall, and small-region preservation.Source: Supplementary Note 11: Spatial… · p. 30

Supplementary Note 12: Spatial-resolution sensitivity of residual metrics

• At 54 nodes, sparse-input refits recovered 5/10, 5/10, 1/10 and 5/10 decreasing contrasts for magnitude, coverage, cancellation per unit residual and cumulative torque cancellation, respectively.The corresponding counts at 864 nodes were 10/10, 8/10, 8/10 and 9/10.Source: Supplementary Note 12:… · p. 31
• At 54 nodes under the original processing pipeline, all five Expert residual fields fell below the positive-residual threshold, leaving cancellation per unit residual undefined.The loss of detectability reflected both reduced sensing density and processing applied to sparse inputs.Source: Supplementary Note 12:… · p. 32, Table 10 · p. 32
• Subsampling full-resolution residual fields retained 7/10 decreasing contrasts for coverage and 10/10 for cumulative torque cancellation at 54 nodes.At 864 nodes, the corresponding counts were 9/10 and 10/10.Source: Supplementary Note 12:… · p. 33

Supplementary Note 13: Temporal sampling of regional coordination

• At 50 Hz, sequence-duration peaks occurred in 4/5 skills, versus 5/5 at 100 Hz, while 50-Hz native-link retention ranged from 93.2% to 95.2% across groups.At 20 Hz, retention was 9.7% for Low, 11.1% for Advanced, and 19.2% for Expert, and the acquire–refine pattern became largely unrecoverable.Source: Supplementary Note 13: Temporal… · pp. 34–35, Table 11 · p. 35, Table 12 · p. 36
• The sampling-rate comparison held region maps and candidate links fixed, while available delays and statistical information varied with rate.The lag search included positive integer delays within 50 ms; rates below 20 Hz were excluded because they cannot represent that delay.Source: Supplementary Note 13: Temporal… · pp. 33, 36

Supplementary Note 14: Personalized force–motion trajectory optimization

• The reward model ranked candidate force–motion trajectories with pairwise preference accuracy of 0.828 for pooled higher- versus lower-proficiency pairs and 0.718 for ordered proficiency-level pairs.Temporal-shift ranking accuracy was 0.726 and 0.720, respectively, and mismatch ranking accuracy was 0.737.Source: Supplementary Note 14: Personalized… · p. 36

Supplementary Note 15: Skill-specific learning outcomes and rating robustness

• Mechanism-guided learners improved across all five skills, with mean expert-rated gains of 0.64–0.81 levels after one session and 1.00–1.39 levels across three sessions.The three-session results came from six learners.Source: Supplementary Note 15: Skill-specific… · p. 37, Figure 16 · p. 38
• Mean first-session gains remained 0.64–0.78 levels and cumulative gains 1.17–1.32 levels when any one expert’s ratings were omitted.Across 240 targets, reliability was ICC(A,1)=0.489 for a single expert and ICC(A,3)=0.741 for the three-expert mean.Source: Supplementary Note 15: Skill-specific… · p. 37, Figure 18 · p. 39

Supplementary Note 16: Mechanism-based guidance versus level-only feedback

• Mechanism guidance yielded +0.72 versus +0.05 skill-level gains over level-only feedback, a +0.67-level difference (95% CI +0.39 to +0.98; two-sided Welch P = 0.0014).All 12 guided learners improved in their five-skill mean rating; five level-only learners improved, six were unchanged, and one declined.Source: Supplementary Note 16: Mechanism-based… · pp. 39–40, Table 13 · p. 40
• Guided learners improved by 0.64 levels in force-release control and 0.62 levels in hand motion–force coordination.Mean overall gains were positive for every skill and remained positive when any one expert was omitted.Source: Supplementary Note 16: Mechanism-based… · p. 40
• Separate interventions could identify the contributions of contact and motion guidance, while longer follow-up could assess sustained retention and transfer.Source: Supplementary Note 16: Mechanism-based… · p. 41

Supplementary Methods S1: Tactile–inertial glove hardware

• Eight tactile arrays provide 864 nodes, while a dorsal six-axis inertial unit records acceleration and angular velocity; both streams are synchronized at 100 Hz.Tactile calibration yields distributed normal-contact measurements; tangential forces were not measured.Source: Supplementary Methods S1:… · p. 42
• Across 2,000 loading–unloading cycles over 0–3 N, median cycle-wise R2 was 0.968 for loading and 0.962 for unloading.Across-site slope coefficient of variation was 7.77%, and median within-site response coefficient of variation was 0.95%.Source: Supplementary Methods S1:… · p. 42

Supplementary Methods S2: Participants and racket-control tasks

• The 50-person discovery cohort performed up to five racket-control skills, and valid trials required a single racket-string contact with the shuttle.An auxiliary eight-person tactile–pose dataset expanded grip-posture coverage for supervised pose estimation.Source: Supplementary Methods S2: Participants… · pp. 42–43

Supplementary Methods S3: Data preprocessing

• Each valid stroke was aligned to its manually annotated impact frame, and preprocessing produced 100-frame segments with timestamps, six inertial channels, and 864 tactile readings.The discovery and learning cohorts contributed 7,736 and 6,989 synchronized stroke sequences, respectively, for 14,725 overall.Source: Supplementary Methods S3: Data… · p. 43

Supplementary Methods S4: Metric definitions and statistics

• Metric definitions paired impact-aligned summaries with participant-level or skill-level inference, preserving repeated observations rather than treating settings or skills as independent people.For the proficiency trends in Fig. 3d, 217 participant–skill observations came from 50 participants, with participant-clustered tests and Holm correction across three outcomes.Source: Table 15 · p. 43, Supplementary Methods S4: Metric… · pp. 44–45

Supplementary Methods S5: Spatial residual analysis

• Spatial residual analysis compared target-group force patterns with a fixed Low reference, while torque-based measures quantified geometric opposition among local contributions.Cancellation per unit residual is unavailable when retained response is zero; these torque measures do not directly measure energy expenditure.Source: Supplementary Methods S5: Spatial… · pp. 45–46

Supplementary Methods S6: Feedback reward and trajectory optimization

• Expert-derived contact and timing differences selected the three largest discrepancies in each category for personalized force-distribution and temporal guidance.The display translated spatial differences into increase-or-reduce contact cues and timing differences into advance-or-delay cues; motion suggestions were scored with tactile input held fixed.Source: Supplementary Methods S6: Feedback… · pp. 46–47

Supplementary Methods S7: Mechanics-informed tactile representation

• Contact-position reconstruction combined pose initialization from diverse labeled grip postures with temporally regularized physical refinement of hand–racket geometry.The evaluation used fixed seven-frame sequences from 50 discovery participants, with ten participants for configuration selection and 40 for evaluation; complete-input mean endpoint displacement increased from 0.150R to 0.199R.Source: Supplementary Methods S7:… · pp. 47–48

Supplementary Methods S8: Control-organization model

• The model maps tactile frames to separate non-negative drive and grip representations, whose weighted histories predict torque-related motion and grip-mediated attenuation.Its decoder uses 30–80 ms of history; participant-specific temporal profiles are fit after control-model training, and proficiency labels are not model inputs.Source: Supplementary Methods S8:… · pp. 48–49

Supplementary Methods S9: Temporal-weight sensitivity experiments

• Temporal-weight sensitivity tests varied optimization, starting weights, latent capacity, participant sampling, and acquisition rate while holding the discovery data and core model components fixed.The supplied table caption identifies Expert-minus-Low contrasts in nominal milliseconds with participant-bootstrap intervals, but gives no contrast values.Source: Supplementary Methods S9:… · pp. 49–50, Table 16 · p. 50

Supplementary Methods S10: Regional coordination from spatial partitioning to temporal order

• Regional coordination was estimated by selecting contact regions from graph-based consensus, testing directed lead–lag links, and organizing retained links into acyclic trees.Tree delays define relative regional timing and completion time; torque consistency and step-to-step alignment compare the resulting ordering with randomized orders.Source: Supplementary Methods S10: Regional… · pp. 50–51

Supplementary Methods S11: Anatomical-region comparison

• Learned maps were fitted on one proficiency-stratified participant split and evaluated on the other, with the roles reversed for sensitivity analysis.The count-matched Learned15 map was formed by merging adjacent regions of the adaptive map; evaluation data were not used to select counts or merges.Source: Supplementary Methods S11:… · p. 51
• Map comparisons measured normalized whole-hand waveform reconstruction error, within-region palm timing dispersion, and within-region palm force-direction coherence.Lower timing dispersion denotes more compact regional activity, while higher coherence indicates more consistent force directions within regions.Source: Supplementary Methods S11:… · pp. 51–52
• The exploratory follow-up used participant-level paired tests and joint Holm adjustment across 24 map contrasts plus ten preceding exploratory comparisons.Confidence intervals were conditional on fitted maps and upstream reconstruction; finer nested partitions favor all three metrics by construction, so the comparison does not determine an optimal region count.Source: Supplementary Methods S11:… · p. 52

Supplementary Methods S12: Resolution-retention definitions

• Boundary recall measures the fraction of reference boundaries preserved after lower-density labels are projected onto the 864-node reference.It is defined as 1 − M/B, where B is the number of adjacent sensor pairs crossing reference boundaries and M is the number assigned the same projected label.Source: Supplementary Methods S12:… · p. 52
• Fine-scale preservation is the fraction of the smallest reference regions whose best projected match reaches Dice overlap of at least 0.5.The smallest quartile of reference regions is used, rounded up.Source: Supplementary Methods S12:… · p. 53
• Temporal retention counts stable 100-Hz links also stable at a lower rate, while Jaccard similarity compares the two stable directed-edge sets.Regional ordering and completion time are recomputed from each rate’s transfer-entropy matrix.Source: Supplementary Methods S12:… · p. 53

Supplementary Methods S13: Paired residual-resolution experiment

• Sensors were recursively grouped by spatial span, retaining the sensor nearest each group centre at 432, 216, 108, 54, and 27 nodes alongside 864.Trials, proficiency labels, and 100-frame windows were fixed across resolutions.Source: Supplementary Methods S13: Paired… · p. 53
• The refits held participant sets, skill-specific ranks, model settings, and three random seeds constant across resolutions.Evaluation used 3,820 segments from 25 participants across 102 participant–skill combinations.Source: Supplementary Methods S13: Paired… · p. 53
• Residual measures captured cumulative magnitude (FR), active sensors (NR), geometric torque cancellation (Dτ), and cancellation per unit residual (qτ), not total force or energy.FR, NR, and Dτ were scaled by 864/N for node-count comparisons; qτ was unchanged.Source: Supplementary Methods S13: Paired… · p. 53
• Directional consistency counted adjacent decreases across five skills, while amplitude summarized signed reductions relative to each skill’s 864-node Low value.These shared-observation contrasts were descriptive and had no trend tests.Source: Supplementary Methods S13: Paired… · pp. 53–54
• At 54 nodes, the original 12-neighbour smoother covered a larger physical area, and all five Expert fields fell below the positive-residual threshold.These controls separate sparse-input refitting from subsampling residual fields inferred at full resolution.Source: Supplementary Methods S13: Paired… · p. 54
• Omitting spatial smoothing changed the directional pattern, while subsampling full-resolution residual fields retained more of the original decreasing contrasts.The smoother retained a fixed neighbour count, so it covered more physical area at lower sensor density.Source: Supplementary Methods S13: Paired… · pp. 53–54

Supplementary Methods S14: Temporal-resolution experiment

• Regional signals were resampled from 100 Hz through 90, 80, 70, 60, 50, 40, 30, 25, and 20 Hz; the 50-ms ceiling allowed one positive lag at 30, 25, and 20 Hz.Rate comparisons required at least 120 effective observations at the lowest rate, equivalent to seven 100-frame strokes per participant–skill combination.Source: Supplementary Methods S14:… · p. 54
• Conditional Gaussian transfer entropy compared reduced and full predictors across eligible lags, with time-shifted surrogates and within-graph Benjamini–Hochberg adjustment.Candidates included every directed regional pair except self-links.Source: Supplementary Methods S14:… · p. 54
• Cohort link retention and Jaccard similarity compared stable directed edges at lower rates with the 100-Hz reference.Group contrasts pooled Advanced and Expert participants and used paired participant-bootstrap intervals across rates.Source: Supplementary Methods S14:… · p. 55
• Sequence duration summed delays along maximum-weight directed trees, while peak summaries compared Advanced duration with the larger Low or Expert value across five skills.Bootstrap estimates were based on participant resampling; each rate comparison used its own matched 100-Hz baseline.Source: Supplementary Methods S14:… · p. 55

Supplementary Methods S15: Training feedback evaluation

• Twenty-four learners were randomly assigned to mechanism-derived guidance plus level feedback or level-only feedback, with 12 learners per group.Three experts rated shuffled, de-identified pre/post videos on a four-level scale; six guided learners also completed repeated sessions.Source: Supplementary Methods S15: Training… · p. 55
• Guided learners gained +0.72 levels (participant-bootstrap 95% CI +0.44 to +1.02) across five skills in the first session.Among six repeated-session learners, cumulative change was +1.23 levels; between-session change was −0.33 levels.Source: Supplementary Methods S15: Training… · p. 56
• The gain difference was +0.6667 levels (bootstrap 95% CI +0.3889 to +0.9778; Welch P = 0.001373) between mechanism guidance and level-only feedback.The comparison used 12 participant-level changes per group.Source: Supplementary Methods S15: Training… · p. 56
• After adjustment for pre-training level, guidance was associated with β1 = 0.6643 levels (95% t interval 0.2944 to 1.0342; P = 0.001223).Skill-specific contrasts were descriptive and were not separately tested for significance.Source: Supplementary Methods S15: Training… · p. 56

Supplementary participant characteristics

• The dynamic-recording cohort comprised 50 participants: eight beginners, 23 intermediate players, 11 advanced players, and eight experts.Proficiency assignments used combined background information.Source: Supplementary participant… · p. 57, Table 18 · p. 57
• The anonymized roster records playing experience, professional training, and highest reported achievement or competitive background.Table-specific anonymous identifiers replace names, and achievements omit named institutions and locations.Source: Supplementary participant… · pp. 57–58, Table 18 · p. 57
• Individual analyses applied their stated eligibility rules to this cohort.The roster distinguishes blank entries marked “Not reported” from explicit absences marked “None reported.”Source: Supplementary participant… · p. 57