We study time-to-arrival (TTA) in sports: the shortest plausible time a player needs to reach an arbitrary location on the pitch given their current kinematic state, estimated as the lower envelope of observed locomotion times. Rather than modeling space ownership through position density estimation or closed-form physics-based models, we cast TTA as a conditional quantile regression problem, estimating the lower quantile of locomotion time so the model learns a player's lower-envelope arrival time. We train the model on optical tracking data from all 64 matches of the PFF FC FIFA World Cup 2022 dataset, and evaluate a lightweight multilayer perceptron against six player-motion models from the literature, re-expressed as TTA predictors, and a learned reachable- hull baseline. Across our evaluation metrics, the MLP consistently outperforms every physics-based baseline. To probe the generality of the learned locomotion model, we further evaluate it on basketball tracking data and a single-game NFL tracking dataset, analyzing the transferability of player motion dynamics across sports. Our project is available at https://github.com/mguti97/TTA-Quantile.
Figures & tables
Figure 1: Predicted TTA surfaces for the attacking and defending teams in football (top left), basketball (top right), and American football (bottom). The color map represents the difference between the predicted arrival times of the attacking and defending teams at each location. The ball is shown in white, and player arrows are scaled proportionally to player speed.
Feature
Meaning
Normalizer
d/120
distance to target (m)
Dnorm=120
cosθ
cosine of angle to target
∈[−1,1]
sinθ
sine of angle to target
∈[−1,1]
v/12
current speed (m/s)
Vnorm=12
ax/10
longitudinal acceleration (m/s 2 )
Anorm=10
ay/10
lateral acceleration (m/s 2 )
Anorm=10
Table 1: The six input features and their normalization constants.
Figure 2: Predicted TTA for a player moving upward at speeds of 2 , 5 , and 8 m/s. White contours correspond to the proposed learned model, while red ones correspond to the two-segment physical model [ 35 ] .
Model
MAE (s)
RMSE (s)
pinball
area @ 99% cov (m 2 )
physics
Constant speed [ 35 ]
3.166
3.75
0.0334
119.3
Constant accel. [ 35 , 46 ]
3.043
3.63
0.0326
46.9
Const. accel. + vmax [ 35 ]
3.101
4.75
0.2370
48.0
Two-segment [ 35 ]
2.992
3.60
0.0581
34.1
Two-segment +vmax (profile) [ 35 ]
2.900
3.50
0.0421
40.4
Free-direction accel. [ 48 ]
2.883
3.48
0.0307
43.6
Table 2: Evaluation on PFF FC test-set. Area is mean reachable area (m 2 ) at Δt=1 s with every model tuned to the same 99% coverage. Learned-model point metrics are mean ± std over five training seeds.
Figure 3: MAE by distance band on the PFF FC held-out test set, for the best precision physics baseline, the learned reachable-hull baseline and both quantile MLPs, stratified into four distance-to-target bands ( 0 – 5 , 5 – 15 , 15 – 30 and 30 m + ).
Figure 4: Mean reachable area at matched coverage , swept over three coverage levels ( 90 / 95 / 99% ) and three horizons ( Δt∈{1,3,5} s), on PFF FC test-set.
Test
Train
MAE (s)
RMSE (s)
pinball
area @ 99% cov (m 2 )
Football
Football
2.602
3.20
0.0280
31.6
Basketball
2.631
3.36
0.0808
35.1
NFL
2.652
3.25
0.0302
46.8
Two-segment
2.996
3.61
0.0581
35.7
Basketball
Basketball
2.462
3.08
0.0265
47.7
Football
2.490
3.09
0.0276
73.0
Table 3: Cross-sport transfer for every sport-trained MLP checkpoint scored on each sport’s own held-out test split, alongside that sport’s own fitted two-segment baseline. NFL rows use within-game (player-based) splitting.
Forecasting future human motion requires jointly reasoning about an agent's global trajectory and 3D body pose, which are tightly coupled, particularly in team sports where multiple interacting players introduce complex social dynamics. We exploit a socio-temporal encoder that fuses trajectory and pose at the input level and models them jointly through shared factorized attention. The model is further enhanced by a per-joint loss reweighting scheme that emphasizes dynamic joints and prevents degenerate solutions, and a frequency-domain trajectory smoothing term that improves trajectory prediction while indirectly benefiting pose forecasting. To ensure fair comparison with prior joint forecasting methods, we identify and correct evaluation biases arising from overlapping sequence construction, adopting instead a non-overlapping protocol and a deterministic, oracle-free strategy for multi-future prediction. Our approach improves over prior joint forecasting methods on both WorldPose and 3DPW, with the largest gains on pose accuracy, demonstrating that the proposed joint formulation generalizes beyond the densely interactive scenarios that motivate it.
Marc Peral, Guillem Capellera, Luis Ferraz +4
Institut de Rob`otica i Inform`atica Industrial, CSIC-UPC · Kognia Sports Intelligence · IT University of Copenhagen
Humanoid tennis requires reactive whole-body coordination under rapidly changing ball dynamics, yet collecting task-specific motion-capture demonstrations that cover diverse approach states, contact locations, and timing conditions is costly. Inspired by how humans acquire new skills by combining reusable motor experience with task-specific demonstrations, we present ATHLETE, a framework for learning reactive humanoid tennis from generic locomotion data and ordinary tennis videos. ATHLETE combines LAFAN1 locomotion with video-derived striking motions and uses Trajectory-Guided Motion Matching (TGMM) to construct diverse task-conditioned whole-body references. These references are transformed into a reactive policy through physics-based teacher--student learning with online DAgger distillation, followed by PPO fine-tuning for the tennis task. The resulting policy responds directly to robot and ball observations without requiring reference-motion inputs at deployment. On a real humanoid robot, ATHLETE achieves forehand and backhand hit rates of 90.00% and 86.67%, respectively, and enables multi-shot rallies with human players. These results demonstrate that ATHLETE can learn dynamic humanoid tennis skills from reusable locomotion data and video demonstrations. Result videos and code can be found at https://anonymous.4open.science/w/ATHLETE2027/.
Zhihao Tian, Zifan Wang, Enzheng Zhu +4
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China.
This paper presents a self-supervised representation learning framework for understanding 3D skeleton-based human motion in soccer, using future motion prediction as the learning objective. Since human motion is inherently uncertain, accounting for multiple plausible futures is essential for capturing the underlying motion dynamics and learning effective representations. To this end, we introduce a conditioning module for motion prediction that models a probabilistic distribution over discretized future motions in 3D Euclidean space, learning multimodality with explicit supervision from future trajectories. Experiments on large-scale soccer player tracking data show that our approach substantially improves motion prediction accuracy. Moreover, the learned representations effectively transfer to multiple soccer downstream applications, demonstrating strong cross-task generalization.
Yizhou Xu, Lars Bretzner, Tiesheng Wang +1
KTH Royal Institute of Technology · EA Sports TRACAB