Short-term performance prediction in team sports using tracking data

Tracking Data for Sports Performance Prediction

Initial applications of tracking data in team sports primarily focused on quantifying physical performance and conducting time-motion analysis (Ferraz et al., 2023). This field has since undergone a paradigmatic shift, moving towards using high-resolution spatiotemporal data for more sophisticated tactical analysis and understanding collective movement patterns among players (Low et al., 2020; Perše et al., 2009). A key area of research involves deriving performance indicators from spatial and temporal aggregations of tracking data, utilizing metrics such as team centroid, space control, and other domain-specific features (Clemente et al., 2013; Low et al., 2020). Building upon this, a significant development is the concept of continuous-time within-play valuation. This includes the development of frameworks for estimating Expected Possession Value (EPV), which quantifies the expected number of points an offense will score on a possession conditional on its evolution, using a multiresolution stochastic process model for basketball (Cervone et al., 2014). The EPV concept has been adapted to soccer with a decoupled deep learning approach that provides a frame-by-frame estimation of the expected outcome of a possession (Fernández, 2020). Similarly, models for estimating Expected Points (EP) and Win Probability (WP) continuously throughout a play have been developed for American football, using Long Short-Term Memory (LSTM) networks to model outcomes based on player locations and trajectories (Yurko et al., 2019). Machine learning techniques, including Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs), allows to automate the identification of tactical patterns and summarize complex player interactions, reducing the reliance on manual annotation (Anzer et al., 2022; Tian et al., 2019). These advanced data-driven models enable the rating of specific actions not just by their outcome probability, but more comprehensively by quantifying the value they add or subtract from the expected outcome of a possession or play (Dick et al., 2021).

While machine learning has been increasingly applied to performance prediction in sports, the specific task of trajectory prediction, i.e. estimating the future position of a ball or player, remains relatively underexplored in the literature. This task is particularly important in team sports like rugby, where anticipating the movement of the ball and players is critical for strategic planning, performance analysis, and real-time decision making. Trajectory prediction has been successfully applied in other domains such as robotics, autonomous vehicles, and aerospace, where forecasting object motion is essential for navigation and control (references). Inspired by these approaches, we developed a machine learning model that predicts the trajectory of the rugby ball using both player and ball coordinates, enabling the estimation of ball position several seconds into the future. This approach captures the complex interactions on the field and provides a data-driven tool to support tactical analysis and game understanding. The present work aims at leveraging the sequential nature of tracking data for modeling short-term performance in Rugby Union and brings novelty by benchmarking state-of-the-art time series models on this task.

Time series Forecasting

Time series analysis involves studying collections of observations ordered by time, with applications across various fields including energy, economics, and meteorology. The main challenge is to understand the temporal dynamics in time series, which includes decomposition, seasonality, long-term dependencies, etc. It has been a very dynamic, long-standing field of study (Klein, 1997), with traditional statistical methods (ARMA and descendants, see Box et al., 1978) and advances in Deep Learning with RNN (Rumelhart et al., 1986), LSTM (Hochreiter & Schmidhuber, 1997), Transformer (Vaswani et al., 2017) and more recently Mamba (Gu & Dao, 2023). Transformer models have been adapted for Time series analysis for their ability to capture long-range dependencies, with a wide focus on the attention mechanism (see review by Wang et al. 2024).

PatchTST (Nie et al., 2023) advances long-term forecasting by introducing a patching strategy that segments each univariate time series into fixed-length subseries, which serve as tokens for a channel-independent Transformer. This design preserves local semantic structure within each patch, reduces attention complexity, and enables much longer look-back windows. By sharing embeddings and Transformer weights across all channels, PatchTST effectively scales to high-dimensional multivariate data.

Non-stationary Transformers (Y. Liu et al., 2022) tackle the inherent distribution shifts in real-world series—issues poorly addressed by classical stationarization techniques. Their framework integrates two components: Series Stationarization, which unifies and later restores statistics to improve predictability, and De-stationary Attention, which reintroduces non-stationary patterns into the attention mechanism to prevent over-stationarization. This leads to more expressive temporal dependencies.

Pyraformer (S. Liu et al., 2022) proposes a pyramidal, multi-resolution attention mechanism that models temporal dependencies at different scales. Its structured attention graph dramatically shortens maximum path length, enabling efficient long-range modeling without the prohibitive memory cost of standard Transformers. Through coarse-to-fine representations and carefully designed cross-scale connectivity, Pyraformer captures periodic patterns and long-term structure effectively.

Crossformer (Zhang & Yan, 2023) directly targets the overlooked cross-dimension dependency in multivariate time series. It employs a Two-Stage Attention (TSA) mechanism: a cross-time attention applied independently within each variate, followed by a cross-dimension attention—with an efficient router mechanism—to capture inter-variable correlations without prohibitive cost. Built atop these components, a Hierarchical Encoder–Decoder (HED) aggregates multi-scale temporal patterns, from coarse trends to fine details.

In contrast to these temporal-token-based approaches, iTransformer (Y. Liu et al., 2023) inverts the conventional time-centric input representation by treating variates as tokens. This architecture applies self-attention across variate tokens to model cross-variable interactions, while the feed-forward network captures temporal evolution.

Zeng et al. (2022) questioned the necessity of using Transformers for long-term forecasting, suggesting that simpler linear models can also achieve competitive results. These models are compared on reference datasets (energy, foreign exchange, weather, etc. see Wang et al., 2024) The present study applies these models to sequences expected to present distinct temporal dynamics than those of the reference datasets.

Ball position estimation

While tacking ball position from videos is a flourishing topic in computer vision (Ohno et al., 2000, Ren et al., 2009, Silva et al., 2012, Chakraborty et Meher, 2012), effort to estimate the ball trajectory without optical or tracking data remain limited, as most studies using tracking data dispose of the ball tracking (e.g. Tian et al., 2019 and Goes et al., 2020). Our work differs from this previous effort as we do not rely on computer vision, but only on player tracking data obtained by GPS, allowing us to be less dependent on video quality and computing power. In a similar setting, Amirli and Alemdar (2022) used neural network on Soccer players’ tracking data and reached a Mean Absolute Error (MAE) greater than 5 meters (from tracking data obtained by video). Kim et al. (2023) combined set transformers and hierarchical architecture to achieve a 3.6 meters MAE over GPS data. Our work differs as we used heuristics leveraging event data.

Tracking and events data were combined in Hughes et al. (2025) in soccer and event data were found to provide contextual understanding of the game and considerably improve the task of reconstructing noisy trajectories. Biermann et al. (2023) highlighted “only a few applications perform a joint analysis of both data sources despite the various involved advantages emerging from such an approach”. In a review of the use of tracking data in Team Sport, Gudmundsson and Horton (2016) also found only a few papers combined tracking and event data. Most of studies obtain tracking data through computer vision and focus on sports such as Soccer (e.g. Anzer et Bauer, 2021) or Basketball (e.g. Ghasemzadeh et al., 2021), where occlusions are less frequent and concern fewer player than in Rugby Union, and it is worth noting that a flourishing body of literature intends to build event datasets from tracking data (e.g. Khaustov et Mozgovoy, 2020 and Hauri et Vucetic,2022).

Ball position extraction method

We used event data to estimate the position of the ball. For each possible type of event (approx. 30 are used by the technical staff), we identified if the event is a ball handler event (e.g. pass, breakthrough, etc.) or not (e.g. support, tackle, etc.). For ball handler events, we added a distinction between “give” events, where the ball handler loses control of the ball soon after the event is recorded (e.g. passes, kicks, etc.) and “keep” events, where the ball handler maintains control of the ball (e.g. breakthrough, contacts, etc.). This event classification was obtained from the technical staff.

We then used for each ball handler event the coordinates of the ball handler as coordinates of the ball for the timestamp of the corresponding event. For all timestamps between two ball handler events (meaning the vast majority of timestamps, as ball handler events do not occur at the same frequency the tracking data is captured), we used the coordinates of the ball handler of the first (respectively second) event if the event is considered a “keep” (respectively “give”) event, and applied Gaussian filter to smooth ball trajectories. We then performed visual inspection of randomly selected reconstructed sequences versus the corresponding videos of the game.

To the best of our knowledge, this dataset is the only publicly available dataset containing Rugby Union Tracking data. We believe its size (47 games) and frequency (10Hz) make it valuable for the broader scope of team sports performance analysis.

Experimental Setup

To assess the relevance of our suggested approach, we compare state-of-the-art time series models with naive baselines and vanilla models. As baselines, we used (i) a Linear Regression model and (ii) two naive approaches: Stand Still: P_t = 0∀t>t₀+s where t₀ is the start of the sequence (considering the action makes no progress during the prediction period) and Constant Velocity: P_t=i * ν_p∀t>t₀+s where ${\nu }_p=\frac{P_{t_0}{}_{+\text{s}}-P_{t_0}}{s},\text{i}\in 1,\dots \text{p}$ (considering the action progresses during the prediction period at the same average speed than during the observed sequence). An illustration of target series and naive baselines is displayed in Figure 1. We selected as vanilla models LSTM (Hochreiter and Schmidhuber, 1997) and Transformer (Vaswani et al., 2017). Finally, we selected several state-of-the-art time series models, highlighted in Wang et al. (2024): iTransformer (Y Liu et al., 2023), PatchTST (Nie et al., 2023), Non-Stationary Transformer (Y Liu et al., 2022), Crossformer (Zhang & Yan, 2023), Pyraformer (S Liu et al., 2022) and DLinear (Zeng et al., 2022).

Fig. 1:

For the time series and vanilla models, we ran the two experiments: the first where only our prediction variable is used to predict itself (univariate to univariate prediction task) and the second where the whole feature vector is used to predict the target variable (multivariate to univariate prediction task). The comparison between both experiments aims at quantifying the prediction ability gained by using tracking data.

Training procedure

Due to the lack of prior knowledge about which model would best fit our data, the considerable size of the hyperparameters space, and for a reasonable use of computing resources, we designed a halving / pruning protocol (Jamieson & Talwalkar, 2015). For each model, we conducted various experiments based on common hyperparameters ranges, taking into consideration authors’ suggestions. We limited the training budget to 100 epochs (an epoch is an iteration of gradient descent in which all observations of the training set are used once) with an early stopping criterion set at 8, and every 4 epochs, we compared the validation loss of all “alive” models and pruned half of them. We used adamw optimizer (Loshchilov & Hutter, 2017), MSE loss, and a customized LR scheduler with warm-up and restarts (applying a decay of 0.5 at each restart) aligned with our pruning cycle.

Testing procedure

At the end of training, we evaluated over the test set the models of which training was terminated either by early stopping or by reaching the training budget (either case meaning the experiment completed the training). We found that in rare cases, during training, a given model M having reached a validation loss z₀ earlier during its training arrives at pruning step with a validation loss z₁>z_p>z₀, where z_p is the pruning threshold. M is therefore pruned, and budget is allocated to other models, of which some will never reach z₀ and yet be tested. In such cases, we reintegrated M for testing.

We finally compared results from univariate and multivariate input models using the MannWhitney U test.

Training and pruning

Figure 2 (and Appendix 1) displays, for each time horizon, the best epoch and the MSE on the validation set for the 5 best experiments by model, for univariate and multivariate inputs. For most models, the best epoch is earlier for multivariate inputs than for univariate inputs. This observation is not surprising as considering more features to predict the same outputs can be expected to lead more easily to overfitting. This finding gets more visible with longer time horizons, which can be explained by the lower number of sequences (see Table 2). The consequence of the best epoch being reached earlier is fewer multivariate inputs models will be pruned, and therefore more will reach testing. During training, in most cases, univariate inputs models reached lower MSE on the validation set than their multivariate counterparts, which could indicate a better ability to fit the data. However, for shorter time horizons (left part of Figure 2), multivariate models reached lower MSE, with Crossformer (Zhang & Yan, 2023) for both univariate and multivariate reaching the lowest MSE. For longer time horizons (right part of Figure 2), Pyraformer (S Liu et al., 2022) for univariate and Crossformer (Zhang & Yan, 2023) and Patch TST (Nie et al., 2023) for multivariate performed best.

Fig. 2:

Testing

Figure 3 (and Tables 1 to 4 of Appendix for comprehensive figures) displays, for each time horizon, the distribution of relative improvements in FDE over the test set against the best performing baseline for models that reached the test step. Those models are those that either completed training or were reintegrated.

Fig. 3:

Our results show robustness across time horizons: in all four-time horizons tested, Linear Regression is the best performing baseline, multivariate input models outperforms both baseline and univariate input models, and in three-time horizons out of four, univariate input models outperforms baseline. In 16-16 (respectively 32-32) time horizon, Crossformer (Zhang & Yan, 2023) ranked best in multivariate and univariate reaching minimum FDE of 3.90 meters and 3.95 meters (respectively 6.60 meters and 6.86 meters) versus baseline reaching 4.50 meters (respectively 7.82 meters). In 64-64 time horizon, Crossformer (Zhang & Yan, 2023) with multivariate input still reached the lowest FDE with 9.83 meters while Pyraformer (S Liu et al., 2022) was the best univariate input model with FDE of 10.43 meters (vs 11.14 meters for baseline). In 128-128 time horizon, no univariate input model reached the baseline FDE of 13.46 meters (lowest FDE among univariate is 13.59 meters for Pyraformer) but multivariate input models still perform best reaching a 12.29 meters FDE for Patch TST (Nie et al., 2023).

We also reported the number of models tested. Surprisingly, while during the training step univariate input models reached lower MSE than multivariate inputs models for longer time horizons, during the testing phase, for all time horizons, the lowest FDE model is a multivariate model, and visual inspection of the boxplots indicates multivariate models outperform univariate models. These observations suggest univariate models over longer time horizons are likely to be overfitting. Due to the lower number of actions and sequences used in longer time horizons (see Table 2), we are probably missing data to validate findings over longer periods.

To assess the statistical significance of our findings, we performed a Mann-Whitney U test. Its results appear in Figure 3. In line with the visual inspection of boxplots, the test reports significant difference in performance between multivariate and univariate inputs models for all time horizons except 16-16, with p-values below 10⁻⁵. It confirms superiority of multivariate input models in these time horizons.

In line with what we observed during the training step, Crossformer (Zhang & Yan, 2023) models achieve the best performance in shorter time horizon in both univariate and multivariate inputs, while in longer time horizons, no model reached the same dominance. The good performance of Crossformer (Zhang & Yan, 2023) indicates the relevance of using a cross-dimension attention mechanism: the consideration of interactions between the players increases the ability to model and predict performance.

Feature importance

To assess the relative importance of the input features, we conducted a permutation analysis on the best performing models over the train set. The result of this analysis for time horizon 128-128 is displayed in Figure 4. This permutation analysis aims at quantifying the importance of feature i ∈ {1, . . . ,61} by computing the mean difference between FDE(f (X_test), Y_test) and $FDE\left(f\left(X_{test}^i\right),Y_{test}\right)$ over k iterations where f is the fitted model, X_test represents the test set, Y_test the corresponding ground truth labels and $X_{test}^i$ the test set with values of feature i randomly permuted and all features j ≠ i maintained in the correct order. k is a hyperparameter defined by the user and was set to 3 in our experiment. In other words, we consider the importance of a given feature for the model to be proportional to the degradation of the predictive power of the model when the given feature is randomly permuted.

Fig. 4:

The left panel indicates position on the x-axis and in a lesser extent velocity features generate higher degradation of prediction when permuted, indicating higher importance for the model. All values of the boxplots fell below the dotted green line indicating the feature importance of the performance feature, indicating the later seems to be the feature bringing most explicative power to the model. This finding is intuitive as difference between univariate input models (where only past values of the performance feature are provided) perform rather close to multivariate (even if multivariate inputs models perfom best). When analyzed by player (center panel), player 6 to 8 (third line) and 11 and 14 (wings) appear to be more important when computing feature importance. Visual inspection of the heatmap (right panel) reveals a distinction between forwards (player 1 to 8) for whom x position is the most impacting feature and backs (players 9 to 15) for whom x position appears of lesser importance than for forwards but for whom velocity appears to be relevant. Angle and y features seems to be of considerably lower importance.