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Prediction of football game states using transformers

Björk, Tobias LU and Salzer, Marcus LU (2025) In Master’s Theses in Mathematical Sciences FMAM05 20251
Mathematics (Faculty of Engineering)
Abstract
Multimodal trajectory prediction is a task commonly found in fields like autonomous driving
in order to model interactions between pedestrians and vehicles, but is also relevant in sports. In the context of football, predicting the future trajectories of the players and ball can be used to control a pan-tilt-zoom (PTZ) camera, allowing for automatic video recording of games. Recently, transformer architectures have gained popularity due to their ability to effectively capture both social and temporal relationships. Previous works based on transformers typically encode past trajectories to predict one or multiple future modes, but usually without quantifying the likelihood for each mode. In this work we propose statistical MART (sMART)
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Multimodal trajectory prediction is a task commonly found in fields like autonomous driving
in order to model interactions between pedestrians and vehicles, but is also relevant in sports. In the context of football, predicting the future trajectories of the players and ball can be used to control a pan-tilt-zoom (PTZ) camera, allowing for automatic video recording of games. Recently, transformer architectures have gained popularity due to their ability to effectively capture both social and temporal relationships. Previous works based on transformers typically encode past trajectories to predict one or multiple future modes, but usually without quantifying the likelihood for each mode. In this work we propose statistical MART (sMART)
which builds on a previous graph based transformer model (MART) by (Lee et al. 2024), extending it to produce probabilities for each future mode. This multimodal output of the model
is used to estimate a distribution, weighted by the probabilities, for each player and ball. The
model is trained and evaluated on football tracking data, extracted from the 2023 − 2024 seasons of Allsvenskan by Signality AB. Performance is measured with common distance based metrics such as average and final displacement error (ADE/FDE), as well as probability based metrics, intended to measure the predicted probability in a region close to the ground truth. Experiments comparing sMART to a naive MLP network and a velocity baseline show that sMART outperforms both these, for predicting the future 4 seconds of trajectories. Specifically, in the probability metric we see an improvement of 24% for the players, and 11% for the ball, compared to the velocity baseline, and approximately twice the probability compared to the MLP. (Less)
Please use this url to cite or link to this publication:
author
Björk, Tobias LU and Salzer, Marcus LU
supervisor
organization
course
FMAM05 20251
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Multimodal trajectory prediction, Graph transformer, Football
publication/series
Master’s Theses in Mathematical Sciences
report number
LUTFMA-3577-2025
ISSN
1404-6342
other publication id
2025:E26
language
English
id
9193466
date added to LUP
2025-09-15 11:08:44
date last changed
2025-09-15 11:08:53
@misc{9193466,
  abstract     = {{Multimodal trajectory prediction is a task commonly found in fields like autonomous driving
in order to model interactions between pedestrians and vehicles, but is also relevant in sports. In the context of football, predicting the future trajectories of the players and ball can be used to control a pan-tilt-zoom (PTZ) camera, allowing for automatic video recording of games. Recently, transformer architectures have gained popularity due to their ability to effectively capture both social and temporal relationships. Previous works based on transformers typically encode past trajectories to predict one or multiple future modes, but usually without quantifying the likelihood for each mode. In this work we propose statistical MART (sMART)
which builds on a previous graph based transformer model (MART) by (Lee et al. 2024), extending it to produce probabilities for each future mode. This multimodal output of the model
is used to estimate a distribution, weighted by the probabilities, for each player and ball. The
model is trained and evaluated on football tracking data, extracted from the 2023 − 2024 seasons of Allsvenskan by Signality AB. Performance is measured with common distance based metrics such as average and final displacement error (ADE/FDE), as well as probability based metrics, intended to measure the predicted probability in a region close to the ground truth. Experiments comparing sMART to a naive MLP network and a velocity baseline show that sMART outperforms both these, for predicting the future 4 seconds of trajectories. Specifically, in the probability metric we see an improvement of 24% for the players, and 11% for the ball, compared to the velocity baseline, and approximately twice the probability compared to the MLP.}},
  author       = {{Björk, Tobias and Salzer, Marcus}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{Prediction of football game states using transformers}},
  year         = {{2025}},
}