# A Strategic Framework for Optimal Decisions in Football 1-vs-1 Shot-Taking Situations: An Integrated Approach of Machine Learning, Theory-Based Modeling, and Game Theory

arXiv: https://arxiv.org/abs/2307.14732 · HTML: https://mlsanity.com/paper/2307.14732/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 27 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Google Research Football: A Novel Reinforcement Learning Environment](https://mlsanity.com/paper/1907.11180/) (2019)
- [Learning Agile Soccer Skills for a Bipedal Robot with Deep Reinforcement Learning](https://mlsanity.com/paper/2304.13653/) (2023)
- [Actions Speak Louder Than Goals: Valuing Player Actions in Soccer](https://mlsanity.com/paper/1802.07127/) (2018)
- [From Motor Control to Team Play in Simulated Humanoid Football](https://mlsanity.com/paper/2105.12196/) (2021)
- [Emergent Coordination Through Competition](https://mlsanity.com/paper/1902.07151/) (2019)
- [Game Plan: What AI can do for Football, and What Football can do for AI](https://mlsanity.com/paper/2011.09192/) (2020)
- [Deep Reinforcement Learning in Ice Hockey for Context-Aware Player Evaluation](https://mlsanity.com/paper/1805.11088/) (2018)
- [Evaluation of creating scoring opportunities for teammates in soccer via trajectory prediction](https://mlsanity.com/paper/2206.01899/) (2022)
- [Evaluation of soccer team defense based on prediction models of ball recovery and being attacked: A pilot study](https://mlsanity.com/paper/2103.09627/) (2021)
- [Transformer-Based Neural Marked Spatio Temporal Point Process Model for Football Match Events Analysis](https://mlsanity.com/paper/2302.09276/) (2023)
- [Adaptive action supervision in reinforcement learning from real-world multi-agent demonstrations](https://mlsanity.com/paper/2305.13030/) (2023)
- [Location analysis of players in UEFA EURO 2020 and 2022 using generalized valuation of defense by estimating probabilities](https://mlsanity.com/paper/2212.00021/) (2022)
- [How does AI play football? An analysis of RL and real-world football strategies](https://mlsanity.com/paper/2111.12340/) (2021)

## Built on by (most cited first, 7 of 7)

- [AutoSoccerPose: Automated 3D posture Analysis of Soccer Shot Movements](https://mlsanity.com/paper/2405.12070/) (2024)
- [Mathematical models for off-ball scoring prediction in basketball](https://mlsanity.com/paper/2406.08749/) (2024)
- [TrackID3x3: A Dataset and Algorithm for Multi-Player Tracking with Identification and Pose Estimation in 3x3 Basketball Full-court Videos](https://mlsanity.com/paper/2503.18282/) (2025)
- [Evaluating Soccer Match Prediction Models: A Deep Learning Approach and Feature Optimization for Gradient-Boosted Trees](https://mlsanity.com/paper/2309.14807/) (2023)
- [Space evaluation at the starting point of soccer transitions](https://mlsanity.com/paper/2505.14711/) (2025)
- [Evaluating Movement Initiation Timing in Ultimate Frisbee via Temporal Counterfactuals](https://mlsanity.com/paper/2508.17611/) (2025)
- [Right Move, Right Time: Multi-Sport Space Evaluation Platform for Ultimate Frisbee, Basketball, and Soccer](https://mlsanity.com/paper/2603.06585/) (2026)

## Abstract (arXiv)

Complex interactions between two opposing agents frequently occur in domains of machine learning, game theory, and other application domains. Quantitatively analyzing the strategies involved can provide an objective basis for decision-making. One such critical scenario is shot-taking in football, where decisions, such as whether the attacker should shoot or pass the ball and whether the defender should attempt to block the shot, play a crucial role in the outcome of the game. However, there are currently no effective data-driven and/or theory-based approaches to analyzing such situations. To address this issue, we proposed a novel framework to analyze such scenarios based on game theory, where we estimate the expected payoff with machine learning (ML) models, and additional features for ML models were extracted with a theory-based shot block model. Conventionally, successes or failures (1 or 0) are used as payoffs, while a success shot (goal) is extremely rare in football. Therefore, we proposed the Expected Probability of Shot On Target (xSOT) metric to evaluate players' actions even if the shot results in no goal; this allows for effective differentiation and comparison between different shots and even enables counterfactual shot situation analysis. In our experiments, we have validated the framework by comparing it with baseline and ablated models. Furthermore, we have observed a high correlation between the xSOT and existing metrics. This alignment of information suggests that xSOT provides valuable insights. Lastly, as an illustration, we studied optimal strategies in the World Cup 2022 and analyzed a shot situation in EURO 2020.