# Leaving Goals on the Pitch: Evaluating Decision Making in Soccer

arXiv: https://arxiv.org/abs/2104.03252 · HTML: https://mlsanity.com/paper/2104.03252/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 7 Apr 2021.

## Builds on (most cited first, 3 of 3)

- [The Probabilistic Model Checker Storm](https://mlsanity.com/paper/2002.07080/) (2020)
- [Review of The Book of Why: The New Science of Cause and Effect](https://mlsanity.com/paper/2003.11635/) (2020)
- [The Advantage of Doubling: A Deep Reinforcement Learning Approach to Studying the Double Team in the NBA](https://mlsanity.com/paper/1803.02940/) (2018)

## Built on by (most cited first, 3 of 3)

- [Automatic event detection in football using tracking data](https://mlsanity.com/paper/2202.00804/) (2022)
- [OpenSTARLab: Open Approach for Spatio-Temporal Agent Data Analysis in Soccer](https://mlsanity.com/paper/2502.02785/) (2025)
- [TacEleven: generative tactic discovery for football open play](https://mlsanity.com/paper/2511.13326/) (2025)

## Abstract (arXiv)

Analysis of the popular expected goals (xG) metric in soccer has determined that a (slightly) smaller number of high-quality attempts will likely yield more goals than a slew of low-quality ones. This observation has driven a change in shooting behavior. Teams are passing up on shots from outside the penalty box, in the hopes of generating a better shot closer to goal later on. This paper evaluates whether this decrease in long-distance shots is warranted. Therefore, we propose a novel generic framework to reason about decision-making in soccer by combining techniques from machine learning and artificial intelligence (AI). First, we model how a team has behaved offensively over the course of two seasons by learning a Markov Decision Process (MDP) from event stream data. Second, we use reasoning techniques arising from the AI literature on verification to each team's MDP. This allows us to reason about the efficacy of certain potential decisions by posing counterfactual questions to the MDP. Our key conclusion is that teams would score more goals if they shot more often from outside the penalty box in a small number of team-specific locations. The proposed framework can easily be extended and applied to analyze other aspects of the game.