# Monte Carlo Pass Search: Using Trajectory Generation for 3D Counterfactual Pass Evaluation in Football

arXiv: https://arxiv.org/abs/2606.11120 · HTML: https://mlsanity.com/paper/2606.11120/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for autonomous driving, one of 11 directions in World models.
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

- World models / [World models for autonomous driving](https://mlsanity.com/wm/world-models-for-autonomous-driving/)

## Builds on (most cited first, 17 of 17)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting](https://mlsanity.com/paper/2301.00493/) (2023)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Actions Speak Louder Than Goals: Valuing Player Actions in Soccer](https://mlsanity.com/paper/1802.07127/) (2018)
- [Learning Visual Predictive Models of Physics for Playing Billiards](https://mlsanity.com/paper/1511.07404/) (2015)
- [TacticAI: an AI assistant for football tactics](https://mlsanity.com/paper/2310.10553/) (2023)
- [A framework for the fine-grained evaluation of the instantaneous expected value of soccer possessions](https://mlsanity.com/paper/2011.09426/) (2020)
- [Evaluation of creating scoring opportunities for teammates in soccer via trajectory prediction](https://mlsanity.com/paper/2206.01899/) (2022)
- [Sports-Traj: A Unified Trajectory Generation Model for Multi-Agent Movement in Sports](https://mlsanity.com/paper/2405.17680/) (2024)
- [TranSPORTmer: A Holistic Approach to Trajectory Understanding in Multi-Agent Sports](https://mlsanity.com/paper/2410.17785/) (2024)
- [Adaptive action supervision in reinforcement learning from real-world multi-agent demonstrations](https://mlsanity.com/paper/2305.13030/) (2023)
- [Time-series Imputation of Temporally-occluded Multiagent Trajectories](https://mlsanity.com/paper/2106.04219/) (2021)
- [Using Physics Simulations to Find Targeting Strategies in Competitive Bowling](https://mlsanity.com/paper/2210.06753/) (2022)

## Abstract (arXiv)

We recast pass evaluation in football (soccer) as a Monte Carlo Tree Search (MCTS)-like evaluation problem whose components mostly exist in the literature under different names: a value model (possession value), a world model (multi-agent trajectories with ball interactions), and a policy over counterfactual actions (sampling pass variants with noise). Building on the first public high-fidelity tracking dataset with 3D ball trajectories from the Bundesliga, we introduce Monte Carlo Pass Search (MCPS), which infers kick parameters for each observed pass, samples execution variants and option variants, rolls each candidate forward with a ball-conditioned world model until the next ball interaction, and scores outcomes with a learned value model to obtain a distribution over gained value. This distribution enables distribution-aware attribution with two complementary execution-surplus scores used for analysis and ranking: mean-based and percentile-based scores. To make the world model sample-efficient under limited public data, we adapt a discrete-token, autoregressive trajectory generator from autonomous driving (SMART) and show it yields strong best-of-20 forecasting accuracy compared to baselines, while supporting fully hypothetical rollouts for downstream evaluation. We have released model checkpoints and code.