Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Understanding team collapse via probabilistic graphical models

Iasonas Nikolaou, Konstantinos Pelechrinis, Evimaria Terzi

TL;DR

This work introduces a probabilistic graphical model of team dynamics in which each player's hidden mental state at time t depends on their own past state and the observed performances of teammates at t-1. A team collapse occurs when a threshold fraction of players enter a low hidden state, and the model encodes diverse intra-team influence patterns through matrices $\mathcal{M}^{ij}$, $\mathcal{N}^i$, and the team-structure $\mathcal{R}$. Parameters are learned with an EM framework that leverages posterior sampling for the E-step and a round-robin convex optimization for the M-step, enabling effective learning despite non-convexity. Real-world NBA data from the 2021-22 season are used to infer team structures, reveal two dominant pattern types, and analyze game-level collapses, illustrating the model’s potential to inform roster decisions and resilience strategies. The work also provides synthetic demonstrations of how pillar-based and self-dependent configurations influence collapse probabilities and times, offering practical guidance for building more robust teams.

Abstract

In this work, we develop a graphical model to capture team dynamics. We analyze the model and show how to learn its parameters from data. Using our model we study the phenomenon of team collapse from a computational perspective. We use simulations and real-world experiments to find the main causes of team collapse. We also provide the principles of building resilient teams, i.e., teams that avoid collapsing. Finally, we use our model to analyze the structure of NBA teams and dive deeper into games of interest.

Understanding team collapse via probabilistic graphical models

TL;DR

This work introduces a probabilistic graphical model of team dynamics in which each player's hidden mental state at time t depends on their own past state and the observed performances of teammates at t-1. A team collapse occurs when a threshold fraction of players enter a low hidden state, and the model encodes diverse intra-team influence patterns through matrices , , and the team-structure . Parameters are learned with an EM framework that leverages posterior sampling for the E-step and a round-robin convex optimization for the M-step, enabling effective learning despite non-convexity. Real-world NBA data from the 2021-22 season are used to infer team structures, reveal two dominant pattern types, and analyze game-level collapses, illustrating the model’s potential to inform roster decisions and resilience strategies. The work also provides synthetic demonstrations of how pillar-based and self-dependent configurations influence collapse probabilities and times, offering practical guidance for building more robust teams.

Abstract

In this work, we develop a graphical model to capture team dynamics. We analyze the model and show how to learn its parameters from data. Using our model we study the phenomenon of team collapse from a computational perspective. We use simulations and real-world experiments to find the main causes of team collapse. We also provide the principles of building resilient teams, i.e., teams that avoid collapsing. Finally, we use our model to analyze the structure of NBA teams and dive deeper into games of interest.
Paper Structure (40 sections, 2 theorems, 41 equations, 17 figures)

This paper contains 40 sections, 2 theorems, 41 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Team and player performance ratings:
  3. Athlete's "choking"
  4. Computational work on interacting HMMs
  5. The model
  6. Notational conventions
  7. Model description
  8. Team collapse
  9. Exploring team profiles
  10. Team profiles
  11. Simulations
  12. Remarks on team profiles
  13. Learning the model
  14. Learning the parameters of the model
  15. E-step
  16. ...and 25 more sections

Key Result

Lemma 1

$\text{Pr}(\cdot \mid \mathbf{O}_{t-1}, H_{t-1}^i)$ induces a probability law.

Figures (17)

  • Figure 1: Graphical model representation of our model for $n=2$ entities and $T=3$ timesteps
  • Figure 2: Team collapse probability vs team profile
  • Figure 3: Negative Evidence Lower Bound (N-ELBO) vs iterations of EM; average and standard deviation over 10 random initializations.
  • Figure 4: Team structure ($\mathcal{R}$) for the Dallas Mavericks, Cleveland Cavaliers, Boston Celtics and Houston Rockets.
  • Figure 5: Team (hidden) state and points difference (PTS +/-) per 3 minute window for different games.
  • ...and 12 more figures

Theorems & Definitions (10)

  • Lemma 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 2
  • proof
  • proof