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Probabilistic Analysis of Various Squash Shots and Skill Study of Different Levels of Squash Players and Teams

Prathamesh Anwekar, Kaushal Kirpekar, Mahesh B, Sainath Bitragunta

TL;DR

This work develops a compact probabilistic model for both two-player and two-team squash, paired with a Gaussian-based skill-comparison rule to quantify performance from point-scoring probabilities. It analyzes shot distributions across court regions using real-match data to contrast professional and intermediate players, and introduces a region-based shot-output framework. Key findings show professionals use a wider shot repertoire and backcourt play to maintain control, with 61% of points won as winners versus 46% for intermediates, and unforced errors at 21% versus 36%. The backhand drop emerges as a high-risk, high-reward shot central to professional success, providing actionable insights for coaching and sports analytics.

Abstract

We introduce a compact probabilistic model for two-player and two-team (four-player) squash matches, along with a practical skill-comparison rule derived from point-scoring probabilities. Using recorded shot types and court locations, we analyze how shot distributions differ between professional-level and intermediate-level players. Our analysis shows that professional players use a wider variety of shots and favor backcourt play to maintain control, while intermediate players concentrate more on mid-court shots, generate more errors, and exercise less positional control. These results quantify strategic differences in squash, offer a simple method to compare player and team skill, and provide actionable insights for sports analytics and coaching.

Probabilistic Analysis of Various Squash Shots and Skill Study of Different Levels of Squash Players and Teams

TL;DR

This work develops a compact probabilistic model for both two-player and two-team squash, paired with a Gaussian-based skill-comparison rule to quantify performance from point-scoring probabilities. It analyzes shot distributions across court regions using real-match data to contrast professional and intermediate players, and introduces a region-based shot-output framework. Key findings show professionals use a wider shot repertoire and backcourt play to maintain control, with 61% of points won as winners versus 46% for intermediates, and unforced errors at 21% versus 36%. The backhand drop emerges as a high-risk, high-reward shot central to professional success, providing actionable insights for coaching and sports analytics.

Abstract

We introduce a compact probabilistic model for two-player and two-team (four-player) squash matches, along with a practical skill-comparison rule derived from point-scoring probabilities. Using recorded shot types and court locations, we analyze how shot distributions differ between professional-level and intermediate-level players. Our analysis shows that professional players use a wider variety of shots and favor backcourt play to maintain control, while intermediate players concentrate more on mid-court shots, generate more errors, and exercise less positional control. These results quantify strategic differences in squash, offer a simple method to compare player and team skill, and provide actionable insights for sports analytics and coaching.

Paper Structure

This paper contains 20 sections, 10 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology.
  3. Scope and assumptions.
  4. Understanding the Court and Different Shots
  5. Court regions and dimensions
  6. Two-player game flow (summary)
  7. Shot taxonomy and outcome categories
  8. Squash shot event modeling and analysis
  9. Modeling and Skill Comparison of Two Teams
  10. Numerical evaluation and Performance plot
  11. Analysis of Shot Types: A Case Study
  12. Region-wise Shot Distribution (SD) for Professional Players
  13. Region-wise SD for Intermediate-Level Players
  14. Shot Outcome for Professional-Level Matches
  15. Shot Outcome for Intermediate-Level Matches
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Illustration of three popular racket sports and their main equipment. A squash racket and ball are shown on the left, a badminton racket and shuttlecock in the center, and a tennis racket and ball on the right. Court structure and rules differ significantly across these sports.
  • Figure 2: Court dimensions and region partitioning used in this study. SB: service box; R1--R4: court regions for shot-location analysis.
  • Figure 3: An illustration on comparison of tail probabilities in a Gaussian Q-function.
  • Figure 4: Points scoring probability as a function of $k$.
  • Figure 5: Output of the Java-based shot-analysis tool for a single professional match.
  • ...and 1 more figures