[Paper Review] A PageRank Model for Player Performance Assessment in Basketball, Soccer and Hockey

Shael Brown|arXiv (Cornell University)|Mar 31, 2017

Sports Analytics and Performance4 citations

TL;DR

This paper proposes a PageRank-based model to rank individual players in basketball, soccer, and hockey by emphasizing playmaking and team flow, rather than just traditional offensive stats. By modeling player passes and game events as a directed graph with a goal node and using a modified PageRank algorithm, the model produces a single performance metric (IPM) that rewards players who initiate and sustain successful plays, with empirical results showing strong alignment with elite performers and meaningful deviations for players with high scoring but low playmaking impact.

ABSTRACT

In the sports of soccer, hockey and basketball the most commonly used statistics for player performance assessment are divided into two categories: offensive statistics and defensive statistics. However, qualitative assessments of playmaking (for example making "smart" passes) are difficult to quantify. It would be advantageous to have available a single statistic that can emphasize the flow of a game, rewarding those players who initiate and contribute to successful plays more. In this paper we will examine a model based on Google's PageRank. Other papers have explored ranking teams, coaches, and captains but here we construct ratings and rankings for individual members on both teams that emphasizes initiating and partaking in successful plays and forcing defensive turnovers. For a soccer/hockey/basketball game, our model assigns a node for each of the n players who play in the game and a "goal node". Arcs between player nodes indicate sport-specific situations (including passes, turnovers, scoring, fouls, out-of-bounds, play-stoppages, turnovers, missed shots, defensive plays etc.), tailored for each sport. As well, some additional arcs are added in to ensure that the associated matrix is primitive and hence there is a unique PageRank vector. The PageRank vector of the associated matrix is used to rank the players of the game. To illustrate the model, data was taken from nine NBA games played between 2014-2016. Many of the top-ranked players (in the model) in a given game had some of the most impressive traditional stat-lines. However, from the model there were surprises where some players who had impressive stat-lines had lower ranks, and others who had less impressive stat-lines had higher ranks. Overall, the model's ranking and ratings reflect more the flow of the game compared to traditional sports statistics.

Motivation & Objective

• To develop a unified, flow-based performance metric that captures both offensive and defensive contributions in team sports like basketball, soccer, and hockey.
• To address the limitation of traditional statistics, which separate offensive and defensive metrics and fail to quantify intangible playmaking ability.
• To create a model that enables direct comparison of individual players across different teams and games using a single, consistent ranking system.
• To emphasize players who initiate and sustain successful plays, rewarding strategic passing and team involvement over isolated scoring.
• To validate the model using real NBA game data and demonstrate its ability to identify high-impact players overlooked by conventional statistics.

Proposed method

• Construct a directed graph where each player and a goal node are represented as nodes, with arcs indicating reverse-pass sequences (i.e., from receiver to passer) to emphasize play initiation.
• Model game events—such as fouls, turnovers, missed shots, and defensive plays—as transitions between nodes, with sport-specific rules applied to each sport.
• Introduce auxiliary arcs to ensure the transition matrix is primitive, guaranteeing a unique, stable PageRank vector.
• Compute the PageRank vector of the transition matrix to generate a unique, normalized rating (IPM) for each player, reflecting their influence in the game flow.
• Use the resulting IPM scores to rank players across games and compare performance across teams and positions.
• Calibrate the model using nine NBA games (2014–2016), with data on passes, scoring, assists, rebounds, and steals, to validate the metric’s sensitivity to playmaking.

Experimental results

Research questions

• RQ1 Can a PageRank-based model effectively quantify a player’s contribution to team success by emphasizing playmaking and ball progression?
• RQ2 How does the model’s ranking compare to traditional player statistics, particularly for players with high scoring but low assist or defensive involvement?
• RQ3 To what extent does the model identify high-impact players who are overlooked by conventional metrics?
• RQ4 Does the model produce consistent and meaningful rankings across different games and teams in basketball, soccer, and hockey?
• RQ5 Can the model serve as a complementary statistic for scouts, coaches, and analysts to evaluate player performance beyond standard box score stats?

Key findings

• In nine NBA games, 7 of the 9 games had a point guard ranked highest in IPM, and forwards were in the top five in all nine games, indicating the model captures role-based influence.
• The winning team had a higher average IPM than the losing team in six of nine games, and the winning team’s starters had higher average IPMs in eight of nine games, showing alignment with team success.
• Among players with at least 15 points and an IPM below 50, 89% had fewer than 10 combined assists, rebounds, and steals—indicating scoring alone is not rewarded highly by the model.
• Of the 30 players with at least 5 assists, 28 (93%) had an IPM of at least 50, demonstrating the model’s strong preference for playmakers over scorers.
• 40% of the top 10 IPM players per game had a combined stat-line (points, assists, rebounds, steals) of 20 or less, showing the model identifies high-impact players with 'average' traditional stats.
• Players like Klay Thompson (41 points, IPM 50.27) and Jimmy Butler (23 points, IPM ~23) had strong scoring but low IPMs, while players like John Wall and Ronnie Price had high IPMs despite modest stat lines, confirming the model’s sensitivity to playmaking.