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In the sports of soccer, hockey and basketball the most commonly usedstatistics for player performance assessment are divided into two categories:offensive statistics and defensive statistics. However, qualitative assessmentsof playmaking (for example making "smart" passes) are difficult to quantify. Itwould be advantageous to have available a single statistic that can emphasizethe flow of a game, rewarding those players who initiate and contribute tosuccessful plays more. In this paper we will examine a model based on Google'sPageRank. Other papers have explored ranking teams, coaches, and captains buthere we construct ratings and rankings for individual members on both teamsthat emphasizes initiating and partaking in successful plays and forcingdefensive turnovers. For a soccer/hockey/basketball game, our model assigns anode for each of the n players who play in the game and a "goal node". Arcsbetween player nodes indicate sport-specific situations (including passes,turnovers, scoring, fouls, out-of-bounds, play-stoppages, turnovers, missedshots, defensive plays etc.), tailored for each sport. As well, some additionalarcs are added in to ensure that the associated matrix is primitive and hencethere is a unique PageRank vector. The PageRank vector of the associated matrixis used to rank the players of the game. To illustrate the model, data wastaken from nine NBA games played between 2014-2016. Many of the top-rankedplayers (in the model) in a given game had some of the most impressivetraditional stat-lines. However, from the model there were surprises where someplayers who had impressive stat-lines had lower ranks, and others who had lessimpressive stat-lines had higher ranks. Overall, the model's ranking andratings reflect more the flow of the game compared to traditional sportsstatistics.

A PageRank Model for Player Performance Assessment in Basketball, Soccer and Hockey