Bayesian Performance Rating (BPR) is a predictive statistical metric used in college basketball to quantify and predict the effectiveness of a team or player. Developed by statistician Evan Miyakawa, and showcased on his website (evanmiya.com), BPR utilizes advanced box-score metrics, play-by-play data, and historical information to assess both individual and team performance. The metric incorporates factors such as offense, defense, game pace, and opponent strength to evaluate a player's or team's performance on the court.

Overview

BPR is an adjusted plus-minus metric, which measures a player's or team's expected points per 100 possessions better than a Division I (D1) average player or team. The metric has separate ratings for offense and defense, with the combination of the two giving a player or team's overall BPR.

Offensive and Defensive Ratings

Each player receives an Offensive BPR and a Defensive BPR, which are combined to form their overall BPR. The average D1 player has both an Offensive and Defensive BPR of 0, with positive values indicating above-average performance in either offensive or defensive aspects of the game. Highly skilled players will typically have high positive ratings in both categories.

Use in Team and Player Analysis

BPR can be used to analyze both individual player performances and team strength. The metric accounts for contextual factors, such as the strength of teammates and opponents, in order to evaluate how an individual player's or team's performance impacts the game.

Types of BPR Analysis

BPR provides insights into various aspects of college basketball performance, including:

Team Ratings: Team ratings evaluate the strength of each team based on game results while accounting for factors such as game pace and opponent strength.^[1]
Player Ratings: Player ratings assess the value of each player to their team, both offensively and defensively. These ratings take into account the strength of other players on the floor during each possession.
Player Projections: BPR can also be used to predict a player's future performance based on their skill level in various statistical categories (e.g., three-point shooting, rebounding, steals). These projections adjust for contextual factors such as opponent strength, expected season-to-season improvement, and recent performance.^[2]
Lineup Metrics and Projections: BPR evaluates the effectiveness of different player combinations on the court, assessing two, three, four, and five-player lineups. The metric adjusts for the strength of opposing players faced by those specific lineups.^[3]
Transfer Portal Rankings: BPR ranks players in the NCAA Transfer Portal, offering insight into the relative value of players moving between programs.
Team Breakdowns: Detailed player and lineup metrics are available for each team, allowing for a deeper analysis of team performance.
Game Predictions: BPR is used to predict the outcomes of college basketball games and compare those predictions to Las Vegas betting lines.

Characteristics of BPR

Data Sources

BPR is built upon various forms of basketball data, including:

Box score data
Play-by-play data

The model is trained on data dating back to 2011, making it one of the most finely tuned player evaluation metrics in college basketball. This allows BPR to generate accurate player ratings even for those with limited game time in the current season.

Statistical Foundation

BPR uses Bayesian statistics, a probabilistic approach that updates predictions based on new evidence. The use of Bayesian statistics in the world of Sports analytics has seen an increase, driving other statistical sports measures such as ESPN’s Football Power Index.^[4]

Creating Player Ratings

BPR employs a multi-stage process to generate player ratings:

First Stage: Historical Stats: The first stage uses a player’s historical statistics and metrics from previous seasons, along with other predictive data such as recruiting rankings. This helps form an initial projection for the player's performance in the current season. Although historical stats are less influential as the season progresses, they are essential in evaluating players who have limited current-season data.
Second Stage: Individual Stats (Box BPR): The second stage estimates a player's impact based on their individual box score statistics, a value referred to as Box BPR. This provides an initial estimate of a player's statistical value on both offense and defense.
Third Stage: Play-by-Play Impact: The final stage examines every possession a player participated in, evaluating their impact on the game's outcome by adjusting for the strength of both their teammates and the opposing players. This stage refines the Box BPR by factoring in a player's actual on-court performance and situational context, which can sometimes significantly adjust the player's final BPR.

Features and Recognition

BPR has gained recognition in the basketball analytics community and has been featured in articles from The Athletic and The New York Times.

Articles Featuring BPR

BPR has gained recognition in the basketball analytics community and has been featured in prominent publications. Some of the articles that highlight the BPR metric include:

References

^ https://blog.evanmiya.com/p/introducing-relative-ratings-and
^ https://blog.evanmiya.com/p/new-tool-player-skill-projections
^ https://blog.evanmiya.com/p/lineup-data-just-got-a-whole-lot
^ Santos-Fernandez, Edgar; Mengersen, Kerrie L.; Wu, Paul (2019). "Bayesian Methods in Sport Statistics". Wiley StatsRef: Statistics Reference Online. pp. 1–8. doi:10.1002/9781118445112.stat08179. ISBN 978-1-118-44511-2.

[1] ttps://blog.evanmiya.com/p/introducing-relative-ratings-and

[2] ttps://blog.evanmiya.com/p/new-tool-player-skill-projections

[3] ttps://blog.evanmiya.com/p/lineup-data-just-got-a-whole-lot

[4] Santos-Fernandez, Edgar; Mengersen, Kerrie L.; Wu, Paul (2019). "Bayesian Methods in Sport Statistics". Wiley StatsRef: Statistics Reference Online. pp. 1–8. doi:10.1002/9781118445112.stat08179. ISBN 978-1-118-44511-2.

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