Welcome to Improved Player Efficiency Rating!
What is PER?
Player Efficiency Rating (PER) is a widely used metric in basketball analytics for assessing a player’s overall performance. The rating was popularized by John Hollinger who, in the early 2000s, provided a single numerical value that summarized a player’s statistical contributions. A higher PER rating generally indicates that a player is more efficient while a lower PER suggests a less productive player.
For example, Joel Embiid, the MVP during the 2022-2023 season, had the second-highest PER in the league of 31.4 (on a scale from 0-35) while Keon Ellis, the player with the mean PER rating, had a PER rating of 14.0 (on a scale from 0-35).
Coaches, technical staff, and analysts use PER to evaluate a player’s contributions to a team which they can use to strategize team formations and make critical decisions.
Metrics Involved With The PER Formula
• PER: Player Efficiency Rating
• MP: Minutes played by the player
• 3P: Total number of three-point field goals made
• AST: Total number of assists
• FG: Total number of field goals made
• FT: Total number of free throws made
• ORB: Total number of offensive rebounds • DRB: Total number of defensive rebounds
• STL: Total number of steals
• BLK: Total number of blocks
• PF: Total number of personal fouls
• FGA: Total number of field goals attempted
• The factor of 2 3 is a constant
• Team AST: Team’s total assists
• Team FG: Team’s total field goals made
Original PER Formula
uPER = (1 / MP) * [ 3P + (2/3) * AST + (2 – factor * (team_AST / team_FG)) * FG + (FT *0.5 * (1 + (1 – (team_AST / team_FG)) + (2/3) * (team_AST / team_FG))) – VOP * TOV – VOP * DRB% * (FGA – FG) – VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA – FT) + VOP * (1 – DRB%) * (TRB – ORB) + VOP * DRB% * ORB + VOP * STL + VOP * DRB% * BLK – PF * ((lg_FT / lg_PF) – 0.44 * (lg_FTA / lg_PF) * VOP) ]
Constants
• factor = (2 / 3) – (0.5 * (lg_AST / lg_FG)) / (2 * (lg_FG / lg_FT))
• VOP = league_PTS / (league_FGA – league_ORB + league_TOV + 0.44 * league_FTA)
• DRB% = (league_TRB – league_ORB) / league_TRB
Highest-Rated Players in the 2022-2023 NBA Season according to PER (Player Efficiency Rating)
How To Improve PER
Although traditional PER metrics have been great at assessing offensive performance through statistics such as points per game (ppg) and assists per game (apg), they overlook critical defensive contributions that can significantly impact a player’s value to a team. That’s why I have used 3 machine learning models (Lasso Regression, Neural Network, and Random Forest Regression) to implement and increase the weightage of advanced defensive metrics in the PER formula.
Improved PER Formula Results
Random Forest Regression
The Random Forest Regressor model exhibited promise in predicting Player Efficiency Rating (PER) for NBA players. Its performance, as evaluated by the Mean Squared Error (which indicates the accuracy of its predictions) and histogram analysis, indicated that the model captures the essence of player efficiency. The Random Forest Regressor demonstrated robustness in predicting PER values, effectively capturing variations and trends within the dataset.
• Robust Predictions: Throughout the entire 70-100 PER range, the model was able to correctly predict the actual PER values based on many variables such as different weights of statistics, new statistics altogether, and many more. While the Random Forest model exhibited strong predictive capabilities, it’s important to identify areas with discrepancies between actual and predicted values.
• Identifying Discrepancies: Throughout the 15-70 PER range, the model often overshot the actual PER values. This can be due to a number of factors such as 3-point shooting inconsistency, fouls, and free throws.
Neural Network
To assess the model’s predictive performance, the top 30 players were ranked based on their predicted PER values. These players, with the highest predicted PER scores, are expected to have a significant impact on the game. This ranking provides valuable insights for teams and analysts, aiding in player assessments and strategic decisions. The model outputted various high-ranking defensive players in the top 30 players. Some of these players included Draymond Green, Rudy Gobert, and Karl Anthony Towns. They were given similar PER ratings to players at the guard spots that many fans, analysts, and coaches argued they should be similar in skill to. There was the opposite, however, where players who shot high-volume three-pointers such as Trae Young (that were ranked ”higher than they should have” on the normal PER metric), were now falling towards the 30-40 scaled PER ranges.
Lasso Regression
The observation of a bell-shaped curve in the histogram of scaled predicted PER values underscores the potential of the Lasso Regression Model as a tool for enhancing the accuracy of player efficiency prediction in basketball analytics. This distribution pattern indicates that the model’s predictions align with the inherent characteristics of player performance in the dataset. Further validation and analysis are required to ascertain the model’s predictive accuracy comprehensively, but this initial observation is promising for the advancement of PER metrics in basketball analytics.
Old vs. New PER Formulas When Ranking The Top 10 PER Performers from the 2022-2023 NBA Season
As per the strengths of the new PER formula, the defensive-oriented players including Kristaps Porzingis, Domantas Sabonis, and Giannis Antetokounmpo were ranked higher than guards known for scoring the ball such as Damian Lillard, Jayson Tatum, and Shai Gilgeous-Alexander. Since the top 3 PER performers are all either Power Forwards (PF), or Centers (C), they are all defensively-oriented and therefore boosted even further by the new formula.