In summary, Player Efficiency Rating (PER) is a complex statistic used to evaluate a basketball player's overall performance. It incorporates various statistical categories such as rebounds, assists, steals, blocks, points, and turnovers, adjusted for positional differences, usage rate, defense, and age. The formula involves weighting these components based on playing time and team total minutes to produce a comprehensive assessment of a player's contribution to their team's success.
Calculating Player Efficiency Rating (PER) in Basketball
Player Efficiency Rating (PER) is a statistic used to measure a player's performance in basketball. It was developed by ESPN analyst John Hollinger and is designed to provide a comprehensive assessment of a player's overall contribution to their team's success. The formula for calculating PER is quite complex, involving several different statistical categories and weighting factors.
Formula
The basic formula for PER is as follows:
\[ \text{PER} = \left( \frac{\text{Offensive Rebounds} + \text{Defensive Rebounds} + \text{Assists} + \text{Steals} + \text{Blocked Shots} + \text{Points}}{\text{Player's Turnovers}} \right) \times \left( \frac{\text{Player's Minutes Played}}{\text{Team's Total Minutes}} \right) \]
Components
1. Offensive Rebounds: The number of times the player recovers the ball after a missed shot on their own team's possession.
2. Defensive Rebounds: The number of times the player recovers the ball after an opponent misses a shot.
3. Assists: The number of times the player assists in a basket scored by a teammate.
4. Steals: The number of times the player takes the ball from an opponent without committing a foul.
5. Blocked Shots: The number of times the player blocks an opponent's shot attempt.
6. Points: The total number of points scored by the player.
7. Player's Turnovers: The number of times the player loses possession of the ball due to a mistake or violation.
8. Player's Minutes Played: The total amount of time the player spends on the court during games.
9. Team's Total Minutes: The sum of all minutes played by all players on the team during games.
Adjustments
To account for positional differences and other factors that might affect a player's statistics, various adjustments are made to the raw PER value. These adjustments include:
- Position Multiplier: Different positions have different expected statistical outputs, so a multiplier is applied based on the player's primary position.
- Usage Rate Adjustment: This adjusts for how much a player contributes relative to their playing time, considering factors like field goal percentage and free throw rate.
- Defensive Adjustment: This accounts for a player's defensive contributions beyond traditional box score statistics, such as steals and blocks.
- Age Adjustment: As players age, their performance tends to decline, so an age factor is included to account for this trend.
Final Steps
After applying all necessary adjustments, the final PER value is calculated by combining these adjusted components according to the original formula structure outlined above. The resulting PER provides a single metric that attempts to encapsulate a player's overall impact on the game across multiple statistical dimensions.