Calculate Player Efficiency Rating (PER)
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Introduction
Understanding how to calculate Player Efficiency Rating (PER) is crucial for basketball enthusiasts and analysts. PER is a statistic that summarizes a player's accomplishments and efficiency on the court in a single number. This calculation takes into account various aspects of gameplay including points, rebounds, assists, turnovers, and other metrics.
The complexity of calculating PER makes it important to have a reliable tool that simplifies the process. In the upcoming sections, we’ll explore how Sourcetable lets you calculate not only PER but also other complex statistics using its AI-powered spreadsheet assistant. For those interested in leveraging this innovative technology, visit app.sourcetable.com/signup.
How is PER Calculated in Basketball?
Understanding PER Formula Components
PER (Player Efficiency Rating) sums a player’s positive accomplishments and subtracts the negatives, factoring in the weighted importance of each stat. The formula considers both individual accomplishments and team dynamics.
Key Stats and Weights
Calculation of PER involves 12 different statistics, each weighted differently to emphasize their importance in a game. These statistics include positive actions like field goals, three-pointers, and steals, while negatives such as turnovers and fouls are subtracted.
The Formula Explained
The formula for PER is 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)]. This formula calculates a per-minute rating of a player's performance, adjusting for team play dynamics and individual performance.
Adjustments for Historical Data
For seasons prior to 1979-80, adjustments are made to the formula by setting three-point field goals, turnovers, blocked shots, and steals to zero due to the lack of comprehensive data.
Calculating Percentages
To convert the raw uPER into a more traditional percentage, multiply the result by 100. This conversion allows easier comparison between players and across different time periods.
Tools and Innovations
John Hollinger developed the original PER calculation. Adjusted PER (APER), an evolution of PER, accounts for more nuanced details like charges taken and differentiations between assisted and unassisted field goals.
How is PER Calculated in Basketball?
The Player Efficiency Rating (PER) is a comprehensive metric devised by John Hollinger to evaluate a basketball player's overall on-court impact per minute. Understanding PER calculation involves breaking down several key stats and applying a formula designed to capture a player's positive and negative contributions during a game.
Understanding Unadjusted PER (uPER)
Calculation of uPER starts with aggregating a player's statistical achievements and setbacks. The formula for uPER integrates points from three-point field goals, assists, and total field goals, among other statistics. It's essential to subtract elements like turnovers and fouls. The mathematical representation is given by 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)].
Adjusting PER for Pace
After calculating uPER, it's adjusted based on the game's pace to derive adjusted PER (aPER). The formula for aPER is: aPER = (pace adjustment) * uPER.
Standardizing PER
The last step involves normalizing aPER to the league average, to make it comparable across different seasons and eras. This normalization is achieved with the formula: PER = aPER * (15 / lg_aPER), where lg_aPER is the league average adjusted PER.
This method ensures that the PER values reflect efficiency relative to the league standard, making it a valuable tool for comparing players objectively.
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How to Calculate PER
Example 1: Basic PER Calculation
To calculate PER, start with gathering the necessary stats: points, assists, rebounds, steals. For a basic example, if a player scores 20 points, delivers 5 assists, grabs 8 rebounds, and makes 2 steals in a game, the formula would be PER = (Points + Rebounds + Assists + Steals) / Games Played. Assuming these stats are from one game, the PER would be PER = (20 + 8 + 5 + 2) / 1 = 35.
Example 2: Multi-Game Average
For multiple games, calculate the total of each stat over all games, then divide by the number of games. Suppose over 5 games, a player totals 100 points, 40 rebounds, 25 assists, and 10 steals. Using the formula PER = (Total Points + Total Rebounds + Total Assists + Total Steals) / Total Games, the calculation is PER = (100 + 40 + 25 + 10) / 5 = 35.
Example 3: Adjusting for Minutes Played
Adjusting PER for different playing times involves adding a minute's metrics. If the player plays 30 minutes in one game and records 20 points, 8 rebounds, 5 assists, and 2 steals, the PER formula would adjust as PER = (Points + Rebounds + Assists + Steals) / (Minutes Played / 48). The calculated PER is PER = (20 + 8 + 5 + 2) / (30 / 48) ≈ 55.2.
Example 4: Seasonal PER
Calculating the PER over a season requires accumulating all game statistics. For instance, over a 82-game season with a player accumulating 1600 points, 650 rebounds, 300 assists, and 150 steals, the PER would be calculated as PER = (1600 + 650 + 300 + 150) / 82 = 32.32
Example 5: Comparing Player Efficiency
To compare players using PER, calculate each player's PER and compare the results. For instance, Player A, with a PER of 30 from the above methods, might be more efficient than Player B with a PER of 25, suggesting Player A contributes more per game.
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How is PER Calculated with Sourcetable?
Understanding the calculation of complex metrics such as Player Efficiency Rating (PER) in sports analytics is made easy with Sourcetable. Simply input your data into the spreadsheet, and ask the AI to calculate PER. The AI assistant not only performs the calculation but also displays the results directly in the spreadsheet. Simultaneously, in the chat interface, it explains its methodology, ensuring you understand the PER formula and its application.
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Use Cases for PER Calculation in Basketball
Comparative Analysis Across Generations |
PER enables comparison of basketball players from different eras, accounting for changes in rules and statistics, aiding in debates like comparing Michael Jordan to LeBron James. |
Injury Impact Analysis |
By calculating a player's PER, analysts can quantify the impact of an injury on a team, making it a crucial metric for sports management and betting strategies. |
Player Contribution Measurement |
PER is instrumental in evaluating how much value a player adds or subtracts from a team during their playing time, making it key in player assessments and contract negotiations. |
Identifying Efficient Role Players |
PER helps in identifying role players who perform efficiently in their limited playing time, thus optimizing team dynamics and performance strategies. |
Team Pace Adjustments |
PER adjusts players’ statistics based on team pace, providing a more accurate performance measure that is comparable across different team styles and game speeds. |
Frequently Asked Questions
What is the basic formula for calculating PER?
The basic formula for calculating PER, or Player Efficiency Rating, is: 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)].
How is the adjusted PER calculated?
The adjusted PER (aPER) is calculated by multiplying the unadjusted PER (uPER) by a pace adjustment. The formula for the league adjusted PER (lg_aPER) further refines this by using the minutes played by each player as weights, and PER is then calculated by multiplying the adjusted PER (aPER) by the ratio of 15 over lg_aPER.
What player statistics are used in the PER calculation?
Player statistics used in the PER calculation include three-point field goals (3P), assists (AST), field goals (FG), free throws (FT), turnovers (TOV), offensive rebounds (ORB), defensive rebounds (DRB), total rebounds (TRB), steals (STL), and blocked shots (BLK).
What are some common mistakes to avoid when calculating PER?
Common mistakes in calculating PER include not properly dividing the entire side of the equation, errors in distribution particularly with the F.O.I.L. method, inaccurately handling negative numbers in calculations, and errors involving exponents such as multiplying an exponent by the base instead of raising the base to the power of the exponent.
What unclear terms are involved in the PER calculation formula?
In the PER calculation formula, some unclear terms include 'factor', 'VOP' (Value of Possession), and 'DRB%' (Defensive Rebound Percentage). These variables are crucial for accurately computing the PER but are not clearly defined in the standard listing of the formula.
Conclusion
Understanding how to calculate the PER (Price/Earnings Ratio) is crucial for investors analyzing stock value relative to its earnings. This metric, essential for sound financial analysis, can sometimes be complex to compute manually.
Simplify Calculations with Sourcetable
Sourcetable, an AI-powered spreadsheet, streamlines the calculation of financial ratios like PER. By facilitating complex computations and allowing users to experiment with AI-generated data, it makes financial analysis more accessible.
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