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Ultimate Guide to the Player Efficiency Rating - PER

What is it that makes an NBA player effective? Is it the number of points they score per game? Is it their shooting percentage? The short answer is: it's a combination of many factors. The Player Efficiency Rating is a metric that attempts to measure a player's effectiveness with a single number.

The Player Efficiency Rating (PER) is a statistical measure used in the NBA to measure the efficiency of a player by taking into consideration all statistics kept by the NBA, and weights the player's production by minutes played per game, and number of team possessions per game.

PER was originally developed by statistician John Hollinger. Hollinger is a writer for ESPN.com, and is also known for his book on NBA statistics, Pro Basketball Forecast.

How PER is Calculated

The goal of PER is to assign a single number to a player, which indicates their effectiveness on the court. This is done by examining all the official statistics kept by the NBA including both positive statistics, such as field goals made and assists, as well as negative statistics, such as turnovers.

Each statistic is assigned a value used to weight the contribution of that statistic to the PER formula. This is done because not all statistical categories are equally important. For example, field goals made are weighted more heavily than assists. Assists are important, but not as important as shots made, since they are the desired end result of any possession. Research has been done by Hollinger and other statisticians in an attempt to determine the exact relative importance (numerically) of each statistic.

The calculation goes further by using per-minute statistics, rather than raw totals or per-game numbers. Per-minute statistics are far more meaningful in representing a player's productivity than any of the aforementioned methods. For example, let's compare a player (A) who scores 14 points per game and plays 20 minutes per game, to a player (B) who scores 15 points per game and plays 35 minutes per game. Player B scores more per game than player A, but because he needs to play many more minutes than player A to accomplish this, player A is actually the more productive player in the time he's on the court.

Another element that increases the accuracy of PER is that all numbers are adjusted by the "pace" of each individual team. A team that plays at a much higher pace (shots per minute, for example) gives its players more of an opportunity to put up numbers, but that doesn't mean that player is better, or playing more effectively than those on slower-paced teams.

How to Interpret the PER

The way the PER formula is constructed, the PER of an average NBA player is always 15. The following is a breakdown of what various PER values indicate: 

  • All-time great season: 35+
  • Hands-down MVP: 30-35
  • Strong MVP candidate: 27.5-30
  • Long-shot MVP candidate: 25-27.5
  • Definite All-Star: 22.5-25
  • Borderline All-Star: 20-22.5
  • Second offensive option: 18-20
  • Third offensive option: 16.5-18
  • Slightly above-average player: 15-16.5
  • Rotation player: 13-15
  • Non-rotation player: 11-13
  • Fringe roster player: 9-11
  • Player who won't stick in the league: 5-9

The all-time leader in career NBA PER is Michael Jordan with 27.91 over his career. Other players in the all-time top ten include Shaquille O'Neal (26.43), David Robinson (26.18), Wilt Chamberlain (26.13) and Bob Pettit (25.37).

Benefits of the PER Statistic

PER is a huge step up from looking at standard boxscore statistics. It is much more detailed and accurate than anything one can do with raw statistical totals or per-game numbers.

Negatives of the PER Statistic

The one major weakness in the original PER concept is lack of consideration for defense. Yes, there are blocked shots and steals, but the formula doesn't account in any way for guys who play great individual or team defense. A solution to this was found by Roland Beech of 82games, who came up with a way to estimate a player's defensive prowess by looking at the PER of the players he defended during the season. This addition made PER an even more powerful analytical tool.

PER - Behind the Number

It is outside the scope of this article to go into great detail on the mathematical formula used to calculate PER, but for those wanting a look, here is the formula itself:

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)]

uPER is actually unadjusted PER. The adjusted PER value is calculated by adjusting the uPER for team pace. This is done by dividing the league average pace by a particular team's pace, then multiplying the result by our uPER value.

The final step involves using a multiplication factor on the adjusted PER value, so the league average PER is always 15, no matter what players, teams or seasons we are analyzing.

Review

The Holy Grail for sports statisticians is the discovery of a single metric that can tell us everything we want to know about the value of a particular player. Most statisticians believe there is no single metric such as this, but there are several one-number metrics that are useful and give us quite a bit of information about player performance and PER is among the best of those.