# Player Efficiency Rating

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Player Efficiency Rating

The Player Efficiency Rating is ESPN Insider writer John Hollinger's all-in-one basketball rating, which boils down all of a player's contributions into one number. Using a detailed formula, Hollinger developed a system that rates every player's statistical performance.

Introduction

PER strives to measure a player's per-minute performance, while adjusting for pace. A league-average PER is always 15.00, which permits comparisons of player performance across seasons.

PER takes into account positive accomplishments, such as field goals, free throws, 3-pointers, assists, rebounds, blocks and steals, and negative ones, such as missed shots, turnovers and personal fouls. The formula adds positive stats and subtracts negative ones through a statistical point value system. The rating for each player is then adjusted to a per-minute basis so that, for example, substitutes can be compared with starters in playing time debates. It is also adjusted for the team's pace. In the end, one number sums up the players' statistical accomplishments for that season.

PER's Relationship to Baseball "Sabermetrics"

Hollinger's work has benefitted from the observations of Sabermetric baseball analysts, such as Bill James. One of the primary observations is that traditional counting statistics in baseball [batting average, runs batted in, wins, earned run average] are not reliable indicator's of a player's value. For example, runs batted in is highly dependent upon opportunities created by a player's teammates. PER extends this critique of counting statistics to basketball, noting that a player's opportunities to accumulate statistics is dependent upon the number of minutes he plays as well as the pace of the game.

Problems With PER

PER largely measures offensive performance. Hollinger freely admits that two of the defensive statistics it incorporates -- blocks and steals -- can produce a distorted picture of a player's value and that PER is not a reliable measure of a player's defensive acumen. For example, Bruce Bowen, widely regarded as one of the best defenders in the NBA (at least through the 2006-07 season), has routinely posted single-digit PERs.

"Bear in mind that this rating is not the final, once-and-for-all answer for a player's accomplishments during the season. This is especially true for players such as Bruce Bowen and Trenton Hassell who are defensive specialists but don't get many blocks or steals."

Neither PER nor per-game statistics take into account such intangible elements as competitive drive, leadership, durability, conditioning, or hustle, largely because there is no real way to measure these things, which are often based on opinion and hearsay.

In addition, some have argued that PER gives undue weight to a player's contribution in limited minutes, or against a team's second unit, and it undervalues players who have enough diversity in their game to play starter's minutes.

Problems with PER Projections

The projections are built by looking at comparable players at the same age and how their stats changed in the following season. For players in most age brackets, this is extremely reliable, but there have been so few players to turn pro out of high school in the past two decades that there is a very small sample to work with. While some players who have come out of high school have shown a lot of promise in their future years, many have floundered and never quite reached their full potential.

Reference guide

Hollinger has set up PER so that the league average, every season, is 15.00, which produces sort of a handy reference guide:

*A Year For the Ages: 35.0
*Runaway MVP Candidate: 30.0 (Only the 12 greatest seasons ever from any player are above a 30. All of them are
*Strong MVP Candidate: 27.5 between 31.84 and 30.23. The seasons are from Wilt Chamberlain 3 times Michel Jordan *Weak MVP Candidate: 25.0 4 times David Robinson 1 time Shaquille O'Neal 3 times and Tracy McGrady? 1 time)
*Bona fide All-Star: 22.5
*Borderline All-Star: 20.0
*Solid 2nd option: 18.0
*3rd Banana: 16.5
*Pretty good player: 15.0
*In the rotation: 13.0
*Scrounging for minutes: 11.0
*Definitely renting: 9.0
*On next plane to Yakima: 5.0

Rank Player PER---------------------------------------1 Michael Jordan 27.912 Shaquille O'Neal* 27.633 David Robinson 26.184 Wilt Chamberlain 26.165 Bob Pettit 25.416 Tim Duncan* 25.177 Neil Johnston 24.788 Charles Barkley 24.639 Kareem Abdul-Jabbar 24.5810 LeBron James* 24.2411 Magic Johnson 24.1112 Karl Malone 23.8913 Tracy McGrady* 23.8814 Dirk Nowitzki* 23.8415 Kevin Garnett* 23.8416 Hakeem Olajuwon 23.5917 Julius Erving 23.5718 Larry Bird 23.5019 Kobe Bryant* 23.4920 Yao Ming* 23.2221 Oscar Robertson 23.2022 Jerry West 22.9223 Elton Brand* 22.7524 Elgin Baylor 22.7225 Dolph Schayes 22.02---------------------------------------
"* = still active"

Calculation

All calculations begin with what is called unadjusted PER (uPER). The formula is:

$uPER = frac\left\{1\right\}\left\{Min\right\} *left \left( 3P + \left[\left(2/3\right)*AST\right] + \left[\left(2 - factor*\left(tmAST/tmFG\right)\right)*FG\right] + \left[FT*0.5*\left(1 + \left(1 - \left(tmAST/tmFG\right)\right) + \left(2/3\right)*\left(tmAST/tmFG\right)\right)\right] - \left[VOP*TO\right] - \left[VOP*DRBP*\left(FGA - FG\right)\right] - \left[VOP*0.44*\left(0.44 + \left(0.56*DRBP\right)\right)*\left(FTA - FT\right)\right] + \left[VOP*\left(1 - DRBP\right)*\left(TRB - ORB\right)\right] + \left[VOP*DRBP*ORB\right] + \left[VOP*STL\right] + \left[VOP*DRBP*BLK\right] - \left[PF*\left(\left(lgFT/lgPF\right) - 0.44*\left(lgFTA/lgPF\right)*VOP\right)\right)\right] ight \right)$

Where
*$factor = \left(2/3\right) - \left[\left(0.5*\left(lgAST / lgFG\right)\right) / \left(2*\left(lgFG / lgFT\right)\right)\right]$,
*$VOP = \left[lgPTS / \left(lgFGA - lgORB + lgTO + 0.44*lgFTA\right)\right]$,
*$DRBP = \left[\left(lgTRB - lgORB\right) / lgTRB\right]$.

Once uPER is calculated, it must be adjusted for team pace and normalized to the league to become PER:

$PER = \left[uPER*\left(lgPace/tmPace\right)\right] * \left(15/lguPER\right)$

This final step takes away the advantage held by players whose teams play a fastbreak style (and therefore have more possessions and more opportunities to do things on offense), and then sets the league average to 15.00.

Also note that it is impossible to calculate PER (at least in the conventional manner described above) for NBA seasons prior to 1978, as the league did not keep track of turnovers before that year.

Distribution

Hollinger distributes the final PER's in his book, the "Pro Basketball Forecast".

* [http://www.alleyoop.com Alleyoop.com] , Hollinger's home site
* [http://sportsillustrated.cnn.com/writers/john_hollinger/archive/index.html Hollinger's articles at SI]
* [http://www.knickerblogger.net/stats/ KnickerBlogger.net]
* [http://insider.espn.go.com/nba/hollinger/statistics ESPN.com Insider (subscription service)]

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