The Player efficiency rating (PER) is John Hollinger's all-in-one basketball rating, which attempts to boil 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. [1]

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, like runs batted in and wins, are not reliable indicators 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 are 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 (which was not tracked as an official stat till 1973)—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."

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.

Lastly, PER rewards inefficient shooting. To quote Dave Berri, the author of The Wages of Wins:

"Hollinger argues that each two point field goal made is worth about 1.65 points. A three point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points. Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA player does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots."

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
• Strong MVP Candidate: 27.5
• Weak MVP Candidate: 25.0
• 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
• The Next Stop: DLeague 5.0

Only 18 times has a player posted a season efficiency rating over 30.0. All of them are between 30.04 and 31.84. Michael Jordan and Lebron James lead with four 30+ seasons, with Shaquille O'Neal and Wilt Chamberlain having accomplished three each, and David Robinson, Dwyane Wade, Chris Paul, and Tracy McGrady having accomplished one each. The 2008-2009 season was unique in that it was the only season in which more than one player (LeBron James(31.76),Dwyane Wade(30.46), and Chris Paul(30.04)) posted efficiency ratings of over 30.0.

As of 19 August 2012 (Courtesy of Basketball-Reference.com)

Some of the players on this list played before the three point shot, blocks, and steals were stats tracked (Wilt Chamberlain, Bill Russell, etc.). Blocked shots and steals were first officially recorded in the NBA during the 1973-74 season. The three point shot entered the league in 1979-80 season.

Rank Player PER
1. Michael Jordan* 27.91
2. LeBron James^ 27.24
3. Shaquille O'Neal 26.43
4. David Robinson* 26.18
5. Wilt Chamberlain* 26.13
7. Chris Paul^ 25.44
8. Bob Pettit* 25.35
9. Tim Duncan^ 24.75
10. Charles Barkley* 24.63
11. Neil Johnston* 24.63
12. Kareem Abdul-Jabbar* 24.58
13. Magic Johnson* 24.11
14. Karl Malone* 23.90
15. Dirk Nowitzki^ 23.63
16. Hakeem Olajuwon* 23.59
17. Larry Bird* 23.50
18. Kobe Bryant^ 23.44
19. Kevin Garnett^ 23.32
20. Oscar Robertson* 23.17
21. Yao Ming 23.02
22. Jerry West* 22.90
23. Elgin Baylor* 22.70
24. Dwight Howard^ 22.49
25. Moses Malone* 22.31
26. Amar'e Stoudemire^ 22.24
28. Julius Erving* 21.97
29. Dolph Schayes* 21.92
30. Pau Gasol^ 21.92
31. John Stockton* 21.83
32. Manu Ginobili^ 21.77
33. George Gervin* 21.74
34. Bob Lanier* 21.69
35. Clyde Lovellette* 21.64
36. Dominique Wilkins* 21.65
38. Harry Gallatin* 21.43
39. Elton Brand^ 21.30
40. Alonzo Mourning 21.24
41. Clyde Drexler* 21.07
42. Patrick Ewing* 21.01
43. Dan Issel* 20.99
44. Chris Webber 20.94
45. Allen Iverson 20.92
46. Chris Bosh^ 20.85
47. John Drew 20.74
49. Kevin Johnson 20.70
50. Paul Pierce^ 20.65

* = Hall of Fame ^ = Active

Calculation

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

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

Where

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

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

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

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 PERs in his book, the Pro Basketball Forecast.