Player Efficiency Rating

The Player Efficiency Rating is 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

The rating is not intended to be the final word on how a player performs, but is designed to inform the debate. There are several factors that aren't included in the ratings. The most notable is position defense - the part that doesn't involve blocked shots and steals. But factors like durability as well as less tangible ones (leadership, for example) are others that can't be rated numerically.

Nevertheless, it's a start, because it takes the statistics that are available and boils them down in a way that's easy to understand. It interprets the things that we do know -- how many shots a player made, how many rebounds, etc. -- in a much more systematic way than any other player rating system to date.

The formula, which Hollinger calls the Player Efficiency Rating (PER), adds the good (made shots, steals, assists, rebounds, blocked shots, free throws), and subtracts the bad (missed shots, turnovers, fouls) by assigning a point value to each item (He arrives at the point values in a fairly torturous way, and that's one of the parts he saves for the book). The rating for each player is then adjusted to a per-minute basis (so that, for example, you can compare subs with starters in the frequent 'he should start ahead of so-and-so' debates), and also adjusted for the team's pace. In the end, one number sums up the players' accomplishments (the statistical ones, anyway) for that season. Hollinger has set it up so that the league average, every season, is 15.00, which produces sort of a handy reference guide:

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
*On next plane to Yakima: 5.0

Career PER leaders

As of the 2005–06 NBA season (Courtesy of Basketball-Reference.com)

Rank    Player                    PER
---------------------------------------
1	Michael Jordan            27.91
2	Shaquille O'Neal*         27.82
3	David Robinson            26.18
4	Wilt Chamberlain          26.16
5	Bob Pettit                25.41
6	Tim Duncan*               25.07
7	Neil Johnston             24.78
8	Charles Barkley           24.63
9	Kareem Abdul-Jabbar       24.58
10	Magic Johnson             24.11
11	Tracy McGrady*            23.96
12	Karl Malone               23.89
13	Kevin Garnett*            23.81
14	Hakeem Olajuwon           23.59
15	Julius Erving             23.58
16	Larry Bird                23.50
17	Dirk Nowitzki*            23.37
18	Oscar Robertson           23.20
19	Kobe Bryant*              23.17
20	Jerry West                22.92
---------------------------------------

* = still active

Calculation

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

uPER = (1/Min) * ( 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))] )

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 fast-break 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. Justin Kubatko of Basketball-Reference.com has made provisions to calculate PER for seasons in which this official data is not available, however, by adjusting thusly:

• Zero out three-point field goals, turnovers, blocked shots, and steals.
• Set the league value of possession (VOP) equal to 1.
• Set the defensive rebound percentage (DRBP) equal to 0.7.
• Set player offensive rebounds (ORB) equal to 0.3*TRB.

Pace Factor cannot be calculate for NBA seasons prior to 1974 as well. To overcome this, you must estimate the Pace Adjustment using Points Per Game:

estimated pace adjustment = 2*lgPPG / (tmPPG + oppPPG)

Distribution

Hollinger distributes the final PER's at his website, Alleyoop.com, and in his book, the Pro Basketball Forecast. However, for those needing an in-season PER fix, KnickerBlogger.net updates the PER, along with Hollinger's other special stats, daily during the season.

External links

• Alleyoop.com, Hollinger's home site
• An in-depth description of how to calculate PER
• Hollinger's articles at SI
• Basketball-Reference.com, Historical NBA statistical site (includes PER)