Player Efficiency Rating

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The Player Efficiency Rating is freelance 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.

1 Introduction
2 Guiding Prinicples of PER
- 2.1 Inspiration of PER
3 Problems With PER
- 3.1 Problems with PER Projections
4 Player Rankings
5 Career PER leaders
6 Calculation
7 Distribution
8 External links

[edit] Introduction

The rating is not intended to be the final word on how a player performs, but is designed to inform the debate. The idea is to come up with an objective measurement of how productively each player is actually playing. There are several factors that are not included in the ratings. The most notable is position defense - the part that does not involve blocked shots and steals. But factors like durability as well as less tangible ones (leadership, for example) are others that can not be rated numerically.

Nevertheless, it is a start, because it takes the statistics that are available and boils them down in a way that is 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), 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, you can compare subs with starters in frequent playing time debates. It is 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 arrives at the point values and adjustments in a fairly torturous way, which is one of the topics he relegates to his book.

[edit] Guiding Prinicples of PER

PER is commonly misconstrued as the ultimate ranking of a player -- however, this is not the purpose of PER. PER was created to give a snapshot view of how well a player contributes to his team. PER 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 - made shots, steals, assists, rebounds, blocked shots, free throws, missed shots, turnovers, and fouls in a systematic way that can objectively interpret player performance. However, Hollinger admits that there are some holes in the PER formula,

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.

PER cannot take into account such intangible elements as competitive drive, leadership, durability, conditioning, or hustle. It is a starting point for objective debate. In a world where sports news is dominated by high flying dunks and thunderous blocks, some stats can get lost in the mix. Hollinger is seeking for a way to clear away the media clutter:

What PER can do, however, is summarize a player's statistical accomplishments in a single number. That allows us to unify the disparate data on each player that we try to track in our heads (e.g., Danny Fortson: great rebounder, high-percentage shooter, turnover machine, fouls like crazy, etc.) so that we can move on to evaluating what might be missing from the stats.

PER is a great objective gauge as to how complete a player's game may be. Hollinger often uses PER to reflect and evaluate on a player's past and in season performances. In this way, PER can be used to debate playing time and starting roles. Hollinger also uses PER to make preseason projections. These projections are often a source of heated debate.

[edit] Inspiration of PER

The main inspiration for Hollinger in creating PER was the Sabermetric revolution which has transpired through the mid 90's. Thanks to the work of people like Bill James and Rob Neyer, professional analysts who tirelessly study the game, the common people don't blindly accept what they're told by coaches and announcers anymore. Many times in proffesional sports, the stats of old just don't tell the whole story of how well a player is actually performing. With the inception of the baseball sabermetric statistic system, people began to rethink what stats are really telling of a good player. In baseball it has reverberated to the point that it's actually changed how teams operate, from pitch counts to free agency to actual in game strategy. The idea of PER, as was the idea of sabermetrics, is to judge players objectively. Hollinger is trying to foster this kind of analytical transformation among the basketball community.

[edit] Problems With PER

There are some imperfections when judging players on the PER system. As previously stated the formula cannot quantify such intangible qualities as leadership, durability, etc. The projections also don't include defense beyond blocks, steals and fouls, partly because the league has opted to make this area a void in terms of stats. In this way, invaluable lock down defenders such as Bruce Bowen, guys who simply shut down their assigned man, holding them to little scoring, are not well reflected by PER. This is why PER and MVP balloting are not always directly on par. Someday PER may have a greater influence on MVP voting but as illustrated in the tables below, the MVP ballots and PER are somewhat in disagreeance. Some experts also argue that PER's negligence of player position defense also weakens the ranking. Their stance is that some positions dictate a higher level of fouls and turnovers and thus some players are at a distinct inherent disadvantage in the rankings.

[edit] 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 highschool have shown a lot of promise in their future years, many have floundered and never quite reached their full potential. This has unofficially become known as "The Darius Miles Effect". Darius Miles's falloff was so staggering and severe that it has proven to be enough of a millstone that the overall projection for players coming out of highschool foresees a decline in PER over the second and third years in the league. Even though the projection forsees a decline, most experts and Hollinger agree that promising young players like Dwight Howard, Josh Smith and Lebron James will most likely continue to excel. As the sample size for players of this characterization grows, the projections will become more and more accurate.

[edit] Player Rankings

PER ratings and PER projections can are useful for ranking players in the real world and also in fantasy sport. Here real world rankings and fantasy rankings can be compared to PER and PER projections. For the meantime PER is a slightly better projector of fantasy rankings as opposed to real world rankings like MVP balloting.

[edit] 2006 Rankings

**2006 Top 10 PER**
Player	PER
1. Dirk Nowitzki	28.20
2. LeBron James	28.17
3. Kobe Bryant	28.11
4. Dwyane Wade	27.68
5. Kevin Garnett	26.88
6. Elton Brand	26.88
7. Allen Iverson	26.02
8. Yao Ming	25.78
9. Shaquille O'Neal	24.47
10. Paul Pierce	23.71

**2006 MVP Voting**
Player	% of Votes
1. Steve Nash	48%
2. Kobe Bryant	17%
3. Lebron James	16%
4. Dirk Nowitzki	8%
5. Dwayne Wade	5%
6. Chauncey Billups	6%

**2006 Yahoo Fantasy Player Rankings**
Player
1. Shawn Marion
2. Kobe Bryant
3. Elton Brand
4. Lebron James
5. Kevin Garnett
6. Ray Allen
7. Dirk Nowitzki
8. Jason Kidd
9. Gilbert Arenas
10. Rasheed Wallace

[edit] 2007 Rankings

**2007 Top 10 Projected PER**
Player	PER
1. Lebron James	31.86
2. Kobe Bryant	27.00
3. Dirk Nowitzki	26.86
4. Amare Stoudamire	26.12
5. Dwyane Wade	25.91
6. Kevin Garnett	24.97
7. Chris Paul	24.96
8. Pau Gasol	23.95
9. Gilbert Arenas	23.78
10. Allen Iverson	23.31

**2007 Yahoo Projected Fantasy Player Rankings**
Player
1. Lebron James
2. Kevin Garnett
3. Shawn Marion
4. Kobe Bryant
5. Dwayne Wade
6. Dirk Nowitzki
7. Gilbert Arenas
8. Elton Brand
9. Chris Paul
10. Chris Bosh

[edit] 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
*On next plane to Yakima: 5.0

[edit] 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

[edit] 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.

[edit] Distribution

Hollinger distributes the final PER's 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.