Player efficiency rating

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 accomplishments, such as field goals, free throws, 3-pointers, assists, rebounds, blocks and steals, and negative results, 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.

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 played 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 until 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 through the 2006–07 season, 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.

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.

PER has been said to reward 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.

Hollinger responded via a post on ESPN's TrueHoop blog:

Berri leads off with a huge misunderstanding of PER—that the credits and debits it gives for making and missing shots equate to a “break-even” shooting mark of 30.4% on 2-point shots. He made this assumption because he forgot that PER is calibrated against the rest of the league at the end of the formula.

Actually, if we took a player that was completely average in every other respect for the 2006–07 season—rebounds, free throws, assists, turnovers, etc.—and gave him a league-average rate of shots, and all of them were 2-pointers, and he shot 30.4%, he'd end up with a PER of 7.18. As long-time PER fans know, that would make him considerably worse than nearly every player in the league.

To end up with a league-average PER of 15.00, the actual break-even mark in this case is 48.5%, which is exactly what the league average is on 2-point shots this season.

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:[2]

All-time great season	35.0+
Runaway MVP candidate	30.0–35.0
Strong MVP candidate	27.5–30.0
Weak MVP candidate	25.0–27.5
Definite All-Star	22.5–25.0
Borderline All-Star	20.0–22.5
Second offensive option	18.0–20.0
Third offensive option	16.5–18.0
Slightly above-average player	15.0–16.5
Rotation player	13.0–15.0
Non-rotation player	11.0–13.0
Fringe roster player	9.0–11.0
Player who won't stick in the league	0–9.0

Only 21 times has a player posted a season efficiency rating over 30.0 (with more than 15 games played in that season), with the highest score being 31.90 (Giannis Antetokounmpo). Michael Jordan and LeBron James lead with four 30+ seasons, with Shaquille O'Neal and Wilt Chamberlain having accomplished three each, Anthony Davis and Giannis Antetokounmpo having accomplished two each, and David Robinson, Tracy McGrady, Dwyane Wade, Stephen Curry, Russell Westbrook and James Harden [3] having accomplished one each.

Career PER leaders

as of 12 August 2020[4]

Rank	Player	PER
1.	Michael Jordan*	27.91
2.	LeBron James	27.49
3.	Anthony Davis	27.42
4.	Shaquille O'Neal*	26.43
5.	David Robinson*	26.18
6.	Wilt Chamberlain*	26.13
7.	Bob Pettit*	25.34
8.	Kevin Durant	25.20
9.	Chris Paul	25.08
10.	James Harden	24.83
11.	Neil Johnston*	24.69
12.	Charles Barkley*	24.63
13.	Kareem Abdul-Jabbar*	24.58
14.	Tim Duncan	24.22
15.	Magic Johnson*	24.11
16.	Karl Malone*	23.90
17.	Stephen Curry	23.83
18.	Hakeem Olajuwon*	23.59
19.	Julius Erving*	23.58
20.	Larry Bird*	23.50
21.	Russell Westbrook	23.49
22.	Dwyane Wade	23.48
23.	Oscar Robertson*	23.17
24.	Kawhi Leonard	23.09
25.	Giannis Antetokounmpo	23.03
26.	Yao Ming*	23.02
27.	Kobe Bryant	22.90
28.	Jerry West*	22.89
29.	Elgin Baylor*	22.69
30.	Kevin Garnett	22.66
31.	Dirk Nowitzki	22.44
32.	DeMarcus Cousins	22.40
33.	Kyrie Irving	22.24
34.	Tracy McGrady*	22.13
35.	Andre Drummond	22.07
36.	Blake Griffin	22.00
37.	Moses Malone*	22.00
38.	Dolph Schayes*	21.98
38.	Damian Lillard	21.98
40.	John Stockton*	21.83
41.	Amar'e Stoudemire	21.82
42.	Bob Lanier*	21.69
43.	Kevin Love	21.56
43.	Dominique Wilkins*	21.56
45.	Clyde Lovellette*	21.55
46.	Dwight Howard	21.48
47.	Adrian Dantley*	21.51
48.	Harry Gallatin*	21.48
49.	Artis Gilmore*	21.40
50.	George Gervin*	21.38
51.	Pau Gasol	21.37
51.	Dan Issel*	21.37
53.	Alonzo Mourning*	21.24
54.	Clyde Drexler*	21.07
55.	Rick Barry*	21.04
56.	Patrick Ewing*	21.01
57.	Chris Webber	20.94
58.	Allen Iverson*	20.92
59.	LaMarcus Aldridge	20.83
60.	John Drew	20.74
61.	Bob McAdoo*	20.73
62.	Kevin Johnson	20.70
63.	Al Jefferson	20.56
64.	Chris Bosh	20.56
65.	Elton Brand	20.51
66.	George Yardley*	20.51
67.	Nikola Vučević	20.45
68.	Ed Macauley*	20.39
69.	Jimmy Butler	20.34
70.	Manu Ginóbili	20.22
71.	Larry Foust	20.19
72.	Marques Johnson	20.11
72.	John Brisker	20.11
74.	Greg Monroe	20.08
74.	Mel Daniels*	20.08
76.	George McGinnis*	20.05
77.	Billy Cunningham*	20.04
78.	Kevin McHale*	20.02
79.	Steve Nash*	19.95
80.	Larry Nance	19.92
81.	Carmelo Anthony	19.91
81.	David Thompson*	19.91
83.	Connie Hawkins*	19.89
84.	Alex English*	19.87
85.	Walt Bellamy*	19.84
85.	Isaiah Thomas	19.81
87.	Cliff Hagan*	19.80
88.	Bob Cousy*	19.76
89.	Paul Pierce	19.73
90.	Terrell Brandon	19.69
91.	Paul Arizin*	19.66
92.	Mark Price	19.62
93.	John Beasley	19.59
94.	Gilbert Arenas	19.57
93.	Brook Lopez	19.55
96.	Sam Cassell	19.48
96.	Michael Redd	19.48
98.	Carlos Boozer	19.46
99.	John Wall	19.43
99.	Paul Westphal*	19.43

Active players are listed in bold. * Indicates member of the Hall of Fame.

PER since 1951–52

Career PER – Michael Jordan vs. LeBron James

Prior to the 2013–14 season, LeBron James was on the verge of surpassing Michael Jordan's career PER to take the number one spot.[5][6] (even if James should take the number one spot from Jordan, he is still mid-career. As the metric is averaged over the length of a player's entire career a decrease in efficiency later in his career means a player can move down in the ranking. For example, Jordan's PER took a big hit in the final two years of his career when he returned to the game with the Washington Wizards, posting 20.7 in his penultimate season and 19.3 in his final season, compared to his career high of 31.7. Jordan's PER was 29.1 without accounting for his Wizards years.).[7] The debate was intensified on 1 October 2013, with Jordan stating that he would have liked to have played against LeBron, and believes he would have won a one-on-one encounter.[8] As a result, many news features[9][10][11] are focusing on comparing the two players, with some using the PER metric to compare the two players. At the conclusion of the 2012–13 NBA season Miami Heat head coach, Erik Spoelstra, stated that comparing players from different generations is the equivalent to comparing "apples and oranges. You’ll never be able to tell [how James stacks up to Jordan or Magic Johnson] because they didn't play against each other. The game is different now than when it was played in the 1980s or even before that".[12]

Players from different NBA generations and Career PER

Comparing players from different generations using PER presents several problems, this is primarily due to the rule changes and the changes in statistical data collected from different eras (although many other factors could be taken into consideration, even down to the increased sample size as the NBA grew through incorporating more teams). Some of the more important rule changes that should be considered include; some of the players on this list played before the three-point shot, blocks, and steals stats were officially recorded (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. During the 1990s and 2000s numerous rule changes were incorporated, the "three point foul" and "clear path" rules were both introduced in the 1995–96 season with the effect of increasing the number of free throws, hand-checking (the amount of contact a defender may make with an opposing player) was banned in 1994 and the use of elbows was banned in 1997 (both rules had seen various degrees of limitation by earlier rule changes) although neither was fully implemented until 2004. The 2004 rule changes, which also included calling the defensive 3 second rule ("[...] a defensive player may not station himself in the key area longer than three seconds"—a longstanding rule which had been ignored by referees) had a major effect, opening up the game and allowing a more free-flowing offense; it encouraged aggressive inside attack based plays (to draw fouls), and has increased the number of fouls given when contact is made on players who drive to the basket.[13] Former ABA and NBA Coach Larry Brown is quoted as saying "The college game is much more physical (than the NBA) [...] I always tease Michael (Jordan), if he played today, he'd average 50".[14]

Calculation

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

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

When multiplied out and refactored, the equation above becomes:

${\displaystyle uPER={\frac {1}{min}}\times \left(3P-{\frac {PF\times lgFT}{lgPF}}+\left[{\frac {FT}{2}}\times \left(2-{\frac {tmAST}{3\times tmFG}}\right)\right]+\left[FG\times \left(2-{\frac {factor\times tmAST}{tmFG}}\right)\right]+{\frac {2\times AST}{3}}+VOP\times \left[DRBP\times \left(2\times ORB+BLK-0.2464\times \left[FTA-FT\right]-\left[FGA-FG\right]-TRB\right)+{\frac {0.44\times lgFTA\times PF}{lgPF}}-\left(TO+ORB\right)+STL+TRB-0.1936\left(FTA-FT\right)\right]\right)}$

Where

• ${\displaystyle \ factor={\frac {2}{3}}-\left[\left(0.5\times {\frac {lgAST}{lgFG}}\right)\div \left(2\times {\frac {lgFG}{lgFT}}\right)\right]}$,
• ${\displaystyle \ VOP={\frac {lgPTS}{lgFGA-lgORB+lgTO+0.44\times lgFTA}}}$,
• ${\displaystyle \ DRBP={\frac {lgTRB-lgORB}{lgTRB}}}$.

With

• tm, the prefix, indicating of team rather than of player;
• lg, the prefix, indicating of league rather than of player;
• min for number of minutes played;
• 3P for number of three-point field goals made;
• FG for number of field goals made;
• FT for number of free throws made;
• VOP for value of possession (but in reference to the league, in this instance);
• RB for number of rebounds: ORB for offensive, DRB for defensive, TRB for (total) combined, RBP for percentage of offensive or defensive;
• others being outlined in basketball statistics.

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

${\displaystyle \ PER=\left(uPER\times {\frac {lgPace}{tmPace}}\right)\times {\frac {15}{lguPER}}}$

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 among other advanced statistics before that year.

References

1. "Basketball Reference - PER". Basketball Reference. Retrieved 5 September 2013.
2. "Hardwood Paroxysm". Archived from the original on 10 September 2017. Retrieved 16 April 2017.
3. https://www.basketball-reference.com/play-index/psl_finder.cgi?request=1&match=single&type=totals&per_minute_base=36&per_poss_base=100&season_start=1&season_end=-1&lg_id=NBA&age_min=0&age_max=99&is_playoffs=N&height_min=0&height_max=99&birth_country_is=Y&as_comp=gt&as_val=0&pos_is_g=Y&pos_is_gf=Y&pos_is_f=Y&pos_is_fg=Y&pos_is_fc=Y&pos_is_c=Y&pos_is_cf=Y&c1stat=per&c1comp=gt&c1val=29.95&c2stat=g&c2comp=gt&c2val=20&order_by=per
4. "NBA & ABA Career Leaders and Records for Player Efficiency Rating". Basketball Reference. Retrieved 19 February 2019.
5. ESPN.com - "2012-13 Hollinger NBA Player Statistics - All Players" - Accessed 6 October 2013
6. Basketball Reference, "LeBron James". Accessed 6 October 2013
7. Basketball Reference, "Michael Jordan" - Accessed 6 October 2013.
8. NBA.com - "Jordan proclaims he could beat LeBron in prime". Accessed 6 October 2013.
9. Busfield, Steve. The Guardian, Michael Jordan vs LeBron James: who is better?" Accessed 6 October 2013
10. Helin, Kurt. NBCsports.com "LeBron says he wants to be greatest of all time, still "far away from it". Accessed 6 October 2013
11. Lariviere, David. Forbes, "LeBron James Will Eventually Top Michael Jordan As Basketball's Greatest Player". Accessed 6 October 2013.
12. Golliver, Ben. Sports Illustrated, "Spoelstra: Comparing LeBron to Jordan is impossible because 'game is different now' Archived 11 October 2013 at the Wayback Machine" - Accessed 6 October 2013
13. NBA.com - NBA Rules History. Accessed 6 October 2013.
14. Aldridge, David. NBA.com - Rules changes have affected defensive philosophies. Accessed 6 October 2013

External links

• CREZ Basketball Systems Inc., Software to score your own basketball games and view PER player and lineup statistics
• An in-depth description of how to calculate PER
• Hollinger's articles at SI
• Basketball-Reference.com, Historical NBA statistical site (includes PER)
• KnickerBlogger.net
• ESPN.com Insider (subscription service)