## Estimated PER Demystified

Many of you know that I like to estimate PER on a game by game basis as a way to see how efficient a player is from game to game. However, I have never explained how I arrive at estimated PER and why I even use it. So I'm going to take a moment and give you some background.

In my quest to calculate in-game efficiency, I looked at various different formulas. I soon realized there were several in-game efficiency measures that had been created, including John Hollinger's own "Game Score" calculation and Larry H Miller's Average. While I could use these formulas, there was nothing out there that was as recognizable as PER.

The problem with PER is that it's creator, John Hollinger, never meant for it to be calculated on a one game basis. Rather, PER measures a player's efficiency over the course of a season. In fact to calculate PER you are required to include such things as league totals for points, field goals, free throws, tree throw attempts, offensive rebounds, rebounds, turnovers, and assists (see calculation).

Knowing the foregoing, I set out on a quest to find a way to estimate PER, and, after much internet research, I found a couple of formulas that purported to estimate Hollinger's PER. The estimate I found to be most reliable was created by Wayne Winston from The Wages of Wins Journal, and it is Wayne's formula that I utilize to estimate PER.

The formula is fairly straight forward and is calculated as follows:

45.75 times (Points divided by Minutes) + 22.55 times (Rebounds divided by Minutes) + 32.8 times (Assists divided by Minutes) + 58.2 times (Steals divided by Minutes) - 48.65 times (Turnovers divided by Minutes) - 39.73 times (Missed FG's per Minute) - 20.6 times (Missed FT per Minute) + 38.37 times (Blocked Shots per Minute) - 18.68 times (Fouls per Minute)

Wayne created the estimated PER formula back in 2012 and indicated that it explained 99% of the variations Hollinger's PER for that season, with the average difference between estimated PER and Hollinger PER being .37. Having said that, let's look at estimated PER versus Hollinger PER as of January 12, 2015 (note I calculated estimated PER (ePER) using the above forumula and compared it to Hollinger's PERs for the players as listed on ESPN's website.)

 Player MIN FG FGA 3P 3PA FT FTA REB AST BL ST PF TO PTS ePER PER Diff % Diff T.Booker 724 110 213 13 35 44 70 181 36 15 20 65 46 277 16.01 15.84 0.17 1.07% T.Burke 1207 175 466 56 178 61 75 98 187 9 32 63 69 467 12.87 12.57 0.30 2.39% A.Burks 899 121 300 26 68 106 129 114 82 5 17 64 52 374 13.62 13.05 0.57 4.37% I.Clark 115 11 32 7 17 5 5 7 7 1 4 8 6 34 8.16 8.09 0.07 0.87% J.Evans 61 6 14 1 2 5 5 17 3 5 3 5 2 18 19.07 19.57 -0.50 -2.55% D.Exum 705 69 178 34 104 18 29 53 73 6 18 62 42 190 8.23 7.83 0.40 5.11% D.Favors 1075 226 409 0 0 108 160 300 50 53 25 93 54 560 23.08 22.92 0.16 0.70% R.Gobert 788 90 140 0 1 54 81 253 33 83 24 75 44 234 20.29 20.81 -0.52 -2.50% G.Hayward 1343 239 531 61 166 180 222 187 155 14 49 77 99 719 20.00 19.1 0.90 4.71% R.Hood 400 37 117 18 65 24 33 51 28 6 9 52 16 116 7.54 6.86 0.68 9.91% J.Ingles 675 49 125 19 75 6 11 73 79 5 28 40 33 123 9.20 8.58 0.62 7.23% E.Kanter 907 201 394 10 31 64 79 246 22 13 12 83 65 476 18.25 18.14 0.11 0.61% E.Millsap 97 8 26 5 11 0 2 13 7 3 7 13 11 21 4.86 3.67 1.19 32.43% S.Novak 71 8 22 8 20 0 2 10 4 1 0 9 2 24 8.88 8.17 0.71 8.69% E.Williams 23 3 8 2 4 0 0 1 0 0 2 0 3 8 6.97 5.57 1.40 25.13%

It would seem, based on the table above, that ePER still approximate actual PER fairly close, though, for whatever reason, the newest Jazz members have large differences, while all other Jazz players are within +/- 10% of Hollinger's laborious computation.

This first chart shows each NBA player's ePER for every game played through January 11, 2015 placed in a "PER bin". A "PER bin" aggregates each player data set by ePER value. Each bin spans 7.5 of PER value. Let me give you some examples. If a player recorded an ePER of 9, that one game count would be placed in the 7.5 PER bin since the 7.5 PER bin goes from 7.5 to 15; and if a player recorded an ePER of 23, that game ePER would be placed in the 22.5 PER bin as it covers the ePERs from 22.5 to 30. Here's the league chart:

League ePER

Note how most ePERs fall into the 7.5 and 15 PER bins (approximately 46.16%). This is what you would expect since actual PER is set so that the average PER is 15.

Next I want to show you league ePER by player position (note that I've utilized ESPN's player assigned positions):

Point Guard

Shooting Guard

Small Forward

Power Forward

Center

Note the variations for the player positions above; point guards and power forwards have relatively even distributions, almost textbook, whereas shooting guards and small forwards overweight the 7.5 PER bin, while centers overweight the 15 PER bin.

Now let's look at our Utah Jazz ePER distributions through January 11, 2015:

These charts were provided from statcondor.com's tools section.

All comments are the opinion of the commenter and not necessarily that of SLC Dunk or SB Nation.