The PER Formula and its Subsequent Weaknesses

John Hollinger is a god send to basketball analytical methods. Not only is his stat PER (or Player Efficiency Rating) an all encompassing stat, but its also catching on with the casual NBA fan. ESPN, like its treatment with SABRmetrics, has devoted pages on PER and its other components Hollinger uses to calculate PER. So, what’s PER, you may ask? Well, Hollinger explains it all in his “insiders only” article very well, but I don’t have ESPN insider, so I’ll just explain it to the people that don’t.

Here’s the formula (Hollinger’s of course: Do not modify or copy it and reprocess it):

uPER = (1 / MP) * [ 3P + (2/3) * AST + (2 - factor * (team_AST / team_FG)) * FG + (FT *0.5 * (1 + (1 - (team_AST / team_FG)) + (2/3) * (team_AST / team_FG))) - VOP * TOV - VOP * DRB% * (FGA - FG) - VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA - FT) + VOP * (1 - DRB%) * (TRB - ORB) + VOP * DRB% * ORB + VOP * STL + VOP * DRB% * BLK - PF * ((lg_FT / lg_PF) - 0.44 * (lg_FTA / lg_PF) * VOP) ]

where: factor = (2 / 3) – (0.5 * (lg_AST / lg_FG)) / (2 * (lg_FG / lg_FT))
VOP = lg_PTS / (lg_FGA – lg_ORB + lg_TOV + 0.44 * lg_FTA)
DRB% = (lg_TRB – lg_ORB) / lg_TRB

Confusing and drawn out, huh? I’ll clarify, but we’re not done.

uPER is then subjected to a pace adjustment, then its standardized so that every season’s average is 15. This makes it possible for all the eras to be compared together. Basically, PER takes what a box score says, assigns value to different tasks like scoring or passing, standardizes it for both pace and minutes played, then spits it out into a singular number. Its quick, convienient, and awesome.

He has a methodology for each component and weight of PER. To see these, I advise you to buy his works, which are also easy to read and very interesting.

Here’s some fundamental problems with PER:

- Defense. Is defense just really blocks, steals and defensive rebounds? Answer is simply no. Ask Bruce Bowen, who has had a poor PER, but is still considered a premier defender in the NBA. PER does not address simple man to man defense and shutting down your opponent because it looks at box score indicators of what defense is.

- Scoring. David Berri says it best: “”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 played 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.”

- Players who play more minutes get overvalued than players than don’t. In Hollinger’s formula, its best for you to play the most minutes you can. That would make you produce more, and hence have a higher PER. PLayers who play roles have to be almost perfect to have great PERs like the Wades, Lebrons and Bryants of the league.

- It doesnt take into account leadership, will, determination, clutch, ect. Or, things that cannot be measured in numbers if you are an NBA junkie.

- PER does not function to wins. Dwyane Wade had a stellar PER season of 30 in the 2009 season, but his team failed to win 50 games. PER is not a team indicator either; you cannot determine the PER of a team. Its just a stat that uses box score production to determine value.

Hope that cleared up any questions you had of PER. If you have any questions, either leave it in the comments, or personally e-mail John Hollinger. I’m sure I’ll get you the answer quicker than he will.

- ricky9