Brandan Wright is a better player than Dwight Howard!
If you've ever watched or even follow a little bit of basketball and heard anybody say the above you'd assume they're joking. Well, according to John Hollinger's PER the above statement is true. PER, or player efficiency rating, is an all-in-one rating system that takes into account points, assists, rebounds, field goal percentage, etc. when trying to figure out exactly how good a player is. PER has becoming increasingly more popular as shown in the Google Trends graph below. However due to the ubiquity of the stat its often used in correctly.
I'm not saying PER is a bad statistic or that Hollinger has no idea what he's talking about. I do think that PER is a good statistic, in context, in evaluating players and I have nothing but respect for John Hollinger & the work he's done in pioneering sabermetrics in the NBA. However with any advanced statistic, such as PER, its important to understand how its calculated and exactly in which context its useful. First we calculate unadjusted PER (uPER), and then normalize it with respect to rest of the league according to the pace a team plays at. We won't get into the discussion of pace normalization today since that's mostly used to compare players across different seasons and we'll be looking at an isolated season. The formula for uPER is:
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) ]
It's a lot to take in, but I'm going to break down each term. The more odd terms are:
factor = (2 / 3) - (0.5 * (lg_AST / lg_FG)) / (2 * (lg_FG / lg_FT))
VOP (value per possession) = lg_PTS / (lg_FGA - lg_ORB + lg_TOV + 0.44 * lg_FTA)
DRB% = (lg_TRB - lg_ORB) / lg_TRB
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) ]
It's a lot to take in, but I'm going to break down each term. The more odd terms are:
factor = (2 / 3) - (0.5 * (lg_AST / lg_FG)) / (2 * (lg_FG / lg_FT))
VOP (value per possession) = lg_PTS / (lg_FGA - lg_ORB + lg_TOV + 0.44 * lg_FTA)
DRB% = (lg_TRB - lg_ORB) / lg_TRB
1. (1 / MP) is just normalizing the rest of the equation on a per minute basis. Its important to note that PER is a per minute stat.
2. 3P is the amount of three pointers made. Three pointers here are given a weight of 1. 3. (2/3) * AST gives a weight of 2/3 for every assist a player gets. 4. (2 - factor * (team_AST / team_FG)) * FG Looks at the weight that a made field goal (2 pointer or 3 pointer doesn't matter). Important to note is that the statistic devalues assisted shots (hence the -team_AST/team_FG). He assumes all field goals are worth the same here (3 pointers will get counted again in term 2). 5. (FT *0.5 * (1 + (1 - (team_AST / team_FG)) + (2/3) * (team_AST / team_FG))) Just as Hollinger normalized the value of field goals, he normalizes the value of free throws here. He uses 0.5 since he assumes field goals are are all worth 2 points, and a free throw is half of that. 6. -(VOP * TOV) Gives negative weight to turnovers, but does it with respect to the value per possession. For example if the value per possession is 1.13 points around the league, 2 turnovers will cost you 2.26 points. |
7. -(VOP * DRB% * (FGA - FG) ) Assigns negative weight to missed field goals, again using the same VOP principle as in term 6, except now accounting for offensive rebounds via DRB%.
8. -VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA - FT) Again, this terms looks at the possession value in reference to a missed FT. The 0.44 accounts for when a player makes a shot and then goes to the free throw line along. It also accounts for missing the first FT our of two (missing the second FT out of 2 is better since it gives your teammates a chance to rebound). 9. VOP * (1 - DRB%) * (TRB - ORB) Looks at the value per possession generated when you get a defensive rebound. Defensive rebounds are generally easier to get than offensive rebounds so this accounts for the difference in weight. 10. VOP * DRB% * ORB Looks at value per possession per offensive rebound. 11. VOP * STL If a player gets a steal, they got an extra possession for the their team. This accounts for that. 12. VOP * DRB% * BLK Looks at value per block. However it also assumes that blocks are rebounded at the same rate as a regular shot. 12. -PF * ((lg_FT / lg_PF) - 0.44 * (lg_FTA / lg_PF) * VOP) Looks at negative weight behind personal fouls and scales it according to league average. |
Hopefully now you have a better idea what exactly goes into PER. Lets look at the assumptions PER makes along these terms.
- The break even point with all the weights for field goal percentage/three point percentage is 30.4% & 21.4% respectively. If any player was shooting these percentages they certainly wouldn't be in the NBA, but uPER considers shots at these percentages to be positive contributions. The theory is that since PER is adjusted to league average it'll be normalized to the correct shooting percentage. However, the normalization occurs after the total uPER is calculated. If somebody were to shoot 100 shots in a game at those percentages and contribute nothing else they would have a large uPER compared to somebody that didn't shoot much and got lots of assists/rebounds/etc. The main takeaway from this is that PER will favor players that score a lot, regardless of the efficiency at which they do so.
- It accounts for and-1's (field goal made + free throw which your team has an opportunity to rebound) via the 0.44 multiplier associated with it. If a player is getting a lot of and-1 chances this multiplier is undervaluing their performance, especially those players that do not convert the free throw (since their teammates have a chance to rebound that miss as opposed to missing the 1st of 2 free throws). This crucial for players such as Dwight Howard that get a lot of and-1 opportunities but miss a lot of free throws.
- A smaller assumption, but still important to note. Hollinger's formula assumes that blocks are rebounded at the same rate as a missed shot, however that varies greatly player to player. Certain players will block shots out of bounds which allows the offensive team to retain possession, however PER credits these plays with getting another possession for their team. This play by Javale McGee is a great example of that. Some players tend to block shots in a way that almost always assure an extra possession for their team, but get rewarded a possession at the DRB% rate according to PER. This play by Andrew Bogut is an example of the exact opposite.
- PER also only accounts for plays that generate numbers (if a player does not contribute any statistic - points, rebounds, steals, etc.). In this play by Lebron James he has a "hockey assist" where he essentially creates the open look from beyond the arc but because of the way assists are scored Shane Battier gets the assist for simply being in the right place at the right time.
- On the above note PER only looks at defense in terms of steals and blocks but discounts defensive plays that that help the team but don't generate statistics. In this play by Tony Allen he forces Andre Miller to turn it over without actually g. enerating any statistics. Defensive specialists like Tony Allen often get a lot of minutes in the NBA, but don't generate any PER-friendly numbers due to their style of play and the type of game they play.
- The biggest assumption is term 1 where uPER is normalized per minute. This assumes that a player is contributing the same after playing for just two minutes or after 35 minutes. This assumption totally discounts the law of diminishing returns and consequently PER favors players that play limited minutes. Obviously if you play less minutes you have more energy and can put up better stats.
Again, I'm not saying that PER is bad statistic. It does a lot of things correctly - it adjusts everything to a league average and the VOP term that Hollinger is absolute genius. Understanding the value of possessions is paramount to understanding a players impact and VOP makes that a little more possible. However, now that we understand how PER works and the limitations of it how can we use it to our advantage.
So if comparing players it's important to:
1. Only compare players that play similar minutes and discount players that barely played. For example Henry Sims was second in PER during the 2012-2013 season, but only played 5 minutes and happened to grab a couple of offensive rebounds and score 4 points in that span.
2. Compare players that played a similar role. Players that played 20 minutes as a defensive specialist like Tony Allen (PER 13.2) would obviously post a lower PER than someone that came in for 20 minutes to try and score as many points as possible like Jamal Crawford (PER 16.8).
3. Understand the nuances of PER in regards to blocked shots, and-1s, scoring efficiency. If the PERs between two players is close, the discrepancy might be due the methodology between calculating PER as opposed to actual player efficiency.
I hope this post was able to shed some light on the inner workings of PER so the next time somebody tells you that Nikola Pekovic is better than Andrew Bogut you can set them straight
So if comparing players it's important to:
1. Only compare players that play similar minutes and discount players that barely played. For example Henry Sims was second in PER during the 2012-2013 season, but only played 5 minutes and happened to grab a couple of offensive rebounds and score 4 points in that span.
2. Compare players that played a similar role. Players that played 20 minutes as a defensive specialist like Tony Allen (PER 13.2) would obviously post a lower PER than someone that came in for 20 minutes to try and score as many points as possible like Jamal Crawford (PER 16.8).
3. Understand the nuances of PER in regards to blocked shots, and-1s, scoring efficiency. If the PERs between two players is close, the discrepancy might be due the methodology between calculating PER as opposed to actual player efficiency.
I hope this post was able to shed some light on the inner workings of PER so the next time somebody tells you that Nikola Pekovic is better than Andrew Bogut you can set them straight