Tuesday, October 17, 2006

In Praise of PERs

Basketball stat guru John Hollinger's 2006 projected Player Efficiency Ratings came out today, and they're sure to inspire the debates that PERs often do. (See, what did I tell you about more fun and exciting posts?)


Actual picture of John Hollinger. Except not really.

For those unfamiliar with the PER, it's a formula that takes into account positive statistics, such as points, rebounds, blocks, etc., and weighs them along with negative ones, such as turnovers and fouls. The beauty of the equation is that it levels all those numbers by factoring in not only minutes played, but also the pace of that player's team; thus, Stephon Marbury isn't penalized for playing on a team with less possessions than Steve Nash. He's just penalized because he sucks.

Although it's pretty complex, the equation is still more comprehensible than the quarterback ratings the NFL uses. I wouldn't be surprised if someone from ESPN--probably The Schwab--has been in a trailer making those up for the past twenty years. "Bernie Kosar? He's about an 86.3."

Hollinger's PER looks like this on paper:

\ 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] .

Chili dog. Then, J-Holl adjusts it for pace:

\ PER = [uPER*(lgPace/tmPace)] * (15/lguPER)

Additionally, that last step sets the league average at 15.0.

Anyway, this equation boils a player's performance down to one figure that's pretty accurate. For example, according to Hollinger's numbers last season, which are different for some reason from Basketball-Reference's, these were the league leaders:

1. Werewolf at Sunset (Nowitzki)- 28.20
2. Bron Bron- 28.17
3. Kobes- 28.11
4. D-Wade- 27.68
5. The Big Ticket- 26.88
13. Your NBA MVP Steve Nash- 23.29

So that proves that any MVP argument for hand-licker is based purely on intangibles like team leadership or (flimsier in his case) position defense. According to the PERs, he's not even the most valuable player on his team, since Marion had a 23.66. The PER is clear, but still refutable, evidence in arguments like this one or the "Hey, he should start" debates.


lycanthropic (adj.)

The beautful thing about Hollinger's system is that it reinforces what we already know. Sure, there are surprises. I was shocked to see that Chris Kaman was only a 15.01 and that Dwight "I had a dream about Jesus and the cross being on the NBA logo" Howard had a 17.40, which also seems low. On the other hand, Gerald Wallace and Jackie Butler are much better per-minute than people give them credit for. But when you think about it, King James is probably, as the numbers indicate, twice as good as Ricky Davis. (Or six times as good as Mad Dog. Pace.) To test the validity of the PER, I created a complicated experiment.

I called up friend of TANBR P.T. and told him we were having a pick-up game with everyone in the NBA. He had first pick, I had second, and we picked five guys each. Our picks when compared to Hollinger's prospective numbers for the players were:

IMAGINARY PICK-UP GAME
P.T. (1.) Bron Bron
Me (2.) Kobes
P.T. (3.) Amare
Me (4.) Werewolf at Sunset
P.T. (5.) Duncan
Me (6.) D-Wade
P.T. (7.) CP3
Me (8.) The Big Aristotle
P.T. (9.) Shawn "The Matrix" Marion
Me (10.) The Big Ticket

HOLLINGER'S PROJECTIONS
1. Bron Bron- 31.86
2. Kobes- 27.00
3. Werewolf at Sunset- 26.86
4. Amare- 26.12
5. D-Wade- 25.91
6. The Big Ticket- 24.97
7. CP3- 24.96
8. Pau "Spanish Fly" Gasol- 23.95
9. Gilby "I sleep on the couch because I don't like women touching me" Arenas- 23.78
10. A.I.- 23.32
165. Nocioni- 13.84
326. Mad Dog- 5.73

Pretty close, huh? All those guys that we picked are in Hollinger's top twenty. Turns out the best players in the league are the players you think are the best. You can't come up with a formula that proves the truth much better that that. I salute you, Mr. Hollinger.

Plus, his projections are occasionally hilarious. Really, Starbury? You're one of the best players in the league? Actually, my boy ranks you at 55.
$15: Not even worth it to ship them ironically from eBay. I'll take two tuna combos from Subway instead.

Best of all, in his book, Hollinger qualifies cut-offs for his numbers.
*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
So while our MVP was a bona fide all-star at best, my hero is probably packing his bags. Don't forget your special underwear, M.D.

If you need your PER fix during the season, the fellas at KnickerBlogger compute them more frequently (every day) than even nba.com.

1 comment:

Brian Cronin said...

When I first came across PER a few years back, I was astonished at just how, well, LOGICAL it was.

I spent some time going through all his equations, and I'm just like, "Wow, that makes perfect sense."

My brother is a huge Nash fan, so we have had a lot of arguments over PER over the past couple of years, and he always tries to put PER down, but he just can't - it's just that solid.

He's like, "I think he underrates ___," and I'm all, "Nah, check it out, he does ___ with that, which makes perfect sense."

Hollinger's awesome.