## Wednesday, February 18, 2009

### A Bevy of Stats

Player Efficiency Rating (PER) can be found in here....

A commenter asked me to break down John Hollinger's Player Efficiency Rating, or PER. To whom I say with a grin, "Sure."

Now, according to Mr. Hollinger himself, "The PER sums up all a player's positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player's performance."

Sounds nice, doesn't it? Now, let's go to the definition of PER from Basketball-Reference.com:

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) ]

Most of the terms in the formula above should be clear, but let me define the less obvious ones:

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

Did any of that make a damn bit of sense to you? I have a degree in mathematics, and the first time I looked at that formula, I said, "huh"? It's certainly clear that field goals, assists, turnovers, rebounds both offensive and defensive, steals, blocks, and some league averages and team averages go in there somewhere.

However, there is nothing intuitive about any of this. If you read Hollinger's book (which I don't have), he'll be glad to go over each component with you in an explanation probably requiring several pages. And all of the above is just the first part of PER!

So our anonymous Jennifer Lacy fan might ask the question, "Pet, if not even you can explain PER, why the hell do you use it?" My answer:

a) I trust John Hollinger,
b) the results pass the "smell test": by that I mean that you'd expect the people you'd think are the best players in the league to have high PER and the worst to have low PER - which they do - and
c) the final number can be translated to something meaningful.

If you've got a PER of 30 or more, you're having one of the WNBA's great seasons. If you've got a PER of 15, you are an average WNBA player. The arithmetic mean (average) of a bunch of unadjusted PER numbers is taken, more adjustments are made, and the number "15" is thrown in there so that the mean PER for the WNBA comes out to be exactly 15.00. We have defined "average mean unadjusted PER" to be precisely equal to 15.00.

Once you get into a PER of 9.00, we're pretty much at what Hollinger called "replacement level", meaning that you could probably find some overlooked college player who just missed being drafted or got cut at training camp, get her up to speed, throw her out on the court and she could probably rack up a PER of 9.00 under good conditions. I don't really agree with that, because Hollinger's analysis was done with NBA players and not WNBA players. I will agree that a PER of 9.00 is nothing to be proud of.

PER has its weaknesses, and its detractors. For one thing, PER undervalues defensive contribution, so a player who is a defensive specialist won't have that value reflected in PER. Those players will have lower PER than a more just and fair allotment of PER should give them.

I keep all of this crap in a spreadsheet which I'll be glad to send anyone. Unfortunately, if you didn't understand any of that above formula (and I'm with you), you might not feel any better. PER suffers from the "black box problem" - you dump a bunch of stats in one end of the black box and out comes one number from the other end, but you don't really know what takes place inside the box.

There were 193 people who took part in the WNBA season last year: here are the top PER performers.

Leaders in Player Efficiency Rating, 2008

1. Diana Taurasi 29.83
2. Candace Parker 27.28
3. Sancho Lyttle 27.17
4. Lauren Jackson 26.63
5. Lindsay Whalen 24.68
6. Janel McCarville 24.57
7. Sophia Young 23.39
8. Tamika Catchings 23.14
9. Candice Wiggins 23.13
10. Jia Perkins 22.94

These numbers seem to make sense, although the computer would have given Taurasi the MVP and not Candace Parker. This might be why computers don't award MVPs, although I think Phoenix Mercury fans would jump up and say, "PER was right! PER was right!"

Who is the WNBA's "Most Average Player"?

61. Ivory Latta 15.03

Now there's a surprise!

Out of the 193 players, where does Jennifer Lacy show up? In the #135 slot.

134. Quianna Chaney 8.33
135. Jennifer Lacy 8.31
136. Sandora Irvin 8.31

"Okay," you might say, "this is just a bunch of numbers. It doesn't prove anything."

I agree. But here's the question: "do the results pass the smell test?" Suppose were were talking to say, Bill Laimbeer or Bill Dolan or whoever. And suppose we were to say, "given all things being equal - that is, we're not looking at salary or team need - who would you rather have on your team, Diana Taurasi or Ivory Latta?"

Is Diana Taurasi better than Ivory Latta? I would say "yes" - and I LIKE Ivory Latta! Likewise, who is better, Ivory Latta or Jennifer Lacy?

I think Ivory Latta is better than Jennifer Lacy. I'm not knocking Jennifer Lacy, I'm just saying that Ivory Latta brings more value on the floor than Jennifer does. In terms of leadership or the locker room or coaching or gameplan, it might be a different story. However, I think that Latta is more productive than Lacy, in which case, I agree with PER.

PER might not be right every time - was Sancho Lyttle worth more to the Comets than Lauren Jackson was to the Storm last year? - but it's right often enough for me to like it.

Of course, the next question would be "why don't you just use traditional stats?" More on that later. I'm just getting warmed up. :D