APBRmetrics

[Charles]

I don’t understand this.


If I take two players and give each an "average" record based on playing 10% of their team's minutes, except one with all his points from two-pointers and the other with all his points from three-pointers the player shooting three-pointers gets 55 less PER credits.

Each player took the same number of shots. Each scored the same number of points. Yet, the two point shooter gets more PER credits (based on less FGx)

Am I missing something, or does a pound of stone actually weigh more than a pound of feathers?

[deepak]

I'm looking at the PER formula right now, and here are the relevant terms:

3P + (2 - factor*(TmAst%))*FG - VOP*DRB%*(FGA_miss)

So, I think you're assuming that TmAst% is 0, DRB% is 1, and VOP is 1. Then, it reduces to:

3P + 2*FG - FGA_miss

Per possession, we expect 1 points to be scored (VOP = 1). If you have a player who scores 60% of the time on 2-pointers, then we expect:

.6*2 - .4 = 0.8 credits earned per shot attempt

And if you have a player who scores 40% of the time on 3-pointers, we expect:

.4*3 - .6 - 0.6 credits earned per shot attempt

So, according to PER, if all misses are rebounded by the defensive team, then it's better to score your X points at a higher percentage inside the arc then at a lower percentage outside the arc. This can easily be rationalized. I imagine that teams tend to be more efficient in their possessions when it follows a miss by the other team, versus a make since defense has less time to get set. So, a miss doesn't only represent lost opportunity on the offensive end, it also impacts the ensuing defensive possession. Not sure if it was intended, by Hollinger's scheme does seem to take this into account in a clever way.

[Charles]

You are correct deepak, I grossly over-simplified, since you can't determine the exact values without league averages. Could you comment on the modified first post.

[Charles]

[Flint]

Here is Berri on PER...

"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.

But again, our model of wins suggests that inefficient shooting does not help a team win more games. Hence the conflict between PERs and Wins Produced. Hollinger has set his weights so that inefficient scorers still look pretty good. We argue that inefficient scoring reduces a team’s ability to win games, and therefore these players are not nearly as effective as people might believe."

Hollinger also has GameScore, a simplified version of PER. Although PER is extremely complicated, it has a 99% correlation with Game Score, or at least so I have read over at the WOWJ. The formula is....

(Points x 1.0) + (FGM x 0.4) + (FGA x -0.7) + ((FTA-FTM) x -0.4) + (OREB x 0.7) + (DREB x 0.3) + (STL x 1.0) + (AST x 0.7) + (BLK x 0.7) + (PF x -0.4) + (TO x -1.0)

[Charles]

Do you agree with Berri on this point, Flint?

I do. I see the PER approach as a compensation for the minimal weight given to shot creation. I realize shot creation is difficult to determine using nothing but official stats, but that's the challenge, because shot creation is essential to understanding the reality of basketball.

When you combine PER's implementation of "lost opportunities" with the error caused by assuming everyone has the same percentage of their shots assisted (Amare actually has about 65% of his baskets assisted compared to 20% for Nash) and a very loose rationalization for the weighting of assists versus points scored) it becomes easy to understand why Nash’s plus/minus has averaged about 7.3 points per 48 minutes higher than Amare’s since they began playing together. Plus minus is noisy, but a seven point difference over 6,000 minutes played is a lot.

Incidentally, I would be reluctant to criticize these weights if they were produced through regression or some other verifiable analysis rather than logic.

[Flint]

Yes. I definitely agree with Berri. And I don't think there is any objective basis for Hollinger's weights.

You were discussing Joe Johnson in the other thread. Here is a comp of 03-04 and last season.

http://www.basketball-reference.com/fc/pcm.cgi?req=1&cum=0&p1=johnsjo02&y1=2005&p2=johnsjo02&y2=2007

To me, it seems very odd that went from a 15 PER to a 19.5 PER. What changed? His ts% was the same, 55.6% and 55.8%.

In y2, 1.4 less rebounds, .8 more assists, 1.6 more tumovers, and of course, 5.4 shots more per 48 and 8.3 points more per 48. To me, that is valuing shot creation a great deal more than necessary.

[Harold Almonte]

Flint, the WOW logic about the team possession lost after a FGMade could be acceptable, but his approach is wrong and he created a big mess. He penalizes scorers (FGMade) by attempts and rewards the inbounds (oppFGMade) in the opp. team, by minutes. He should have done this also by attempts (if he considers FGMade a matter of individual attempts rather than team), and then scorers just recuperate the most of this team possession lost/gain-with the ball and the clock out of play (just a rule). There's no any straight relationship between FGA and player minutes for him to attempt to cancel one thing with the other, and he's just rewarding low FGA-high minutes players.

PER could be overrating a bit, but WP is overpunishing there. They did the opposite with Rebounds.

[Guy]

[Flint]

Guy - What do you think of PER?

[Charles]

[Guy]

Flintberri: My point is not to argue for (or against) PER. My point is simply that WP does not value efficiency more highly, as claimed, as demonstrated by its lower correlation with shooting efficiency. The metric is so dominated by rebounds that it can't give proper credit even to many of the efficient shooters that Berri celebrates.

Charles: I wasn't trying to draw a distinction btwn shot-taking and usage, and wouldn't claim to know the right way to value usage. (My intuition would be to try to establish a reasonable replacement level, which certainly would be lower than league average.) But I feel pretty confident that these equations from the WP perspective are wrong:
* 0-0 = 2-4 = 12-24
* 2-4 > 11-23
* Net value of all shooting by NBA players = zero.

WP says that all below-average shooters hurt their teams, so logically I assume that means these players should stop taking shots. But here's the problem: in this new WOW version of the game, half of those still permitted to shoot will be below the new, higher ts%. So WP will then tell us again that they too should stop hurting their team by shooting, having committed the sin of being below average. Eventually, I suppose each team will have one player who takes all of its shots. Personally, I don't find this terribly plausible. Perhaps Flintberri can make sense of it?

[asimpkins]

[gabefarkas]

[94by50]

Is it just me, or are the following possible?

* The break-even marks for 2pt and 3pt shooting in PER are too low.
* The break-even marks for 2pt and 3pt shooting in WP are too high.
* The ideal mark is somewhere in the middle.

Just eyeballing it, for example, if I take the 30% break even mark for 2pt shooting in PER, and split the difference with league average 2pt shooting (the break even mark in WP), which is, what, about 49%... the average of the two is in the high 30s. I suspect the ideal break even mark is somewhere in that neighborhood. Just a hunch.

Also, regarding the idea that "inefficient shooting does not help a team win more games"... well, of course it doesn't. The question is, how poorly does a player have to shoot before they shouldn't be shooting at all? The Sixers were more than willing to live with Allen Iverson's 40% field goal percentage for quite a while. Why is that? (And I don't think the correct answer is, "Because Iverson is a scorer and teams overvalue scorers.")