APBRmetrics

I want to look at the way salaries scale against production but I'm concerned on whether this would be a useful application of PER. Specifically, I want to see if identical improvements in the relevant PER stats of a good player and an average player pay out equivalently, but it wouldn't make sense to do that if PER didn't scale linearly (not sure if that's a correct usage of linearly, but I mean that wherever you are on the PER scale, same improvements to relevant categories improve your PER the same amount).

I'd like to know whether this is true or false:
if given a player A with a PER of 20 and a player B with a PER of 15 who have identical pace factors, improvement of 1% for both players in DRB% means that their PER increases identically.

"I'd like to know whether this is true or false:
if given a player A with a PER of 20 and a player B with a PER of 15 who have identical pace factors, improvement of 1% for both players in DRB% means that their PER increases identically."

I think the general answer is that they increase by the same proportion but not the same amount as average PER performance is scaled to display as 15.

The exception might be with assists and shooting in general as team assist rate is part of the PER calculation and can vary by team.

http://www.basketball-reference.com/about/per.html


"I want to look at the way salaries scale against production but I'm concerned on whether this would be a useful application of PER. Specifically, I want to see if identical improvements in the relevant PER stats of a good player and an average player pay out equivalently, but it wouldn't make sense to do that if PER didn't scale linearly (not sure if that's a correct usage of linearly, but I mean that wherever you are on the PER scale, same improvements to relevant categories improve your PER the same amount)."

Improvements to relevant categories improve your PER in different amounts based on the relative importance / magnitude of impact of that category on PER. A 1% increase in usage,scoring or rebounding will have much more impact than a 1% increase in blocks because usage,scoring and rebounding are more frequent events than blocks and therefore bigger parts of the PER formula and output.


It would be interesting to look at the way salaries scale against production on average and across the distribution and by position. What does $4 million buy in production for a PG versus a $6 million PG or $8, 10 or 12 million and what does it buy compared to $4 million for a wing or a big man? I've looked at that some in the past but there are differnet levels of detail for the analysis. If you want to go at it in a big way you might want to look at other metrics too (EZPM, adjusted plus-minus, maybe winshares or wins produced) to go beyond incomplete boxscore metrics like PER (has no attention to shot defense).

So if I excluded the component that standardizes PER to 15, would that solve the problem of scaling by the same amount? Proportions would be a lot harder to deal with than just a sheer linear increase.
"Improvements to relevant categories improve your PER in different amounts based on the relative importance / magnitude of impact of that category on PER. A 1% increase in usage,scoring or rebounding will have much more impact than a 1% increase in blocks because usage,scoring and rebounding are more frequent events than blocks and therefore bigger parts of the PER formula and output."

What I'm more concerned about specifically is given all other things equal, does an increase in a particular stat for two players of different PER's correspond to an identical change; not so much comparing an increase in two different stats for two different players. That way, I won't have to worry about unequal valuing of something like a single DRB between bad and good players. I don't want to penalize good players for being good, essentially.

As far as what metrics to use, it would be interesting to do it across the board. Part of the reason I'm doing this is to learn some programming and I needed a project, so I want to start with something that I understand (although I think it's clear that I don't understand PER as well as I thought I did). Once I can get the "simple" case working correctly, I'm sure modifying it will be easier.

"So if I excluded the component that standardizes PER to 15, would that solve the problem of scaling by the same amount?"

I think so. You could use unadjusted PER.

If you want simpler to work with than PER you could use winscore, the new version with the adjusted defensive rebound weight. If you do both you can look at the relationship between pay and performance from 2 angles and maybe see which matches GM choice / market behavior closer. Of course the debate about which metric (out of all of them) should be used will continue.

I'd probably still adjust it for pace to be fair, but I'd exclude the standardization. I'll have to look at winscore because I'm not too familiar with it.

Thanks for the feedback.

Yeah pace adjustment is worth doing.

Instead of working with unadjusted PER, you could also use the simple version of it called game score:

Game Score = PTS + 0.4 * FGM – 0.7 * FGA – 0.4*(FTA – FTM) + 0.7 * ORB + 0.3 * DRB + STL + 0.7 * AST + 0.7 * BLK – 0.4 * PF – TO

If you want to compare to WinScore:

revised Win Score = PTS + STL + ORB + 0.5*DRB + 0.5*AST + 0.5*BLK – TOV – FGA
– 0.5*FTA – 0.5*PF

http://wagesofwins.com/2011/12/11/wins- ... -stronger/

A couple of points:

1. PER isn't necessarily a good tool to evaluate player contribution to winning.
2. Player's salary is also correlated to minutes played, PER is a metric adjusted for minutes.
3. Players also get paid for the entertainment factor, star players attract more people, more jersey sales.
4. There are salary restrictions like max or min salaries, which have a HUGE influence on the payments.

http://bbmetrics.wordpress.com/player-ratings/2010-11/

There is a salary listed. That is based on the assumption that an average player (0 SPM and average amount of minutes played) should get average salary ($5.8m). The overall salary sums up to the overall paid salary last season (ESCROW included). As you can see James should have gotten around $30m based on that model, while in reality he got $14.5m. In reality that means that some players got more money than their performance level suggested. That is just an issue creating by the salary restrictions.

Overall I hardly see much value in such analysis based on PER alone anyway, and given the structure of the CBA, you can't draw much conclusions out of this.

If you are going to look at play vs performance you have to start with some base... and then deal with the layers of complexity.

There are several version of SPM which have been translated into "value". I haven't seen it done with APM. It would be pretty straightforward to do and would be worthwhile to see much it differs from the value conclusions from SPM. There are some cases whether the valuations would be very different. Westbrook, Collison, Anthony, Amir Johnson, Tolliver, probably John Wall, Derozan, Monta Ellis, maybe Batum, etc.

I'm not really attempting to draw conclusions from this as much as I am just trying to teach myself programming. I guess I should rephrase the thread subject to "Question about PER" rather than "Using PER" and discussing what I wanted to do with it.