APBRmetrics

[DSMok1]

I've been pondering win shares as a proxy for all other 1 number evaluation metrics, and have worked on some additional research in a couple of areas.

First: mean performance, in terms of WS/48. I wanted to get a mean value for a Bayesian prior, based on non-statistical inputs. After a lot of experimentation, I settled on using 3 inputs: Team Efficiency Differential, player Minutes Per Game, and Age.

This chart shows the results:

(Age is set to 27 for this chart.)

What does this show? Basically it states what is well known in chart form. The better the team is, the better a player playing minutes for them will be. The worse the team is, the worse the low-minutes guys will be. "Replacement Level" is .025; note it's position on the graph. If your team is above league average, you won't be playing replacement level players even for 1 MPG (at least not likely).

The age adjustment was independent of MPG and Team Margin. Basically, if a player was younger, he probably wasn't as good (given a specific MPG on a specific quality of team). Younger players are given the benefit of the doubt a little--they are played a bit more than their quality would say they ought to be. However, the effect in these terms is minimal. A young player is only expected to be about .003 worse than a veteran getting the same playing time. Basically negligible.


The overall regression looked like this:

[DSMok1]

Here is some rough work on WS/48 aging curves.

I followed the procedure outlined here: http://www.insidethebook.com/ee/index.php/site/article/basic_aging_curve_for_hitters_1957_2006/

Obviously, survivor bias is a huge issue, and one I don't fully know how to compensate for.

I used matched pairs of all players that had 100 MPG in both years. The fact that a player had 100 MPG in each year biases the older sample towards decline, since in order for a player to get 100 MPG in Y+1 he had to perform to a certain level in Y, perhaps even be lucky. The same is true in early years, biasing towards increase, though not so badly.

To try to solve this, I regressed the first year results, using the 200 minutes of expected WS/48, and compared that to the unadjusted second year results.

Here is the aging curve, showing raw WS/48 and the regressed WS/48. I'm not sure if I regressed the right way....



I'm showing the peak is at 26, rather than 27. That said, I like the looks of the regressed curve, particularly when compared to the minutes we see at each age. If the number of minutes starts to drop significantly at age 27, the players are probably passing their peak. I do expect the minutes to peak earlier than the players themselves, as players in development are given more minutes because of potential improvement.

Note I normalized these curves so the peaks would be at 0.100. In other words: if a player is at a true talent of 0.175 at age 25, he would be projected to be at 0.161 at age 30.

Here are the actual numbers, both for the Raw WS/48 and the Adjusted WS/48:

[jim]

Really good stuff, DSMok1.

[DSMok1]

A few updates:

I ran some year-to-year correlations to estimate the stability of WS/48. I controlled the players used to minimize changes in roles--I used players that had similar MPG, total minutes, and games played in subsequent years. (I was basically attempting to simulate a split-half correlation test, like those used at 525600 Minutes: How do You Measure a Player-in a Year) This estimate of stability can then be used to generate a regression equation, like Tom Tango has done for baseball: r=x/(x+n), where x is the number of minutes, r is the correlation, and n is the number of minutes of baseline/prior expectation to use.

I ended up with 407 year over year data points that fulfilled my criteria. I simply ran a correlation on the 407 points WS/48 points, and also looked at what the average number of minutes in the two years was: 2256 minutes, correlation of 0.7424.

Using Tango's equation (http://www.insidethebook.com/ee/index.php/site/comments/pre_introducing_batted_ball_fip_part_2/, that yields a regression equation for WS/48 of
Regression Rate = 782/(n+782)
where n is the number of minutes. Since we are using year-to-year correlations to approximate this, I rounded this down to 750:
Use 750 minutes of the Bayesian Prior to regress WS/48

Note, I may be doing this all wrong.... but that's why I'm posting here, for review. I'm not totally certain that Tango's regression equation is applicable here.

Anyway, it appears that the use of 200 minutes for regressing WS/48 was low. After correcting for that, here are the top 40 players from last year, in regressed WS/48:

[BobboFitos]

Strange bump maybe, but I've been thinking a ton about aging curves lately. It would be interesting if, rather then lumping "all nba players" together, to break up various player types. The reason for this is certain guys who buck the trend (Nash/Stockton, for example) are/were pass first, insanely good shooters. It seems their games didn't decline at all.

There are a bunch of player classification, but even a simple one based on height first could perhaps show different peaks/etc...
_________________
-Rob

[Manchvegasbob]

I was looking to see what was available for discussion on aging curves and was glad to this thread bumped up.

I had an article posted Forecasting Garnett: 2011 and Beyond and got a kick out of the classic parabolic curve.

I recalled that this 2nd order polynomial predictor show's up in the classic (see NBAstuffer.com)