APBRmetrics

[Ryan J. Parker]

They're now available online: presentations & videos.
_________________
I am a basketball geek.

[fundamentallysound]

watching the Wayne Winston video - heard his bit on Multicollinearity and wondered about ways of fixing it.

There's a paper written about a multicollinearity fix, here:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1339926

I don't know enough about regressions and stats to know what it all means, but it might be useful for you all here.

[deepak]

I'm definitely no statistician, but here's a thought on addressing the multicollinearity issue.

For each "time segment" with 10 players on the floor, the regression proposed by Dan Rosenbaum went like this:

MARGIN = b0 + b1X1 + b2X2 + . . . + bkXk + e

For 5 home players n=h1,h2,h3,h4,h5, each Xn=1 (so it sums to 5). For 5 road players m=r1,r2,r3,r4,r5, each Xm=-1 (so it sums to -5). It seems like what we want to do is somehow take into account how well each player played in the time segment, and adjust those coefficients accordingly to change the credit/penalty they get towards the margin.

I'll just consider a positive MARGIN (home team outscored road team) and the Xn for home players right now. I'd just like someone to let me know if my thinking is way off on this.

Take an example of a particular time segment in which the 5 home players had the following "box score rating" (let's say SPM), in increasing order: -7, -2, +1, +4, and +10. This means the worst player on the home team played as a -7 according to the box score, and the best player played as a +10. I'd calculate their adjusted coefficients as Xn = 1.48, 1.19, 1.01, 0.84, 0.48, for n=h1,h2,h3,h4,h5. Where:

Xn = 1 + (average(SPM_i, i=h1,h2,h3,h4,h5) - SPM_n) / (SPM_h5 - SPM_h1)

So in the regression the worst performing home player will get the highest positive coefficient (forcing his APM value lower?), and the best performing home player will get the lowest positive coefficient (forcing his APM value higher?).

Am I breaking any rules by fudging those coefficients like that? Would this have the desired effect of ultimately giving more credit to the players that performed better by the boxscore?

[Crow]

Did Wayne Winston go into any detail discussing the differences between his ratings (and method) vs basketballvalue?

Using 18 player cases I could quickly assemble where he gave out his marks the average difference to bv is about 2.2. 5 cases were a difference of more than 2.5, 4 cases of 4 points difference and then Dirk was an 8.5 point difference. In 4 of these 5 cases WW was higher. For the rest is almost evenly split which was higher. Take away these biggest variances the rest were different by less than 1 on average.

I guess Dirk could be an outlier but it is an interesting extreme case. Hard to imagine method differences, which I assumed were at the margin, causing such a large difference. But maybe.
Different methods will report somewhat different answer sets.



This is a off the cuff question but rather than finding the Adjusted +/- solution that fits the data the very best of all possibilities (for one method), what if you looked at the top 10 solutions or 100 or whatever useful max or all within x distance of the best solution and took the average or weighted average or reported the range? Is there are president or support for doing this? Would this provide something akin to the value of a Monte Carlo simulation?

And then perhaps going further and blending the results from runs of somewhat different methods? Would this help improve confidence in the average Adjusted +/= numbers? Is relying on the single best solution too small or weak or unique a base for several hundred ratings?

[fundamentallysound]

[Crow]

Thanks for the response.

[gabefarkas]

[tpryan]

I drop in to see what is happening and I see that I have a call to duty from Gabe. I am busy with a variety of things at the moment but I will try to look at this in a day or two. I also want to read that paper that fundamentallysound linked.

[mtamada]

Ditto.

Grrr, the power strip on my computer went dead just as I was hitting "submit". Here's what I think I wrote (and was lost when my PC went black):

This is double-dipping in a sense, but any system that combines APM with SPM is going to be double-dipping from the +/- and the box scores.

So, the idea is not to treat all five players on the floor equally, but to use SPM or box score stats to try to estimate who made the most contributions in that time frame, and use those results to weight or pre-judge the data before we put it into the regression? Might be a helpful idea. I don't like the formula at first glance, but I have not thought it through. But the underlying idea might be a good one.

I conjecture that we'll get the usual pros and cons -- the result might over-reward a stat-hungry gunner who hits the offensive glass instead of getting back on defense, or a player who goes for the steal instead of playing solid team defense. But maybe the benefits outweigh the disadvantages.

If a fivesome has a successful APM, but mainly via good defense rather than via their own scoring (e.g. if your fivesome plays against Chris Paul, Kobe, LeBron, Duncan, and Dwight Howard for four minutes, and finishes that 4-minute period with a score of 2-2, they did mighty well, but you don't want to give disproportionate credit to the one guy on your fivesome who sank a field goal), then we might want to give less weight to the SPM weights and rely more on ordinary APM. Whereas if they were outscored 10-14 during that stint, you might want to put more weight on the SPM stats, since that group didn't seem to be doing much on Defense anyway, but had okay contributions on offense, which likley can be measured by the box score stats better than the defensive contributions can be.

[mtamada]

[gabefarkas]

[deepak]

[Crow]

[gabefarkas]

[Crow]

rather than finding the Adjusted +/- solution that fits the data the very best of all possibilities

what if you also looked at the next top solutions within x distance of the best solution (those Adjusted solutions sets with just a little bigger standard error than the very best solution set)

and took the average or weighted average for the player Adjusted +/- values found by the set of top solutions instead of the values found by just the very best one]?



That is still the summary of my "answer", brief and conceptual, slightly revised to try to improve clarity.