APBRmetrics

[Dan Rosenbaum]

[Dan Rosenbaum]

Here is an exchange over at the Wages of Wins blog that I think neatly encapsulates the essense of Dave Berri.

http://dberri.wordpress.com/2007/03/21/nba-babble-babble/#comments

After having it pointed out for the umpteenth time that the team adjustment is critical in Wins Produced explaining team wins, Berri pens a several thousand word post that manages to cover no new ground on that issue, except to offer yet another ad hominem attack of yours truly.

Then a poster (not me) asks a very simple and straightforward question.

[Mike G]

Well Dan, he's already had this book printed; what's he going to do -- recall it?

And what did we do before we had the word 'obfuscate'? Wiktionary lists synonyms 'confuse' and 'muddle'; and this:

"To deliberately make more confusing in order to conceal the truth.

Before leaving the scene, the murderer set a fire to obfuscate any evidence of his or her identity. "

I guess 'obfuscation happens' -- but generally over less than murder.
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36% of all statistics are wrong

[Eli W]

OK, I used Berri's formula for estimating Wins Produced without using a team adjustment. This is basically Win Score per minute, adjusted for position (I used the position designations from Doug's Stats, which likely vary from those used by Berri), multiplied by 1.621 and added to 0.104. This gives an estimate of Wins Produced per 48 minutes. I then converted this into estimated Wins Produced by multiplying by minutes and divinding by 48. Using 2003-04 data, I summed estimated WP by team to get an estimate of team wins. Then I looked at how much these corresponded to actual team wins, and compared this to how Wins Produced with a team adjustment corresponded to actual team wins (this is found in a chart on page 110 of the Wages of Wins).

For WP with a team adjustment the average error was 1.67 wins, and the correlation of summed WP to actual team wins was 0.982.

For estimated WP without a team adjustment the average error was 7.10 wins, and the correlation of summed estimated WP to actual team wins was 0.721.

Here's the data:

http://spreadsheets.google.com/pub?key=pLWcAQTLnESuYe23RjQEFUg
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Eli W. (formerly John Quincy)
CountTheBasket.com

[Dan Rosenbaum]

[DLew]

I suspect that given what you just found Berri's actual numbers without the team adjustmet would explain around 75% of team wins. This is pretty much what we expected.

What this means is that his method is not nearly as useful as he claims it to be. First off, assuming all of a team's players return from the previous year and post exactly the same box score statistics, we can still expect a very significant variation in team wins due to that unexplained 25%.

Secondly, this means that any linear weights model that explains 75% of team wins (probably not a particularly tough criteria, but I haven't tried) can be given a team adjustment is then just as good as Wins Produced in every way shape and form.

[Eli W]

Great stuff, Dan. You put my little "study" to shame.
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Eli W. (formerly John Quincy)
CountTheBasket.com

[Dan Rosenbaum]

PREDICTING FUTURE TEAM WINS

As was demonstrated in the previous post, any metric with a team adjustment will explain wins with the same level of accuracy. A more useful barometer for these metrics is how well they predict future team wins. To do this, I have to make a couple assumptions.

(1) Player productivity per minute is the same as in the previous season. (Yes, points per game is used as a per minute productivity metric.)
(2) I assume that all players who played less than 250 minutes in the previous season are perfectly predicted. This abstracts away from predictions on rookies and low minutes players.

I look at the same metrics as in the previous post over the 1993-94 through 2004-05 seasons. Since I am predicting future team wins, the outcome is a season ahead in the 1994-95 through 2005-06 seasons.

OWNW = own wins
WP1PT = Wins Produced with a position and team adjustment
WS1P = Win Score with a position adjustement, but no team adjustment
PTSPGT = Points per Game with a team adjustment
NE1PT = NBA Efficiency with a position and team adjustment
WS2PT = Win Score with a position and team adjustment, where the weight on field goals missed has been changed to -0.7, the weight on free throws missed has been changed to -0.35, the weight on offensive rebounds has been changed to 0.7, and the weight on defensive rebounds has been changed to 0.3.

This alternative Win Score metric is simple and falls more in line with the findings in "A Starting Point for Analyzing Basketball Statistics."

http://www.uncg.edu/eco/rosenbaum/jqas1.doc

[Eli W]

[Dan Rosenbaum]

[Eli W]

Very interesting. I think the most damning finding is that points per game with a team adjustment explains team wins just as well as Wins Produced and predicts future wins better than Wins Produced.

Dan, what metric would you recommend to sports economists for use in their research, assuming they don't have access to adjusted (or even statistical) plus/minus?
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Eli W. (formerly John Quincy)
CountTheBasket.com

[Dan Rosenbaum]

An Update:

Two more posters (neither of which are me) ask what fraction of team wins are explained by Wins Produced without a team adjustment, and we get another response from Berri that refuses to provide the number.

He has already made an argument for why that number is not important, so it really weird that he doesn't just provide it.

But he has an argument about the team adjustment.

[NickS]

Thank you Dan, this whole set of posts is really excellent.

BTW, how does this adjusted WS compare to, for example Mike G's production rating (prior to his team adjustments).

[Dan Rosenbaum]

[Dan Rosenbaum]