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If the Berger-Pope study (NY Times, March 15) becomes widely accepted, we eventually will see accounts like this.
WILEY’S BRILLIANT PLOY
Battling against University’s fabulous five for the National Championship, State trailed by a single point as halftime approached. We know from Berger and Pope’s work that wins stem more often from one point halftime deficits than from ties or from one point leads.
As the halftime buzzer sounded, University’s Coach U. R. Cagey aimed numerous obscenities at the referees. Cagey knew a technical foul and a State free throw would deny State its hard-earned motivational halftime edge. But State’s coach I. M. Wiley intervened ingeniously by choosing Joe Clank, their worst shooter, to take the foul shot. Clank’s ensuing miss preserved State’s fragile halftime advantage.
After intermission, State’s players, embarrassed but energized by their deficit, exploded for an insurmountable second half lead. In the following weeks, State’s fans, basking in their first NCAA Championship, canonized Wiley and Clank as heroes, Wiley for his brilliant substitution, and Clank for his fouled shot.
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Note: Berger and Pope actually said their statistical test was against a hypothesized win rate of less than 50% (about 46%). But beating 50% is why the article is being ballyhooed, and the exposition has misled many readers on this point. -CNM
3 responses so far ↓
1 Jason Rosenfeld // Mar 20, 2009 at 11:58 pm
I very much agreee.
I mainly think that this article is an example of one that looks pretty hard for something significant and then writes about the result that is sexiest. Of course, you are bound to find something interesting if you look hard enough.
In any case, that’s not at all to say that their numbers are wrong, and it was certainly an interesting little study–but I fear it is more misleading than anything else. The title indicates precisely that being behind by a point actually increases your chance of winning…that’s the main message delivered.
But, as Professor Gelman blogs, ” It all depends on the comparison point. No, the difference in probability of winning is not statistically significantly lower if you’re up by 1 than if you’re down by 1. But, Yes, the difference is significant between the data and their continuous model. ” http://www.stat.columbia.edu/~gelman/blog/
In other words, it seems like they got a result different from expected, but then used that to jump to the conclusion that being behind translates to later being ahead.
side note-From one of their graphs, it appears that being ahead at halftime by 4 is actually worse than begin ahead by 3, but being ahead by 3 is better than being ahead by 2. From this should I conclude that being ahead by 4 makes a team too complacent, while being ahead by 3 is enough to give them an edge but not enough to make them lackadaisacal?
2 Alex D'Amour // Mar 22, 2009 at 1:17 pm
This post is hilarious, and makes it clear why we should be wary about claims that seem to imply that win probability is not strictly increasing in point scoring.
The blog posting that Jason is referring to is very good in clarifying what the results of the paper actually state. Unfortunately, Prof. Gelman’s blog doesn’t have permalinks, but the post is called “More on the question of whether it’s better to be one point behind at halftime”.
I’m not sure if Berger and Pope intentionally made their language ambiguous, but it is true that their result is much weaker than what the New York Times headline would imply. As Jason points out, we’re not comparing the down-by-one team to the up-by-one team. We’re comparing the down-by-one team to a hypothetical down-by-one team that doesn’t get the boost.
The question is how to generate a baseline against which to compare a team’s actual winning percentage to see whether they win more often than the point differential would imply. Given Berger and Pope’s assumptions, teams behind by 1 point do win statistically significantly more than they ought to. I think it is an open question whether polynomial fitting or splining is actually the best way to test this hypothesis. As Jason points out again, the results also show interesting deviations from the baseline at 4 and 7-point differentials.
It might be interesting to construct a stochastic model that models basketball and other sports more mechanistically to generate the baseline. We might also consider a non-parametric test where we shuffle the order of plays to test the dependence of their outcomes on being behind at halftime.
3 Mayweather vs Marquez // Jun 4, 2009 at 11:58 pm
Hope you’ll succeed in whatever decision you will make in the future. Good luck everyone.
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