Before this probable nonsense about 'fouling while leading' gets spread

Hi everyone,

I thought about letting it slip, but then I read this quite from an SI.com article:

"28. The most staggering NBA stat from Sloan? Fouling when winning can increase your chances by 11 percent, according to a paper written by Franklin Kenter of Rice University. The paper shows that fouling near the end of games pretty much makes sense in every situation, whether you’re trailing or leading. When behind, it advises fouling one minute out for every six points you are behind. When leading, it suggests fouling one minute out for every three points you lead."

Side note here: 'The paper shows that fouling...' is a typical case of 'reporter overstates what scientist says'. I guess 'The paper says that their model indicates...' would be more realistic.

But more or less, that's what the paper said. Their reasoning was the following:

"The concept of fouling when ahead may be counterintuitive. However, toward the end of the game, the main goal of the trailing team is to increase the total variance in order to widen the window of possibilities that win the game. One main component in this wider variance is the riskier 3-point shot. The trailing team can limit this variance by fouling. the leading team may give up points, on average, but limit the trailing team to 2 points per possession. This decreases the total variance and, with a sufficient lead, increases the leading team’s chances of winning."

Now, I could go on a very lengthy statistical rant about this. I tried to figure out where they made the mistake in their model, but the paper was too vague in terms of their methods.
The point is this:

1. Fouling stops the clock earlier than shooting. Even if you wait 3 or 4 seconds, the possession is still much shorter than what you would need until you get a half way descend three point shot
2. This easily doubles the number of possessions
3. Increased number of possessions increases the variance

This last point is crucial. If you have two times more possessions, the variance increases by square root of two. 

And that the number of possessions would only double is a very weak assumption. If you foul to late, things like this can happen easily.

I don't want to say that the whole paper is nonesense. But regarding the part that contains the punchline (the leading team should foul), either the assumptions of the paper are very generous, or just plain wrong. So, please don't start fouling while ypou are leading in your rec league games.

Cheers,

Hannes