Bill James takes a look at when leads become insurmountable in college basketball. In other words, when should CBS cut away from the UNC-Mt. Saint Mary's game to show us the barn-burner between Vanderbilt and Siena?
James' formula uses the lead in points, who has the ball, and seconds remaining to tell us if the lead is completely insurmountable. Here it is in a nutshell:
- x= (Lead - 3 +/- .5) 2 -- [+.5 if winning team has possession, -.5 if not]
- If x > time remaining in sec, the lead is insurmountable
I'd agree that it is highly unlikely that such a team would win, but I think James has been taken in by the gambler's fallacy. He writes "The theory of a safe lead is that to overcome it requires a series of events so improbable as to be essentially impossible. If the "dead" team pulls back over the safety line, that just means that they got some part of the impossible sequence—not that they have a meaningful chance to run the whole thing."
It seems to me that if a team climbs back into contention, it's in contention. If a sequence of events are independent, it doesn't matter how lucky or how impossible previous events were. They're water under the bridge. For example, (from Wikipedia) the probability of flipping 21 heads in a row, with a fair coin is 1 in 2,097,152, but the probability of flipping a head after having already flipped 20 heads in a row is simply 0.5
The only thing that matters is the current situation. It's like saying, "There's no way they'll hit another 3-pointer. They just hit five in a row. They're due to miss."
What does this have to do with football? It would be interesting to look at something similar in the NFL. When is a lead so safe that a team should stop throwing? Or when is it so safe a team should only throw on 3rd down? And so on. Basically, when should a winning team stop trying to gain a bigger lead and start trying to simply prevent big mistakes?