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
Pretty cool. This is the kind of thing James is really good at. Unfortunately, I think he buys into a logical fallacy later in his article. He says that if a team is deemed to be "dead," that is to say too far behind, but it is able to climb back inside the limits of "insurmountability," it doesn't matter. The losing team is still dead.

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?

1. Phil Birnbaum says:

Yeah, that was weird, when he says the team that comes back is still dead. I guess the one case he cites where the dead team actually came back to win, they were still dead even when they had the lead?

Maybe he means *for the purposes of this stat,* they're still dead.

2. Anonymous says:

For your interest,not entirely relevant to James' equation,but it's in the same ball park,

just started charting last season and I've a few figures on teams play preferences where games are tight and in games where they are well ahead.

The teams who go most run orientated on first down when they are well in front compared to their own run/pass splits when games are close are,in order;Houston,NYJ,Oakland,Tampa,Seattle,
Dallas,Cleveland and Indy.

The top three almost certainly owe their presence to small sample size for games where they are well in front.

The teams who change their run preference least on first down as they protect a big lead are,again in order,Washington,Rams,Zona,KC,Cinci,
Atlanta and Baltimore.

The first three teams in this list actually run proportionately more often on first down in close games than they do when they're well ahead.

NWE are an interesting case.They throw three passes to every two runs on first down when the game is close and although they call slightly more runs than passes when they lead well,they are the team most likely to pass on first down when ahead.

Just second,third and fourth down to go.