The Wall Street Journal has an article that attempts to defend New England Patriots football coach Bill Belichick's decision to go for a first down rather than punt at the end of Sunday night's game against the Colts:
Brian Burke, a statistician who has studied the results of fourth-down situations in the NFL, says a team in the Patriots' situation had a 79% chance of winning by going for it (either by converting the fourth-and-two or stopping the opponent thereafter). That compares favorably to a 70% probability of preventing a foe from driving down the field for a touchdown following a punt.
The article talks about how "when faced with a decision involving risk, people have an overwhelming tendency to make the supposedly safe choice—to err on the side of caution—even though doing so may lead to worse results." There's a lot of truth in that, and it can apply not only in football but in other situations, from investing to politics and business. It's not clear that Mr. Belichick's decision, even risk-adjusted, was the correct one, though; the Journal article doesn't say whether Mr. Burke's statistics take into account field position or the amount of time left in the game, both of which may shift the probabilities.
The focus in much of the commentary on the odds of success or failure in going for a first down misses the point of what success brings and what failure brings. If New England had punted, then the question is what the probability would be for a team to drive 70+ yards in 2 minutes or less. That was the downside of the punting decision.
Since New England did not punt, the question is what the probability would be for a team to drive 30 yards in 2 minutes or less. That is the downside of the "go for" decision. At least this is just a game, unlike the gambles that policymakers in Washington have to make regarding the economy -- save Lehman? Let it fail? Etc.