|Not writing to rub salt in the wound. Just thought the "controversy" over Belichick's decision to go for it on 4th and 2 from the Colts' 30 could be a good topic for your blog post. From what I'm hearing so far, the vast majority of pundits and talking heads are saying the decision is terrible. I haven't done the math myself, but it's fairly straightforward calculation:|
Probability of converting the 4th down + [(1 - Probability of converting the 4th down) * (Probability of stopping the Colts' from the Pats 30 with 2 minutes left)]
You could also take into account probabilities of stuff like the Colts scoring right after a failed conversion, and then the Pats scoring again after that, but I think that would only be a very minor factor.
Anyway, I don't have the raw data to calculate whether or not Belichick's decision was mathematically correct according to the equation above, but I suspect it's close. What really bothers me is that 99% of analysts, including former football coaches, don't even bother to think about the math and just say automatically say that the correct decision is to punt. I think most analysts and coaches automatically choose the "playing not to lose" strategy without actually doing a full analysis of the situation.
I think Belichick's decision may have been an example of an instance where there is incentive for an NFL coach to make uncontroversial, yet mathematically incorrect, decision because most GMs and fans (i.e. the people with hiring and firing capacity) are too ignorant to actually evaluate the merits of many coaching decisions. Fortunately for Belichick, he is pretty untouchable at this point.
Well, one calculation I know for sure is that the Pats Super Bowl chances just decreased by about a factor of 10.
I forget where I read it, but apparently going for it on fourth down is worth it a much larger chunk of the time than conventional wisdom suggests.