A wide range of commentators have weighed to argue that yes, Bill Belichick made the right call to go for it on 4th and 2 from their own 28 yard line. Many of them use fancy numbers like this post from Advanced NFL Stats:
With 2:00 left and the Colts with only one timeout, a successful conversion wins the game for all practical purposes. A 4th and 2 conversion would be successful 60% of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53% of the time from that field position. The total WP for the 4th down conversion attempt would therefore be:
(0.60 * 1) + (0.40 * (1-0.53)) = 0.79 WP
A punt from the 28 typically nets 38 yards, starting the Colts at their own 34. Teams historically get the TD 30% of the time in that situation. So the punt gives the Pats about a 0.70 WP.
But here’s the problem with football stats — and apologies to people who listen to me bloviate every Sunday about this — but first, they’re based on relatively small sample sizes. An NFL season is 16 games, and in such a small collection of data points, almost anything can happen that would be less likely to occur in a set of 82 games with tons of possessions like the NBA or a 162 game baseball season. So there’s that.
But outside of these sort of larger epistemic questions though, there’s the problem of using this data in real world situations. Simply put, not all 4th and 2 opportunities are created equally. No matter what the statistical averages suggest, there’s no such thing as an “average” situation in sports in the way there is in blackjack or craps. There are 4th and 2 situations when you’re up big, when you’re down big, when you’re playing a bad team, when you’re playing a good team, when your offense is tired, and many, many, many others, all of which are markedly different playing experiences and will lead to markedly different outcomes.
This lack of a truly “average” situation is only complicated by the limits of inference attributable to historical performances in sports. For example, there’s no theoretically sound reason that it would be impossible for a football team to convert on literally every single fourth down opportunity they faced, or, alternatively to fail on every single opportunity. Unlikely? Of course. But the point remains that there’s no immutable law of probability binding these outcomes. As such, how much faith can you really place in a 9 percent increase in Win Probability — especially when you only have 16 games to play?