There is clearly a big disconnect between what projected-point models say you should do, and what conventional wisdom says you should do (see
this as one dramatic example). Neither camp is all right or all wrong, there is a lot of nuance to the discussion.
So the projected point model I details says the average offense against the average defense should go for it on 4th and 2 from the 8 as opposed to kicking the FG. The probability says this decision will on average yield 0.5 more points. If this scenario comes up 100 times, you would score about 50 more points going for it every time than kicking it every time (310 pts vs. 255 pts). However, it does not come up 100 times in a game, but rather just once or twice. Do you really trust your probabilities, or go with your gut? Also, tweak the percentages a little bit and things change. Using NFL data, 1 and goal from the 6 yields about 5.5 pts per possession (not 6.2). So that makes the break-even point 46%. That is, probability states that you should go for it if you feel your chance of getting it is greater than 46%. With a beat-up O against a nationally ranked D, you could certainly make the case that your chance falls below that level. So gut-feeling, coaching intuition, etc. need to factor into the decision making.
However, certain aspects of "conventional" wisdom simply do not hold water. Such as, "always take the points early in the game." Early in the game is when you should maximize point probability. You have no way of knowing what will happen later in the game, but you know that more points is better than fewer points. Thus, the option that yields the highest point probability is the best course of action. You lay out the scenario where Iowa attempted and made the FG instead of going for it, which would have resulted in Wisconsin trying to tie the game late instead of take the lead. But what if Wisconsin had scored multiple TDs during the course of the game, and kicking that FG still leaves Iowa down by 10 points with only 1 likely possession left. Then we could say, "See, we should have gone for the TD instead of kicking the FG." The point is, you never know how the rest of the game will unfold, so you maximize point probability.
Or, "always take the points on the road." Why? In general, home teams have an intrinsic advantage, and all else being equal, will be favored. It is usually advised that the favorite use a more conservative decision making strategy, while the underdog should rely upon higher-risk, higher-reward strategies. So why should a road team, the underdog, choose the conservative strategy instead of maximizing their point probability.
Not everyone is a believer, and that is fine. Run probabilities work great in baseball where you have 162 games, and over the course of a long season those probabilities will come out in your favor. Football is much trickier with only a dozen or so games, each one seeming like a life-or-death affair. Coach Ferentz certainly fell into the conventional wisdom camp up until a couple of years ago. But Belichek bought in a while back, he has clearly convinced the younger Ferentz, and some combination of factors has eventually convinced the elder Ferentz. I, for one, am enjoying it.
