[starbird]

If we pretend that kicking the extra point is 100%, the issue becomes very clear: going for it wins the game outright (vs. a guaranteed tie) when the first attempt works, and loses the game outright when both attempts fail. So we're comparing x vs. (1-x)^2, and we can go for it even though x is less than 50%.

(The breakeven point is 38.2% in this case; under your 98% assumption, breakeven falls to 37.1%.)

The NFL coaches remind me of poker players who don't believe in ICM considerations -- they can see that going for two is -pointEV (since .42 is less than half of .98), but don't see that it is nevertheless +gameEV.

Part of the problem, I think, is that head coaches tend to be (a) nonmathematicians, with (b) big egos. It's a lot to ask of such a person that he delegate the key playcalling decisions of the game to some non-football pocket-protector type upstairs.

And the risk is hard to quantify. It's not sufficient to educate the owners (indeed, sometimes it's not possible), because the owners also face pressure from the public. Angry sports-talk fans may not be rational, but they can have a concrete impact on the bottom line. It's entirely possible that maximizing gameEV does not maximize careerEV for the coach, or $EV for the owner.