JV-
These aren't bad questions to ask, but are pretty easily dispensed. You want to know if Bronco is aware of and uses these statistics? You'd have to ask him--I doubt anyone here knows. I do know that he pays attention to the trends that Wrubell gives him (and that just makes me wish Greg were an awesome econometrician, not that I fault him for not being one).
But even if Bronco were well aware of these stats, there are some good reasons why he'd still make the choice he did. You mentioned guts, and that's one. A bit more rigorously, Bronco might also be making some legitimate critiques on the use of Romer's paper (and really, Romer's is by far the best analysis out there and your second reference is almost wholly reliant on the first--Romer). I'll also say that I'm a fan of David Romer. But in this article, he has a few problems in application.
1) The data in Romer's paper are all subject to self-selection bias; that is, each choice is made to give the coach or team or owner or fans the best chance of maximizing his optimization function (be it job security, wins, profits, or some convex combination), and that choice may be entirely rational. We don't know because there is no counterfactual--we don't know what would have happened had the opposite decision been made in that same situation. And because we don't know that, it's reasonable to assume that whoever is making the choice is doing so in an optimal way. For example, it may be that coaches choosing to go for it do so because they know they have an ace up their sleeve, or that those choosing to kick know they have little chance of success otherwise but that they have a great punter and solid D (hm hm). It's not like these guys are rolling dice and randomizing over their choices so as to let a researcher come along afterward and figure out what the optimal choice would be on average over all plays for all teams--they're making an informed choice play by play. Romer only has data on the observed outcomes. And he doesn't do anything to try to overcome this selection bias.
2) Even if there were no selection bias (and clearly there is), these data are for the NFL game, and they are valid around the average. Bronco could be making the decision that his offense is performing worse than the average NFL offense (or more accurately, that the gap between his offense and an average NFL offense is larger than the gap betweenTulsa's defense and the average NFL defense), and so his expected payoff is lower. With a hurt QB, an sputtering run game, invisible TEs, and an underperforming O-Line against a Tulsa D that was performing better than advertised, I think that's probably a valid conclusion.
Result: I think Bronco made a good choice, one which is not in contradiction to the best (though still inadequate) statistical analysis out there, and in fact may even support it.
So while I may have a few quibbles with Bronco now and then, No, I certainly don't have any problems with him.
