End of game strategy in football

Something that isn’t captured very cleanly by the game theory distinction between perfect and imperfect information games is this kind of situation:

Houston has the ball at the Detroit 40, fourth and four yards to go, 1:56 remaining, tie game. Detroit has two time outs left.

Formally speaking this isn’t a perfect information game, because the two teams move simultaneously on each play, and neither knows what the other is going to do, so it’s more rock/paper/scissors than chess. Also the moves can involve deception, as in poker (you can bluff a blitz, fake a handoff etc.), so information is imperfect in that sense as well.

Other complications in terms of third party analysis include that coaches certainly know things that fans don’t about the mental and physical state of individual players and so forth.

All that said, it’s remarkable how bad so many coaches, including some otherwise apparently excellent coaches like DeMeco Ryans, are at making end of game decisions.

In the above situation Ryans opted to have his kicker attempt a 58-yard field goal. This seemed like an almost bizarrely bad call to me. First while Houston has a great kicker — a related topic is how absurdly good NFL kickers have now gotten — only two of his 230 career field goals have been as long as 58 yards, although he did have a 59-yarder earlier this year, along with a 61-yarder three years ago. I mean realistically what are his odds of making a 58-yarder? 50% seems generous to me, even if we don’t discount for the extreme pressure of the situation.

Now here’s the part that makes no sense: EVEN IF HE MAKES IT this gives the ball back to Detroit’s high-powered offense against an understandably worn out Houston defense with nearly two minutes to go and two time outs. With Detroit using all four downs on every possession, and having a great long distance kicker of its own, the odds that the Lions will either tie the game to sent it to OT or win it outright in regulation have got to be north of 50%. Meanwhile, if Houston’s kicker misses the attempt, Detroit is extremely likely to gain the less than 20 yards it needs to have an excellent shot at a game-winning FG with no time remaining.

On the other hand, if Houston goes for it on 4th and four and makes it, this accomplishes two equally critical things: you go from a FG attempt at the very edge of the kicker’s range to a much easier attempt, and you get to run out the clock in the process, so your worst case scenario, if you make the first down, is that you end up going to OT.

I can’t see any combination of back of the envelope probabilities that makes going for the first down anything but the obviously correct call here. And every week we see similarly inexplicable decisions from the coaches at the top of the profession, including coaches who are obviously excellent at most aspects of a very complicated multi-faceted job. But not this part of the job for some reason.