Numerate Coaching in Sports

Moneyball documented the rising importance of numeracy in baseball coaching, starting with Billy Beane at Oakland in the late 1990s: gratifyingly for nerds this has spread to other sports.  There was a hint of this in a Thanksgiving game of American Football this evening (it's a good game for armchair coaches).

Dallas was behind by 22 points early in the fourth quarter.  The scoring system is that you score six points for a 'touchdown', and that qualifies you to attempt to kick a 'point after' - like a conversion in rugby.  As an alternative to the point after you can opt to try to score again from the two yard line: that's worth two points.  More easily than scoring a touchdown, you can get three points for a 'field goal' - the difference of 22 points was a difference of four converted touchdowns against two field goals.  In practice the success rate for two-point attempts is about 48%, whereas points after are a near certainty, assuming a regular kicker in reasonable playing conditions, so the two-point option is selected only at certain scores late in the game.

And this was one of them.  Dallas scored a touchdown, and tried (successfully) for two points.  This is clearly the correct strategy.  The only real chance of getting anything out of the game from 22 points down was to outscore their opponents by three touchdowns to none over the remainder of the game, and to get at least one two-point conversion.  It was right to make the attempt at the first opportunity because if it succeeded they could revert to points after following the next two (presumed) touchdowns*, whereas if it failed they could attempt to compensate with two more two-point attempts.

There's a more common application of this sort of strategy for a team behind by 14 points late enough in the game that its only chance is to score two touchdowns to none.  The correct strategy** is to attempt two points after the first touchdown, because if you fail you can attempt to compensate by scoring two points after the next, whereas if you succeed you can win the game with a point after the next touchdown.

However, having reduced the deficit to 14 points, Dallas did score another touchdown, and kicked a point after instead of trying for another two.  So perhaps I've overestimated the coach's intelligence.  Or perhaps he understood what he ought to do, but lacked the courage to do it.

Unsurprisingly enough, none of this affected the result.  Dallas lost.
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*This consideration is sufficient to demonstrate the correctness of the strategy, but as the rest of the post suggests, it's not the whole story

**Assuming that points after are certain, this latter strategy is correct if the two-point success rate is more than (3-sqrt(5))/2, about 38.2%.