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Comment by jib | Hacker News Reader

The 4th and 2 on the 2 argument bothers me every time someone brings it up. To me it feels like its an incorrect use of statistics. EV isn't the end all - kicking the field goal has way lower variance. If your goal is winning consistently then giving up high variance high EV plays for low variance slightly lower EV plays is often the right choice, as a football season is made up of a very low number of discrete events.

About 45% of all games finish with a spread of 7 or less according to a quick search. Making a play that has a close to 50% chance of making you be down 3 points is costing you a lot of the margin if you think you are a close favorite.

You can't win more in football but you can lose a sure win, so if you believe you are say a 3-4 point favorite then the right play is to take the field goal every time - giving up the safe points means you take half the games and make them a crap shoot.

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The question specifies "early in the game"; the correct call can and will vary in a late game or late first half situation (and of course depends on the strengths and weaknesses of the teams involved).

As Bill Barnwell of Grantland is fond of saying, in the first half, your only goal is to maximize your expected points. You don't know exactly how many points you're going to need in the game until the end.

The Bill Barnwell aphorism reads pretty empty to me. You could just as easily flip it to: "In the first half, your only goal is to minimize your opponent's expected points. You don't know exactly how many points they will need until the end."

His phrase doesn't really have any impact on the argument being made here unless you really dissect the relative importance of offense versus defense in the game, which requires a lot more evidence to make a case one way or the other.

You have missed the point of what Barnwell is saying. He is saying that tactical calling of plays to trade expected point value against variance do not make sense in the first half, because you don't know how close it's going to be.

To illustrate: in an infinitely long game, you always pick whatever gives you the highest expected value. In a game with one play left, you always pick the play with the highest probability to put you over the amount of points the opponent has, even if has a lower expected value than other plays.

The quote is saying that the first half is more similar to playing an infinitely long game than a game with one play left.

Indeed, the pure point-differential EV isn't enough. And beyond variance, there are mental factors involved: cascading micro-rewards from scoring, thinkability of a win or loss, social dominance.

I believe the NYTimes "4th Down Bot" actually performs a likelihood-of-winning analysis, as well.

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