[jstnrgrs]

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If the success rate is 50% on two point conversions, obviously your expected value is one point. So assuming 100% extra point attempt success rate and 50% 2 point success rate, the two options have equivalent EV(+1), but much different variance.

Of course 100% is obviously not accurate, and from my brief research i think the 2 point conversion success rate is probably more in the 40-45% range.

The key is recognizing the situations where you want higher or lower variance. Obviously if the game is tied with 1 second left, you'd want to reduce variance and kick it, and if you were down 2 with 1 second left, you'd want to increase your variance. Throughout the game obviously the decision would be less clear cut but would depend on the situation. All things equal though you'd want to choose the play with the higher EV, which in my opinion is kicking the extra point for most if not all teams.

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The reason that this is not correct is because by going for 2, you are not just risking the 1 point that you could have kicked. You are also risking other points that come into play when the other team adjusts their strategy to the result of your 2 point attempt.

Suppose a team has a 55% chance of making a 2 point conversion. If they run back the opening kickoff for a touchdown, should they go for 2? I think not.

45% of the time, they miss, and the other team can take the lead with a touchdown.

55% of the time, they are sucesful. Of this 50% of the time, the other team can tie with a touchdown (when they go for two because you did).

So 45% of the time, you would trail by a point if the other team scores.

27.5% of the time, you would be tied if the other team scores.

Only 27.5% of the time, you would lead by two points if the other team scores.

Add to this the fact that if you miss, the other team can tie with 2 field goals, and the argument against going for 2 becomes even stronger.

Unless you are playing a game in which scoring is done with basketball frequency, maximizing your expected points is not the same as maximizing your chance to win.