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Quickie – The distance-elasticity of extra point successes September 14, 2015

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The NFL moved the lineup for the point-after-touchdown from the 2 to the 15; since the ball is snapped back eight yards, and the end zone is ten yards deep, the kick moved from a twenty-yard kick to a 33-yard kick.

There were a couple of oddities this week so far, including a 48-yard extra point kicked by the Browns yesterday. Also, an unusual number of PATs were missed. In 68 extra-point attempts, 64 were successful, for a completion rate of 94.11%. Last year, in week 1’s Sunday games, 60 attempts were made, and 59 were successful (98.33%). If you include all Week 1 games, that percentage rises to 98.61% (71 out of 72). We can roughly estimate the PAT’s sensitivity to distance using an elasticity formula, percentage change in completions over percentage change in distance.

Percentage change in completion rate = 100*(98.61 – 94.11)/94.11 = 4.78

Percentage change in distance = 100*(33-20)/20 = 65

4.78/65 = .07, meaning that a 1% change in the distance would yield about a .07% change in completion rate. Since teams pretty rarely kick field goals from the 15, it’s tough to calibrate that to other data, but it’s likely that this isn’t a constant-elasticity function. A small change close to the goal line probably has a very small effect (as demonstrated), but a small change further away would likely be a much bigger deal.