I’ve been looking at this model recently, and thinking.

Backstory references, for those who need them: here and here and here.

Pro Football Reference’s AYA statistic as a scoring potential model. The barrier potential represents the idea that scoring chances do not become 100% as the opponents goal line is neared.

If the odds of scoring a touchdown approach 100% as you approach the goal line, then the barrier potential disappears, and the “yards to go” intercept is equal to the value of the touchdown. The values in the PFR model appear to always increase as they approach the goal line. They never go down, the way real values do. Therefore, the model as presented on their pages appears to be a fitted curve, not raw data.

The value they assign the touchdown is 7 points. The EP value of first and goal on the 1 is 6.97 points. 6.97 / 7.00 * 100 = 99.57%. How many of you out there think the chances of scoring a touchdown on the 1 yard line are better than 99%?

More so, the EP value, 1st and goal on the 2 yard line is 6.74. Ok, if the fitting function is linear, or perhaps quadratic, then how do you go 6.74, to 6.97, to 7.00? The difference between 6.74 and 6.97 is 0.23 points. Assuming linearity (not true, as first and 10 points on the other end of the curve typically differ by 0.03 points per yard), you get an extrapolated intercept of 7.20 points.

The PFR model has its issues. The first down intercept seems odd, and it lacks a barrier potential. To what extent this is an artifact of a polynomial (or other curve) fitted to real data remains to be seen.

Update: added a useful Keith Goldner reference, which has a chart giving probabilities of scoring a touchdown.

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