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NFL Sunday critical field goals -- OT (math)

Posted By: Chuck Bower
Date: Wednesday, 25 January 2012, at 5:57 p.m.

In Response To: NFL Sunday critical field goals -- OT (math) (Casper van der Tak)

Did you try to estimate a log form? No.

Did you take into account the number of observations in your weighting (not sure about how you weighted)? Yes. variance = ri(1-ri)/ni computed for each i (that is, for each FG distance).

Technically, you cannot use least squares because your success rate is between 0 and 1. You are supposed to use an estimator like Probit... I suppose you mean "should not" as opposed to "cannot". :) Not familiar with the limitation you express (nor the estimator 'Probit').

I am not sure, but maybe you need to look into error in variable models. Normal regressions assume that distance is measured exactly, not sure that that would apply here. This is complicated, so if you believe distances as reported are reasonably accurate (say plus minus 1 yard), better forget about it. The precision of the NFL data is in 1 yard increments, (rounded, I believe, except that when referring to field positions: if closer to 0, 1 is used). I assume (based upon limited observation) the accuracy is of similar size.

I do appreciate positive suggestions, from some people more than others (and you're included in the former, Casper). It would probably be better if I posted a plot but there is some proprietary info (not all of it owned completely by us). If I were writing an article for a refereed journal it would be more important to dot every i and cross every t. As it stands (this forum and the NFL related entities, including the popular press) I'm pretty confident no one has done a better job than I have on this particular topic, but more importantly any better job would be "gilding the lilly" in the sense that the difference in the two methods would be small compared to the statistical uncertainties inherent in the limited amount of data.

Ideally one would prefer to break things down by environmental conditions and performance of specific players. I don't believe the data set is sufficiently large to draw much of a conclusion here, though. BTW, this is particularly evident in the longest distances (say > 50 yards) partly because the NFL rules bias against this length of kick and partly because of coaching bias. The best data (IMO) for long distances would be practice kicks which actually occur before games. AFAIK these data are not officially recorded, and probably not unofficially recorded, either.

Not surprisingly, Wikipedia has a nice writeup on the subject of this kind of field goal. It was nice to see some "existence proofs" like this one:


although a little more detail (e.g. wind conditions) would have been nice.

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