How incredible was it? A semi-bogus 10th-grade statistical analysis

Last night during the NFC Championship game, Troy Aikman said something along the lines of, "I don't know if fans grasp how incredible this season by the Patriots has been. I'm not sure that I do."

It got me thinking: Could we assign a theoretical probability to this feat? The answer, I concluded, is, "Probably, but I doubt it's whatever half-assed way you'll come up with." While that's most likely true, it didn't stop me from pursuing that half-assed method.

My thinking was that if we treated NFL team win totals from the last fifteen years (arbitrary round number within the salary cap era) as a standard distribution, we could just base the probability on the Z-score for 16 wins. This is problematic for a few reasons: 1) A normal distribution shouldn't have such a limited number of discrete values; 2) a normal distribution should not have reachable limits (i.e. 0 wins and 16 wins); 3) using a normal distribution assumes win totals less than zero and greater than 16 are possible; 4) this is not a normal distribution, but it's not horribly bad either:


Over the last fifteen years, the standard deviation for NFL team wins was 2.96 and has not varied much from year-to-year or decreased because of the salary cap / revenue sharing.


So what does this caveat-loaded analysis tell us? 16 wins represents a Z-score of 2.70, or a probability of 0.35%, or about 1 in 285 NFL team seasons. Divide by 32 teams, and you get about a one-in-nine year event. Again, though, this is actually the probability of a team winning 16 or more games because I don't know enough about statistics to account for a reachable upper-limit, nor do I know how much this flaw distorts the result.

So Troy, the answer to your question is, I don't know, and I was probably the wrong guy to ask.