Expected wins hide how rare a clean 17-0 really is

A roster that is "a 13-win team" sounds close to perfect. It is not. Expected wins are an average. A perfect season is a tail.

Suppose each week is an independent draw and the team's win probability is 13/17, about 0.765. The expected record is 13-4. The probability of 17-0 is 0.765 to the 17th, which is about 1.1 percent. Most of the probability mass sits on 12, 13, and 14 wins. The undefeated outcome is a thin slice of the same distribution people quote when they say the team is "great."

Correlation makes the slice thinner. A short week, an injury, or a bad field does not reshuffle before the next game, so the losses bunch and the right tail shrinks. That is the gap between a season-long win total and a season with no losses at all.

The useful check is to resimulate the card instead of staring at the mean. Draft a short all-time roster from random NFL teams and eras, run the 17 weeks, and count how often the record is actually clean. I do that in a free browser challenge, 17-0 Game. One slot change moves the mean a little and the undefeated rate a lot, which is the whole point of looking at the tail instead of the average.