Brett Favre became a grandfather last week, and all indications are that he would become the first ever grandfather to play in the NFL if he comes back for the 2010 season. Granting that the league has a 90-year history and certainly lacks records for many of the players from the olden days, how unlikely is it that an NFL roster should include a grandfather?

The average length of an NFL career is about 3.5 seasons. Even if you make some conservative allowances, that means the average player is done by age 28. Only 49 players have ever played to age 40; there are seven out of 1,696 available roster spots in the league. Favre is older than 0.295% of the other players from 2009 NFL rosters -- he's an exceptionally old NFL player!

On the other hand, people become grandparents at age 47, on average. So 40 is young, but not that young -- a quickie check with GSS data suggests that it's about one standard deviation from the mean. Presumably there's less variance in NFL player age than grandparent age, which makes him that much more of an outlier comparatively.

If I'm thinking this through right, and my assumptions are close to correct, that means about 16% of grandparents became grandparents at 40 or younger. Moreover, about 22% of American adults are grandparents, meaning about 3.5% of American adults 40 or younger are grandparents. By these calculations, you might be saying, the NFL should have 60 grandfathers! But, that's only the case if we assume age is normally distributed among NFL players, which it of course is not -- it's quite skewed toward the young end, which is much less likely to contain grandfathers. When the average NFL player's career ends he's still almost three standard deviations away from the mean age of grandparenthood. By the time you optimize that 3.5% at age 40, there are only seven players left to look at. So, on average, we'd expect that about a quarter of one player in this group (or zero players, rounded) would be grandfathers. It's a pretty low number. On the other hand, it's high enough that you might expect there to have been another NFL grandfather in the relatively recent past. That there wasn't suggests the work of some additional variables -- income is certainly one on which NFL players differ from the general population significantly.