Is baseball more hazardous than football in the long run?

Yesterday, I started some research into the question about the life expectancy of pro football players. I chose 100 players at random from the 1960 pro football rosters who were born in 1934 or 1935, and I did likewise with the 1960 major league baseball rosters. All these guys should be between 74 and 76 years old if they are still alive. 29 of the 100 football players on the list are already dead. 30 of the baseball players are likewise.

So I repeated the experiment with a younger group, taking the 1970 rosters and looking at guys born in 1944 or 1945. Now the age range of survivors is between 64 and 66 and we should expect the number of survivors would go up and the number of dead to go down, and these random samples meet these common sense expectations. 9 of 100 pro football players on the random list are dead, while 13 of the 100 major leaguers are gone.

If we do a chi-square significance test, the difference between 13 of 100 and 9 of 100 is not enough for us to say we will see a big difference in the underlying populations. This could easily just be random variation. If I had taken the 100 older ballplayers from yesterday's work and looked at mortality exactly 10 years ago, 11 of that 100 would have been gone. Only 10 of the older football players from yesterday were gone as of March 2000. In other words, we have several samples that say about 10% of 25 year olds don't make it to 65.

Here's the thing. If instead we work with the period life tables conveniently provided by the Social Security Administration, we see that out of 100 American males in the 24-26 age range in 1960, we would expect 37 not to survive to 2010. If we took a similar sample from 1970, about 16 would not survive. In other words, both baseball players and football players show greater longevity than their peers in everyday life.

Are these differences statistically significant? At the sample size of n=100, no. But at larger sample sizes, yes. That's a problem with statistics, and some folks like Dr. Deming considered it a major flaw. But whether the differences are significant or not, this data indicates that athletes actually have greater longevity on average.

Could my data have flaws? Yes. My sampling method might not be random enough, and it could be that Wikipedia and the Baseball-Reference.com and nfl.com have missed some obituary notices, which would mean I incorrectly numbered some dead ballplayers among the living. But the overall message is this. In this case, the news has taken completely bogus numbers to argue for the solution of a problem that doesn't exist. No matter what your political persuasion, you have to believe that this isn't the first time.

Do football players die younger than the rest of us?

I was wandering around the 'Net this week when I ran into a report that pro football players die significantly younger than the general public, and that each year a pro stays in the game takes several years off his life. You can read such reports here, here and here, some written by doctors and others quoting studies by doctors. The article from Newsmax starts with this paragraph.

It is not a widely disseminated, downloaded or discussed fact that the average life expectancy for all pro football players, including all positions and backgrounds, is 55 years. Several insurance carriers say it is 51 years.

Wow, that's written by doctors and backed up by insurance companies. It must be true. Except that other doctors say it's 59.

I know a little about life expectancy from teaching statistics and this set my spider sense tingling. For one thing, people kept quoting different numbers. For another thing, life expectancy in the 50s is what you get in the absolute worst parts of sub-Saharan Africa, and a large part of those numbers being so low is high rates of infant mortality skewing the numbers down. The data for pro sports athletes won't be influenced at all by infant mortality. You have to live past your first birthday to play pro sports.

I don't have the time to compile massive sets of data, so I designed an experiment to see if these numbers had any validity. I took the 1960 rosters from professional football and professional baseball, selected 100 guys from each sport who where born in 1934 or 1935, then checked on Wikipedia to see if they were dead or alive. If a name didn't come up, I went to the Baseball Almanac or nfl.com. I used Wiki first because its search engine is way better. Also, nfl.com just says "deceased" instead of giving a date of death, and I only had to go there for the most obscure players, a total of three guys.

Since these athletes were between the ages of 24 and 26 half a century ago, we would expect by actuarial probability that some would be dead by now, and of course this is correct. 29 of the 100 NFL veterans born 1934 or 1935 are listed as dead as of March 13, 2010, compared to 30 of 100 MLB players. a completely insignificant difference. The ages at death are slightly different but not that much.

decade NFL MLB

20-29__1__0

30-39__0__1

40-49__1__2

50-59__5__4

60-69__15__10

70-76__8__13

Baseball players who died in this study are more likely to have died after the age of 70, while more football players are somewhat more likely to have died while in their 60s. Even so the average age of death for football players was 63 and baseball players was 64. While these numbers seem low, recall that all the guys on this list will eventually die, and 70% on both lists will be over the age of 74 when they go, so the averages will be over 71 at the absolute minimum, probably several years higher.

If I may critique my own study, it makes sense to do a similar data set for guys born in the mid 1920s and mid 1940s to see if baseball vs. football mortality rates show a greater disparity for those different demographic groups. But this first data set makes the idea that football players have an average life expectancy under 60 to be very far fetched indeed.

To the doctors who put their names on these studies, I'll make you a deal. I won't perform any surgeries or prescribe any drugs, and you should stick to addition, subtraction, multiplication and division, because it turns out math is hard for some of us.

But not me.