Grantland recently published an article, "Mere Mortals," by Bill Barnwell, which claims that:

Baseball players who accrued at least five qualifying seasons from 1959 through 1988 died at a higher rate than similarly experienced football players from the same time frame. The difference between the two is statistically significant and allows us to reject the null hypothesis; there is a meaningful difference between the mortality rates of baseball players and football players with careers that emulated the [National Institute for Occupational Safety and Health] NIOSH criteria.

The author then goes on to collect data on football and baseball players who played at least five years between 1959 and 1988, and his results are below :

Baseball Football Qualifying Players 1,494 3,088 Alive 1,256 2,694 Deceased 238 394 Mortality Rate15.9 percent12.8 percent

From this table, to his credit, Barnwell calculated confidence intervals for the mortality rate, as well as performing Fisher's Exact Test to test for independence between the rows (dead or alive) and columns (baseball and football). For football players, the 95 percent confidence interval for the mortality rate was (11.6, 13.9), and, for baseball players, the 95 percent confidence interval was (14.1,17.8). The Fisher's Exact Test gives a p-value of about 0.004 and from this he concludes, correctly, that the mortality rate is significantly different between the groups at the 0.01 level.

So, the big question is, as he poses it:

Why is it that baseball players from the '60s, '70s, and '80s are dying more frequently than football players from the same era? Truthfully, as a layman, I can't say with any certainty, and I don't think it's appropriate to speculate. A deeper study into the mortality rates of baseball players that emulated the NIOSH focus on specific causes of death versus the general population might prove valuable.

I'll field this one. Baseball players are dying more often because they are, on average, older than football players. The author never controlled for the age of the players, or any other risk factors, for that matter. In 1959, there were, as far as I can tell, 12 NFL teams each with 40 players. That's 480 players. In 1988, there were 28 teams with 59 players each: a total of 1652. In baseball, in 1959, there were 16 teams with roughly 40 men each, for a total of 640 players. That number in 1988 was 1,040—26 teams with 40 players. So there were almost three and half times more players in the NFL in 1988 than there were in 1959. The number of baseball players only increased about 1.6 times over this same period.

These numbers aren't exact, but the point still stands: The group of football players that has been collected here has a greater proportion of younger people in it than the baseball group. So it's not exactly apples to apples. In fact, it's not even close. You'd expect, just based on the ages of the players in these groups, for baseball players to have higher rates of mortality than the football players. Basically, Grantland demonstrated that the old die more often than the young.

* * *

I wanted to confirm that Grantland's study really had this flaw, so I went and collected data myself and ran a quick analysis to check. My findings? *When age is added to a model predicting death, the effect of the sport on mortality rate completely disappears.* This means that if two players are the exact same age and one played professional football and the other played professional baseball for at least five years and one of those years was between 1959 and 1988, there is no evidence that the baseball player is more likely to be deceased than the football player, and vice versa.

#### Data collection

*Football*
Using R, I scraped Football Almanac to get a list of players' names. I then used this list of players' names to scrape Pro Football Reference to get information about each player's date of birth, age at death (if he has died), the start and end years of his career, height, and weight. (A note about a shortcoming of my data collection for football: If a player had the same name as another player, I collected only one. I believe this is a small issue and will not affect the overall results, but it is worth noting.) In total, the football player data set had 14,396 players.

*Baseball*
Using R, I scraped Baseball Almanac to get a list of players' names. I then used this list of players' names to scrape Baseball Reference to get information about each player's date of birth, age at death (if he has died), the start and end years of his career, height, and weight. For baseball players, I was able to collect all players, including those who had the same name as another player. In total, the baseball player data set had 5,587 players.

#### Time Frame

Both the baseball and football data sets were whittled down to consider only players who played at least five seasons and any of those seasons fell between 1959 and 1988. (These are slightly different standards than in the Barnwell article, but, again, the larger point should remain the same.) This left 2,436 football players and 967 baseball players. The mean age of baseball players in my sample was 64.19 while the mean age of football players was 60.91. (Barnwell tweeted that the difference in ages between his two groups, which were defined slightly differently, was about 24 months.) The mean ages of my two groups is significantly different with a p-value of <0.00000000000001. That's a big deal.

The distribution of the ages of the football and baseball players is displayed below using a density estimator in R. You'll notice that there are many more young players in the football group than in the baseball group. This indicates that mortality rates cannot be compared directly to one another as is done in the Barnwell article.

Think for a minute about the graph below. Without knowing anything about which color represents which sport, which of these two groups should have a higher mortality rate? (Hint: The blue one!)

#### Analysis

*Fisher's Exact Test*
Out of the 2,436 qualifying football players, 259 were deceased, according to Pro Football Reference, for a mortality rate of 10.63 percent. Among baseball players, 137 out of 967 were dead, for a mortality rate of 14.17 percent. Both of these rates are lower than Barnwell's, but are of similar relative magnitudes. Using a Fisher's Exact Test, the null hypothesis of no association is rejected with a p-value of 0.004407, which is essentially identical to Barnwell's p-value of 0.004. So there is a statistically significant difference between these groups. That's a fact.

But ...

*Logistic Regression*
This type of analysis estimates the probability of a certain event—in this case, death—while taking into account multiple factors that could be related to the event. Running a logistic regression model with death as an outcome and only sport as a dummy variable predictor yields a p-value of 0.00384 for the significance of sport being associated with death. This is largely the same result as the Fisher's Exact Test as neither controls for any other variables besides sport.

When age—technically years since birth, since some people are deceased—is added to the model, the effect of sport disappears entirely. The p-value for age is < 2^{-16} and the p-value for sport is 0.441, which is not significant.

#### Conclusions

The conclusions reached in Barnwell's article are at the very least misleading; at worst, they understate the potential dangers of playing football. Is it possible, as Barnwell suggests, that baseball players die at a younger age than football players? I suppose, but I think it's unlikely. In any case the phenomenon is not demonstrated in Barnwell's data.

To reiterate what we've found: A baseball player who enjoyed at least a five-year career (with one of those years falling between 1959 and 1988) is *no more likely to be dead* right now than a football player of the same age who enjoyed at least a five-year career in the same time span.

While it is true that baseball players from this time period are more likely to be deceased than their football counterparts, I have demonstrated here that it is not *because* they played baseball; it's because they are older. It turns out that your age is a more significant predictor of being dead than the sport you played.

*Greg Matthews is a post-doctoral research fellow in biostatistics at the University of Massachusetts. He blogs at Stats in the Wild, where this post originally was published*.