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By Root 538 0

will throw; whether his hand-eye coordination works just perfectly as he takes his swing; whether that brunette he met at the bar kept him up too late or the chili-cheese dog with garlic fries he had for breakfast soured his stomach. If not for all the unpredictable factors, a player would either hit a home run on every at bat or fail to do so. Instead, for each at bat all you can say is that he has a certain probability of hitting a home run and a certain probability of failing to hit one. Over the hundreds of at bats he has each year, those random factors usually average out and result in some typical home run production that increases as the player becomes more skillful and then eventually decreases owing to the same process that etches wrinkles in his handsome face. But sometimes the random factors don’t average out. How often does that happen, and how large is the aberration?

From the player’s yearly statistics you can estimate his probability of hitting a home run at each opportunity—that is, on each trip to the plate.19 In 1960, the year before his record year, Roger Maris hit 1 home run for every 14.7 opportunities (about the same as his home run output averaged over his four prime years). Let’s call this performance normal Maris. You can model the home run hitting skill of normal Maris this way: Imagine a coin that comes up heads on average not 1 time every 2 tosses but 1 time every 14.7. Then flip that coin 1 time for every trip to the plate and award Maris 1 home run every time the coin comes up heads. If you want to match, say, Maris’s 1961 season, you flip the coin once for every home run opportunity he had that year. By that method you can generate a whole series of alternative 1961 seasons in which Maris’s skill level matches the home run totals of normal-Maris. The results of those mock seasons illustrate the range of accomplishment that normal Maris could have expected in 1961 if his talent had not spiked—that is, given only his “normal” home run ability plus the effects of pure luck.

To have actually performed this experiment, I’d have needed a rather odd coin, a rather strong wrist, and a leave of absence from college. In practice the mathematics of randomness allowed me to do the analysis employing equations and a computer. In most of my imaginary 1961 seasons, normal Maris’s home run output was, not surprisingly, in the range that was normal for Maris. Some mock seasons he hit a few more, some a few less. Only rarely did he hit a lot more or a lot less. How frequently did normal Maris’s talent produce Ruthian results?

I had expected normal Maris’s chances of matching Ruth’s record to be roughly equal to Jack Whittaker’s when he plopped down an extra dollar as he bought breakfast biscuits at a convenience store a few years back and ended up winning $314 million in his state Powerball lottery. That’s what a less talented player’s chances would have been. But normal Maris, though not Ruthian, was still far above average at hitting home runs. And so normal Maris’s probability of producing a record output by chance was not microscopic: he matched or broke Ruth’s record about 1 time every 32 seasons. That might not sound like good odds, and you probably wouldn’t have wanted to bet on either Maris or the year 1961 in particular. But those odds lead to a striking conclusion. To see why, let’s now ask a more interesting question. Let’s consider all players with the talent of normal Maris and the entire seventy-year period from Ruth’s record to the start of the “steroid era” (when, because of players’ drug use, home runs became far more common). What are the odds that some player at some time would have matched or broken Ruth’s record by chance alone? Is it reasonable to believe that Maris just happened to be the recipient of the lucky aberrant season?

History shows that in that period there was about 1 player every 3 years with both the talent and the opportunities comparable to those of normal Maris in 1961. When you add it all up, that makes the probability that by chance alone one of those players would