I’m polishing up a longer piece about the very best Ted Williams fun fact, but it’s not quite there yet. Let this tangent, which has been on my mind while writing that piece, tide you over.
In The Kid: The Immortal Life Of Ted Williams, Ben Bradlee, Jr. writes of “when Ted, in perhaps the defining moment of his career, declined the invitation of his manager to sit out the final day of the year to protect his .39955 average, which would have been rounded to .400.”
This is a story I heard countless times in my childhood. Other than the final number itself—.406, the last American or National League batting average over .400—it is probably what I knew best about Ted Williams. It spoke to his confidence, his failure to compromise, his courage in a sense. Truthfully, though, I’m not convinced it was any of those things.
Williams entered the final day’s doubleheader with 179 hits in 448 at-bats. As the story says, that was enough to say .400 on the scoreboard, but of course you, I and our uncles all know that .39955 isn’t “over” .400. That isn’t to say we wouldn’t give Ted Williams any credit for hitting what he hit—and even calling it .400—but, of course, of course it would be a slightly diminished achievement. This would have been especially true in 1941, when hitting .400 wasn’t the unattainable, unthinkable, anachronistically divine round number it is today. Five AL/NL players had hit .400 a total of eight times in Ted Williams’ lifetime, including Bill Terry just 11 years earlier. Two other hitters since 1935 had hit .400 into mid-September, and Joe DiMaggio (.409 on September 9, 1939) seems like he would have finished over .400 had his manager not forced him to slump through an eye infection in the season’s final weeks. Williams in 1941 wouldn’t have known or thought that he was going to go down as the last .400 hitter ever; he would have thought, at .39955, he would go down as the worst .400 hitter.
And, so, to really really hit .400 he needed to do more than sit out the last day. This might seem scary and risky. But Ted was a smart guy. Smart enough, I think, to recognize this odd statistical fluke: If a batter enters a doubleheader hitting .399, he is more likely to improve his average than decrease it, even if his true talent is as low as, say, .300.
How can this be! How can a .300 hitter be favored to hit better than .400 in a single day? The succinct answer is that he benefits from the ability to stop whenever he wants. The slightly less succinct answer is that batting average is a binary-outcomes measure, which means the averages in small clusters are illusions.
Say Ted Williams starts the last day of the season hitting .399. Say his true talent is not .400 but .300. He commits to taking his first two at-bats and seeing where he stands. He can go:
Out, Hit (which a .300 hitter would do 21 percent of the time): His average for the season goes up to .40000
Hit, Out (21 percent): .40000
Out, Out (49 percent): .39777
Hit, Hit (9 percent): .40222
So a .300 hitter is slightly favored to hit .500 (or better!) in a single two-at-bat sequence. This would push his average to a real, unrounded .400 (or better!) after two at-bats. In the first two of those bulletpoints, he can safely remove himself from the rest of the day’s play, knowing that nobody will ever invent an asterisk to put next to his .400 batting average. In the last, he can keep going, since it would then take three more outs in a row to drop him below .400, and he could always safely opt out after just two.
Even in the disaster scenario—the 49 percent of sequences in which he goes 0-for-2, and falls further from .400—he’s not in a hopeless situation, since there will be plenty of at-bats still to go. It’s a doubleheader, after all. If he can just go 2-for-his-next-2, 3-for-5 or 4-for-7, he’ll get back over .400. Again assuming he is only a .300 true talent hitter, he’s got almost a one-in-four chance of climbing back over .400 from .39777. That means that, on the day, he has about a 60 percent chance of getting back over .400 at some point in a doubleheader if he starts it just a fraction under.
And that’s assuming he’s a .300 true-talent hitter! Ted was better than .350 for his career at that point, and a .350 hitter would have a 58 percent chance of being over .400 after two at-bats, and more like 70 percent to top .400 at some point in a doubleheader.
And everything that day was in Williams’ favor. In that final-day doubleheader, the Red Sox were facing two rookie starters who had made a combined six major league starts, and who were both right-handed, so that was all in his favor. Philadelphia was a last-place team with the worst overall pitching staff in the American League, so that was in his favor. And, while Philadelphia pitchers were at pains to declare that their manager had forbade them from grooving any pitches, well, they and their manager had to say that. Given the way these things were treated in the era, there was always the chance these opposing pitchers could feed Ted pipe shots, quietly rooting for the chance to contribute to history.
But wait, you say. Ted had vowed that week to play every game, so we can’t assume he would have quit mid-game once he was legitimately above .400. Sure, but: Probably he was lying? People say things like that all the time. We all compromise in our lives, but we generally don’t broadcast those compromises ahead of time. Anyway, his manager said no such thing. His manager made it very clear that he’d pull Ted if he needed to to protect .400. He deferred to Ted on starting the final day’s doubleheader because, like Ted, he knew Ted hadn’t really accomplished the big thing yet.
This isn’t to deny that Ted Williams met the moment and came up big under pressure. That final day—he had hits in his first four at-bats and went 6-for-8 in the doubleheader—was, in fact, perhaps the defining moment of his career. It’s the decision to play that wasn’t. That decision was kind of obvious. He had a lot less to gain by sitting out than the premise pretends, and he had a lot more likelihood of success than the task seems to suggest.
We just watched Good Will Hunting with the kids for family movie night, so I’m now SO motivated to hang a white board in their hallway with “PROVE: If a batter enters a doubleheader hitting .399, he is more likely to improve his average than decrease it, even if his true talent is as low as, say, .300.”
This one was a blast! What a cool way of looking at the decision.