As I write this, we are about to start the 2020 Major League Baseball Season, long delayed by the COVID-19 pandemic and full of so many variations from the usual that I’m calling it the Asterisk Season. I had a conversation with some fellow baseball fans about this, and the question came up: are we likely to see someone achieve a .400 batting average in what will be only a sixty game season? It hasn’t happened since Hall of Famer Ted Williams notched a .406 batting average in 1941. There are a lot of contributing factors, but I’ll stick to just one which relates to Lean Six Sigma, called “The Reversion to the Mean.” If you flip a fair coin, on average it will be heads fifty percent of the time and tails the other fifty percent of the time. However, that 50/50 split is not often achieved with just a few flips. You could flip a string of heads in a row without getting a tail. But, over time, the average will move back toward, or revert, to that 50/50 expectation. Let’s move that idea to the baseball park. What makes the .400 batting average so difficult to achieve is that a typical player might have 500 at bats or more a year. But that’s for the standard 162 game season, not the shortened 60 game season. So let’s say I as a player start out really hot, say, batting .500 for the first twelve games. Given five at-bats per game, I have 30 hits in 60 at-bats. And I’m already through 20 percent of the season. There’s less time to “revert to the mean” batting average. According to a table I found online, that number ranges from the low .240s to as high as .271 since the 1941 season, when Ted Williams hit .406. If I get five at bats in each of the remaining 48 games, or another 240 at bats, I only need another 90 hits, for a total of 120 hits in 400 at bats, which is an exactly .400 batting average. 90 hits in 240 at bats is still a pretty blistering pace of .375. But if I have the whole rest of a real season to go after twelve games, I have to bat a lot more times. The chances that my average will go below .400 are much greater, because there’s more time to “revert to the mean.” On the other hand, if it’s me, I’m more likely to get zero hits in the first twelve games. Assuming I’m not demoted to the Triple Z minor leagues, I have to make up the deficit to .400 a lot faster with only 48 games remaining than with 150 games remaining. I’d have to get 120 hits in the 240 at bats that are left, which means I have to hit .500! I’m not mathematically eliminated, strictly speaking, but practically speaking, I’d be good just getting up to the, well, average average. Well, that was a lot of numbers. Besides the hypothetical ability to get one’s name in the record books next to Ted Williams, there are other places to apply “reversion to the mean,” which we’ll cover in future posts. Meanwhile, play ball! ... |