Will a Player Hit .400 This Season? by Craig Edwards July 1, 2020 The 2020 season, assuming it happens and is completed, is sure to have some quirky statistics that will be tough to wrap our heads around. The home run leader might not even get to 20 dingers this year. A three-win season might lead all of baseball. And while batting average has fallen out of favor as the be-all, end-all of a hitter’s talent at the plate because walks matter and getting a double is better than getting a single, hits are an undoubtedly good pursuit for batters. As such, the aura of batting average still maintains some glow when contemplating the history of baseball. The pursuit of a .400 batting average in a shortened season due to a pandemic will not and should not be viewed with the same historical significance as Ted Williams’ run in 1941, or even George Brett’s 1980 campaign or Tony Gwynn’s strike-shortened 1994 season, but it would make this season a little more fun. Ty Cobb, George Sisler, and Rogers Hornsby all put up batting averages above .400 nearly 100 years ago, while Ted Williams was the last player to hit that mark nearly 80 years ago. The list of players who have even hit .375 since then is a short one: Stan Musial’s .376 (1948), Williams’ .388 (1957), Rod Carew’s .388 (1977), George Brett’s .390 (1980), Tony Gwynn’s .394 (1994), and Larry Walker’s .379 (1999). The last player to hit above .350 was Josh Hamilton, who hit .359 in 2010. History has shown that if a very high batting average is your goal, the odds are very much stacked against you in a full season. Shrink the season down to just 60 games, though, and we might get a fighting chance. For recent examples of players who has gotten close, Eno Sarris pointed to Cody Bellinger, who hit over .400 for quite a while to start last season. Jayson Stark mentioned José Altuve’s 60-game run at .388 back in 2017, and this C. Jackson Cowart piece put together a list of 60-game leaders going back to 2002, with Chipper Jones’ .409 in 2008 the best of all the starts. But what about this season? To keep things as simple as possible, I looked at the projections in our Depth Charts and considered every player projected to receive at least 150 plate appearances. I looked at their projected batting average and current talent level, and ran them through a binomial distribution. To provide some context, here are the top 20 players as well as their chances of hitting .400 if given 540 at-bats in a season. Odds of Hitting .400 in a Full Season Name Projected AVG Probability of .400 (162) Odds (1 in:) Luis Arraez .311 0.000007443 134359 Christian Yelich .303 0.000001052 950777 Jose Altuve .301 0.000000626 1596448 Howie Kendrick .299 0.000000369 2712592 Nolan Arenado .297 0.000000214 4664672 J.D. Martinez .297 0.000000214 4664672 Mike Trout .296 0.000000163 6144816 Freddie Freeman .296 0.000000163 6144816 Rafael Devers .296 0.000000163 6144816 Charlie Blackmon .296 0.000000163 6144816 Alex Verdugo .296 0.000000163 6144816 Ketel Marte .295 0.000000123 8119312 Juan Soto .294 0.000000093 10761145 Daniel Murphy .292 0.000000052 19078906 Jeff McNeil .291 0.000000039 25522544 Michael Brantley .291 0.000000039 25522544 Ozzie Albies .290 0.000000029 34249244 Xander Bogaerts .290 0.000000029 34249244 Cody Bellinger .290 0.000000029 34249244 Vladimir Guerrero Jr. .290 0.000000029 34249244 Those odds are not very good. Even assuming the odds of getting a hit in 31% of at-bats (as with Luis Arraez above) only results in a 1-in-134,000 chance of hitting .400 over an entire season. The odds of seeing a perfect game in any particular game are eight times more greater than a talented player hitting .400. That’s part of the reason it doesn’t happen over the course of a normal season. But what happens in a 60-game slate? Here’s the same list above except with just 200 at-bats. Odds of Hitting .400 in a 60-Game Season Name Projected AVG Probability of .400 (60) Odds (1 in:) Luis Arraez .311 0.47% 211 Christian Yelich .303 0.22% 452 Jose Altuve .301 0.18% 552 Howie Kendrick .299 0.15% 677 Nolan Arenado .297 0.12% 835 J.D. Martinez .297 0.12% 835 Mike Trout .296 0.11% 928 Freddie Freeman .296 0.11% 928 Rafael Devers .296 0.11% 928 Charlie Blackmon .296 0.11% 928 Alex Verdugo .296 0.11% 928 Ketel Marte .295 0.10% 1033 Juan Soto .294 0.09% 1151 Daniel Murphy .292 0.07% 1435 Jeff McNeil .291 0.06% 1605 Michael Brantley .291 0.06% 1605 Ozzie Albies .290 0.06% 1796 Xander Bogaerts .290 0.06% 1796 Cody Bellinger .290 0.06% 1796 Vladimir Guerrero Jr. .290 0.06% 1796 Those odds are much better. If you take those 20 hitters, the odds of one of them hitting .400 this year is around 1-in-50, and if we use all hitters, we end up with around a 3% chance that somebody hits .400 in 2020. That’s a really good chance. I’ll also point out that in 61 Double-A games in 2018, Vladimir Guerrero Jr. hit .402, with his average on the season across three levels ending up at .382. While the cumulative probability of some player hitting .400 is 3.1% using a binomial distribution, the odds are actually higher than that, as pointed out by Dan Szymborksi here: You see this in ZiPS in shorter seasons. In a 200 AB season, ZiPS sees Altuve having a 1-in-130 chance of hitting .400 compared to the 1-in-589 you'd get for a .305 hitter binomial would tell you. — DSzymborski (@DSzymborski) June 28, 2020 Projections are in part an estimate of a player’s true talent. After Arraez above, the next 19 players are within 13 points of each other in terms of batting average. It’s a tightly bunched group, but we can use reliability tests to show why those players are not actually as tightly grouped as we might think; those single estimates are more accurately a range of estimates. Because we are talking about hitting .400, let’s start there. If we observed a player hitting .400 over 540 at-bats in a season, we could rightly estimate their true talent as somewhere between .302 and .350, with some volatility and randomness pushing their batting average up to .400 during that time. We might then say we would estimate their talent level/projection at .326 (averaging .302 and .350), but we are really just estimating based on a large range. If we do the same exercise above over only with 200 at-bats, we could fairly estimate the player’s true talent as somewhere between .266 and .332, with an average right at .299, which is where we see Howie Kendrick above. In a normal year, a player would need a very high talent level to even think a .400 season was possible. In the last 40 years, Wade Boggs, Ichiro Suzuki, Todd Helton, Albert Pujols, Tony Gwynn, Mike Piazza, Vladimir Guerrero, and Joe Mauer were the types of players who might have had a shot at .400. Over just 200 plate appearances, though, we open the possibilities to a whole other tier of hitter. The possibility may still be unlikely, but it is certainly more realistic. As Dan noted in the next tweet in his thread, the chances of hitting .400 go up considerably if you move up a player’s talent level, but don’t fall that much if you drop the level down due to the already slim chance. For example, if you took the top 20 hitters and moved half of them up by 15 points and half of them down by 15 points and repeated the binomial distribution, the odds of a .400 season go to about 1-in-14 even though the total averages remain the same. If we think of the projections more like a spread than a spot-on determination, we can better simulate the odds of a .400 season for the league, even if we aren’t going to get too much closer on an individual basis. Doing thousands of simulations of a 60-game season or having Dan run ZiPS probabilities for .400 hitters might make for a more exacting approach, but simply taking the top 100 hitters and randomly spreading out the projections 20 points or less in either direction gives a 5.3% chance of seeing a hitter put together a .400 season. One out of 18 might not seem outrageously high, but it’s definitely better than we’ve ever seen and could provide an added bit of intrigue to the summer.