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Using Real Left/Right splits is better...or is it?

By Tom Tippett
January 9, 1997

As game owners know, Diamond Mind publishes modern season disks using each player's real-life stats against left- and right-handed opponents. We also publish Classic Past Seasons that are based on overall stats and have the same left/right differential for every player. This may come as a surprise to many of you, but I'm going to make the argument that the approach of using standard differentials may be the more realistic way to play.

There's been a lot of talk in recent years about new professional baseball leagues. So, to help make my case, I'm going to create a very special one called the Equality Baseball League. Every player in this league has exactly the same skills. The ballparks are exactly the same. Every game is played under perfect, and identical, weather conditions. All managers use the same strategies. Every umpire has the same strike zone. Every batter is right-handed.

But there is one difference. Seventy percent of the pitchers throw right-handed and thirty percent are southpaws. And because it's easier for a RHB to hit against lefties, every one of our identical hitters has the native ability to bat .260 against lefties and .240 against righties. Now, we're not saying that everyone will bat exactly .260 against lefties. Yes, it's true that each time a batter steps to the plate against a lefty, he has a 26% chance of getting a hit. But batters don't get hits .24 or .26 at a time. They get a series of 1's (hits) and 0's (outs) that may or may not average out over a full season.

It is widely accepted by baseball researchers that things usually don't average out over a full season. Pete Palmer asserts that the standard deviation for year-to-year changes in batting averages is about 25 points. The STATS Baseball Scoreboard has featured studies showing that (a) every year some players hit more than their share of line drives that are caught and that (b) their batting average suffers noticeably during those seasons, and (c) most of the time, their average bounces back the next year as these balls start to fall in again. And a review of the baseball encyclopedias provides plenty of anecdotal evidence, too.

To illustrate this last point, I flipped open my copy of Total Baseball and looked at a few guys with long careers. Eddie Mathews' year-to-year change in batting average was up 60 points, down 12, down 1, down 17, up 20, down 41, up 55, down 29, up 29, down 41, and down 2. Willie Mays was down 26, down 23, up 37, up 14, down 34, up 6, down 11, down 4, up 10, down 18, up 21, down 29, and down 25. Kirby Puckett was down 8, up 40, up 4, up 24, down 17, down 41, up 21, up 10, and down 33. Some players are more consistent, but they're the exceptions. In most cases, the player's skills weren't changing dramatically from season to season. It's just that some years a few more balls were hit right at someone. And other years the bloopers fell in a little more often.

Let's go back to our hypothetical EBL. Our hitter has a 26% chance for a hit each time up, so we would expect to see 130 hits in 500 atbats. I ran a simple simulation in which a "coin" was tossed 500 times to represent a full season of atbats. It's a coin that comes up "hit" 26% of the time and "out" 74% of the time. In 5000 seasons, a .260 average was indeed the most common outcome. But I also saw that our hitter would get 150 or more hits, enough for a .300 batting average, 3% of the time. In other words, if there are 100 players in the league who get 500 atbats in a season, we can expect 3 of them to bat .300. Or, to come at it from yet another angle, if our .260 hitter gets 500 atbats every year in his career, he probably won't ever hit .300, but he just might be lucky enough to do it once or even twice.

Returning to Total Baseball for a few more examples, I found that Larry Bowa, a career .260 hitter, batted .300 once. So did Jack Boyle, a career .253 hitter. Jackie Brandt, a career .262 hitter, never did it, but he got within three points twice. Sid Bream, a career .264 hitter, never batted .300 in a full season. Hubie Brooks, a career .269 hitter, did it twice. Jeff Burroughs, with a career average of .261, had a pair of .300 seasons, though just barely. Does anyone really think of Mike Bordick as a legitimate .300 hitter? No. But he did it once, and he has a .262 career average. So it's not unusual for real-life .260 hitters to come up with a .300 average over a full season every once in a while.

But this article isn't about full seasons. It's about left/right splits. In the EBL, the everyday player with 500 total atbats would have 150 of them against lefties. In 150 atbats, we'd expect him to get 39 hits for a .260 average. But there's also a 15% chance that he'd bat .300 or better. Note that the chance of his hitting .300 in 150 atbats is five times better than the chance that he'd hit .300 over a full season. Furthermore, a part-time player who gets only 60 atbats against lefties would have a 29% chance of batting .300, solely due to good luck.

Every big-league season features a relatively small number of everyday players and a much larger number of platoon players, utility players, September callups and others who played only when starters were injured. Suppose playing time is distributed in the EBL the way it was in the majors in 1995. We'd have 582 non-pitchers who came to the plate, and here's how things would break down:

AB vsLH   Players   .300 Chance   Number batting .300 

-------   -------   -----------   ------------------- 

  150+       24        11.6%              3

120-149      77        15.1%             12

 90-119      87        18.6%             16

 60-89       84        22.5%             19

 30-59       99        29.2%             29

  0-30      211        38.2%             81

 Total      582                         160 

Ok, let's take a minute to go through these numbers. There would be 24 players who got at least 150 atbats against lefties. Keep in mind that these are 24 identical players, each of whom has the native ability to bat .260 against lefties. We know they got at least 150 atbats, so lets be conservative and assume they got as many as 200. That still gives them an 11.6% chance of being lucky enough to bat .300 or more. In other words, we can expect three of these players to bat .300 even though their skills say they're .260 hitters.

As we work our way down the list, the number of players in each group gets larger, the number of atbats gets smaller, and the chances grow that luck can produce a .300 hitter. And we find that luck is likely to produce 160 players who bat .300 or better against lefties out of a total pool of 582 players. That's more than a quarter of the player population.

So, we created a fictional league in which everybody had identical talent and identical playing conditions. We said that all of our players batted right-handed and hit .260 against lefties. We allowed for the same amount of luck to be present as we believe exists in real baseball. We distributed playing time using a real-life season as our guide. And we found that, under these conditions, we can expect 27.5% of our players to bat .300 against lefties even though we know, by definition, they are really .260 hitters.

Back to real life. In 1995, there were 582 position players who appeared in at least one game. Exactly 158 of them, or 27.2%, batted at least .300 against left-handed pitching. Does that mean that all of these players are really .300 hitters against lefties? That they would continue to hit .300 if they faced lefties day after day for many seasons? Nope. Not even close. Guys like Frank Thomas, Paul Molitor, Kirby Puckett, Jeff Bagwell, Edgar Martinez, Chuck Knoblauch, and Tim Salmon are that good. But there are a lot of guys who batted .300 against lefties because the bounces went their way in a limited number of plate appearances.

In a real life season, it doesn't really matter if you know that 29 guys who get between 30 and 59 atbats versus lefties will get enough breaks to bat forty points higher than their true talent level would suggest. Why not? Because you don't know which guys are going to do it. And as the season goes along, you don't know which of the lucky ones are going to cool off and which ones will continue to have things go their way. So it doesn't necessarily change how you make your decisions.

But in a computer game that (a) shows you all the stats and (b) rates players based on their real-life results, you can use perfect hindsight to change things dramatically. You can draft the lucky ones and leave the unlucky ones in the free agent pool. You can use the lucky ones to pinch hit in those critical late-inning rallies. And these lucky players end up playing a role in your league that's out of proportion with their real talent level and how they were used in real life.

If you're playing with one of our Classic Past Seasons, you don't see the real-life splits. So you manage based on overall stats (which are also influenced by luck, but less so because there are more plate appearances to go on) and the knowledge that right-handed batters have a certain advantage against lefties. That's what a real-life manager does, and one could argue that it's a lot more realistic than using a pinch hitter just because you know he batted .345 (10 for 29) against lefties last year.