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