It’s fairly common knowledge that in major league baseball
left-handed batters, on average, hit better than their right-handed
counterparts. A cursory look at the career leaders in batting average will
convince you that lefties have some kind of advantage. Seven of the
top 10, and 19 of the top 30, are left handers. And remember, most
batters hit right-handed—so a majority of lefties atop the
leaderboard is even more noteworthy.
Batting titles seem to be won disproportionately by left handers as
well. Over the last 50 years, 54 of the 100 batting titles have been
won by left-handed hitters, 35 by righties and 11 by
switch hitters. Again, the lefties seem to have a sizable
advantage. Historically, considering all hitters, lefties have hit for a higher average than
righties, by about 10 to 20 points, although since 2000, the
difference is only about seven points (.270 for lefties, .263 for
If you have ever wondered about the reasons for the lefty advantage,
the first thing you probably thought of is that the left-handed batter
is a couple of steps closer to first base, thus enabling him to beat
out more close plays.
But is that the end of the story? A few more minutes of exercising the
ol’ gray matter and you probably came up with a second reason:
left-handed hitters have the platoon advantage, i.e. they face
opposite-hand pitching, much more often than righty swingers. This is
likely a sizable effect, since left-handed batters (since 2000) have
hit about 20 points higher against right-handed pitching than they have
There is a third possible cause, a more subtle effect, what I call
positional bias. This comes about because certain defensive positions
are only open to right-handed throwers: catcher, second base, third
base and shortstop. Three of these are premium defensive positions and
we can expect reduced offensive production from them, since teams are
willing to sacrifice offense for a strong glove at these key positions.
But since these below-average hitters tend to swing right-handed as
well as throw right-handed, they will bring down the level of the
average right-handed hitter. Does that make sense? The end result would lead to
a higher batting average for left-handed hitters.
I thought it might be interesting to investigate which of these
effects is important in explaining the left/right difference that we
see among hitters. I am going to eliminate switch hitters from the
analysis, since I’m only interested in the left/right difference and switch hitters just confuse the issue. To
keep things simple, I’m also going to confine myself to examining
Closer to first base
Let’s tackle the issue of how much being closer to first base is an
advantage for a left-handed hitter. The first thing to realize is that
speed will only help your batting average on balls fielded by
infielders. If your hit goes through to the outfield, you will get a
hit whether you are Jacoby Ellsbury or David Ortiz. In other words, we
can measure the lefty advantage of being closer to first base by
looking at the frequency of infield hits.
The play-by-play data at Retrosheet have the information we need to
determine how often lefties and righties get infield hits. The table
below shows how often a batter beats out a ground ball for an infield
Infield Hits for Lefty and Right Hitters, 2003-2006 +------+---------------+---------+-----------------+ | bats | GB Fielded | IF Hits | IF Hit Fraction | +------+---------------+---------+-----------------+ | L | 63188 | 4679 | 0.074 | | R | 111969 | 8790 | 0.079 | +------+---------------+---------+-----------------+
The second column gives the number of ground balls that were actually
fielded by an infielder, i.e., I’m removing balls that went through to
the outfield, which all result in hits. The third column gives the
number of hits on these infielder-fielded balls (the infield hits)
and the last column gives the percentage of hits.
Actually, it turns out that left-handed batters, despite being two
steps closer to first base, actually beat out fewer infield
hits than their right-handed counterparts. Whoa! That’s kind of
unexpected, isn’t it?
The reason for this is actually fairly simple: more infield hits are
made on balls hit to the shortstop or third baseman, due to the longer
throw. In particular, very few balls that are fielded by the first baseman go for
infield hits. And right-handed batters hit more grounders to the left
side of the infield, while lefties tend to pull the ball to the first
or second basemen.
In other words, the lefties’ advantage of being closer to first base
is offset by the righties’ advantage of hitting more grounders to the
left side. The end result is that right-handed batters have a
slight advantage in beating out infield hits. That leaves us still
looking for the causes of the lefty advantage in batting average.
Lefty platoon advantage
It is well known that batters tend to hit better when facing an
opposite-hand pitcher. Here are the numbers for 2000-2006
(switch hitters removed):
Platoon Splits, 2000-2006 +------+-----+-------+-------+-------+-------+ | bats | Adv | AVG | OBP | SLG | OPS | +------+-----+-------+-------+-------+-------+ | L | B | 0.275 | 0.356 | 0.452 | 0.808 | | L | P | 0.253 | 0.328 | 0.396 | 0.724 | | R | B | 0.271 | 0.346 | 0.443 | 0.788 | | R | P | 0.260 | 0.323 | 0.414 | 0.737 | +------+-----+-------+-------+-------+-------+
The “Adv” column specifies whether the batter or pitcher had the
platoon advantage. A simple calculation using these platoon splits and the frequency
of having the advantage (77% for lefties, 28% for righties), we might
expect a seven-point advantage for left-handed hitters (in batting
average). Recall that seven is exactly the difference we have seen in
L/R batting averages since 2000. So that’s it, the L/R difference in
batting average is accounted for by platoon effects. We’re done. Right?
Well, no, we’re not quite done. Because there is an important effect
that I mentioned above that we need to look at, namely that the
weak-hitting defensive positions (SS-2B-C) are disproportionately
filled by right-handed batters. These positions require a right-handed
thrower, so the players who play them will tend to hit
right-handed. You can see this in the following table, which shows
the fraction of plate appearances for left-handed, right-handed and
switch hitters, broken down by defensive position:
Proportion of PA's by Position +-----+-------+-------+-------+-------+ | Pos | Left | Right | Both | AVG | +-----+-------+-------+-------+-------+ | C | 0.114 | 0.736 | 0.150 | 0.259 | | 1B | 0.563 | 0.363 | 0.073 | 0.278 | | 2B | 0.154 | 0.588 | 0.258 | 0.273 | | 3B | 0.189 | 0.681 | 0.130 | 0.268 | | SS | 0.054 | 0.660 | 0.287 | 0.269 | | LF | 0.465 | 0.437 | 0.098 | 0.278 | | CF | 0.433 | 0.401 | 0.165 | 0.271 | | RF | 0.424 | 0.497 | 0.079 | 0.276 | +-----+-------+-------+-------+-------+
You can see the tendency for positions with fewer left-handers hitting
for a lower average. So, any investigation into the difference of
left- and right-handed hitters should take this into account.
We can do this by comparing left-handed and right-handed batters who
play the same position. If all the difference in L/R batting
averages is due to this positional effect, the L/R difference should
disappear when we look within a given position.
Actually, instead of making eight different comparisons (one for each
position), I’m going to simplify things by splitting the players into
two groups: 1) 1B-OF, where there is no requirement for a right-handed
thrower and 2) C-2B-3B-SS, where only right-handed throwers may play.
Here are the results for the two groups:
Left- and Right-Handed Batting Average, by Position +------------+--------+--------+-------+-------+-----------+ | Pos | AB_L | AB_R | AVG_L | AVG_R | L_minus_R | +------------+--------+--------+-------+-------+-----------+ | 1B-OF | 243784 | 223599 | 0.276 | 0.275 | 0.001 | | C-3B-SS-2B | 65579 | 343551 | 0.269 | 0.266 | 0.003 | +------------+--------+--------+-------+-------+-----------+
The last column on the right gives the L/R difference in batting
average, left-handers AVG minus right-handers AVG. Here we see that
our seven-point difference in L/R batting average is greatly reduced
once you take into account positional bias. For the 1B-OF group, there
is virtually no advantage to batting lefty. For the other group, the
right-handed-throwers-only guys, there is still a difference, but it’s
much smaller than the overall seven points.
Let’s take a breather
Alright, let’s take a minute to re-group. What have we learned so far?
Well, first, the old saw about lefties having an advantage because
they are closer to first base—well, that’s just bunk,
just another one of those things that we know that happen not to be
On the other hand, left-handed batters do have a much larger
percentage of their plate appearances against opposite-hand pitching and an estimate
of the magnitude of the advantage is in line with the overall L/R
difference in batting average that we observe.
Finally, we have found that once you split the players up into two
groups based on defensive position: players that must throw
right-handed and players who can throw with either hand, the L/R
difference within the two groups is much smaller than the overall
How can we reconcile the last two points? Well, I have a theory and
it goes like this: an apparent advantage, like the platoon advantage
for lefties that we have seen, will generally not show up in the pool
of major league players, once you control for other effects—such as positional bias.
To see how this could be, let’s simplify the problem a bit. Let’s
consider our L/R problem, but assume there is no positional bias—let’s confine ourselves to thinking only about outfielders,
for example. Now, let’s also assume that in our group of major league
outfielders, left-handed batters have an advantage and as a group they
are better hitters than the righties.
Now, if the distribution of talent at the major league level is
similar for left- and right-handed hitters—and there’s no reason to
think it is not (given our assumptions of no positional bias)—then we
might suppose the worst left-handed hitter is better than the worst
righty. We might also suppose that down in the minor leagues, there
is a left-handed hitter who is better than the worst right-handed
major league hitter. This follows if you assume that the very best
minor leaguers are virtually equal to the very worst major leaguers.
So, if there were a discernible gap between left- and right-handed
batters in the major leagues, that gap would be filled by minor league
lefties. This reasoning works if the pool of major and minor league
baseball players form a perfect labor market—true talent
levels are known, there is perfect mobility of players between majors
and minors, etc. This isn’t quite the case, which could be the reason
for the residual difference that we found in L/R batting averages even
after taking positional bias into account. There is also the
possibility that there are other biases of which I haven’t thought
that would lead to a residual L/R difference.
I guess we can sum things up this way: left-handed batters have a
definite advantage over right handers. If Albert Pujols woke up one
day miraculously transformed into a left-hander, he would very likely
be a better hitter than he already is. This has nothing to do with
being closer to first base when he bats, but is rather a consequence
of the fact that he’d face a lot more opposite-hand pitching as a
lefty. (There could be other reasons, too: I have not looked at the
effect of defensive positioning, e.g. holding a runner on at
first base, on left- and right-handed hitters.)
However, the seven-point difference in batting average between lefties
and righties, or most of it anyway, exists
only because of the positional bias. If not for that effect, the
supply of replacement players would even out the L/R difference among
major league batters.