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

righties).

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

against southpaws.

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

batting average.

###### 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
target="new">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

hit:

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?

###### Positional effects

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

true.

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

difference.

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.

###### Conclusions

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.

Baros said...

Another stat to consider which I have never seen discussed is when a leadoff hitter gets on 1rst. According to my point of view and my observations the next batter should always

bunt and put him in scoring position with one out. The chances of scoring a run in that

inning is greatly increased instead of the next hitter hit away. I don’t know why all managers

don’t do this as only good things can happen and no double plays,etc,etc. If stats are looked at I am sure this is true.