# The advantage of batting left-handed

by John WalshNovember 15, 2007

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 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.

*John Walsh dabbles in baseball analysis in his spare time. He welcomes questions and comments via e-mail.*