On July 9, 2013, Sir James Paul McCartney performed at Boston's Fenway Park on one leg of his Out There Tour, which has seen him rocking in an amphitheatre from 30 A.D. and coming under attack by thousands of grasshoppers. While he was at the oldest big league park, footage of him holding a baseball bat was taken, as you can see at the 0:44 mark of this video. Two things immediately appear to the attentive baseball fan: 1) the former Beatle features a Ty Cobb-like split hand grip and 2) he swings from the right side despite being a southpaw.

McCartney is not alone in the latter trait, Rickey Henderson and the elder George Bush being notable precedents. However, throwing from the portside while swinging from starboard is not advantageous, as you forfeit the frequent platoon advantage at the plate, plus the possibility of playing three infield positions.

And catcher.

The longtime ban on lefty backstops is tied to a clear limitation in throwing to the bases. It's not because right-handed batters block the throwing path; righty catchers manage to gun down base stealers with lefties at the plate. (In my modeling, I don't see any difference in caught stealing percentage by batter handedness.) Rather, it’s because of the natural tailing action on thrown baseballs that, for left-handed catchers, would make the assist veer away from the oncoming baserunner.

But is that disadvantage enough to punt altogether on a portion of the talent pool? There are a few reasons why I don't end the article right here with a resounding yes.

First, the attempted steal is not a strategy that happens all that often. Sure, the stolen base is on the upswing now that scoring is down, but would a no-arm catcher have cost his team many runs in the homer-happy ’90s?

Second, in the past few years we have been able to quantify the value of framing pitches, which in a single season has much more of an impact than erasing runners. If a framing wizard like Jose Molina happened to be left-handed, would it be wise to pass up 40 runs saved with a good target because of 10 runs lost as a result of throws tailing the wrong way?

Finally—and this is the big one—what if left-handed catchers actually have an advantage in framing pitches?

The runs lost on the basepaths
Since 1988, the worst catchers in the controlling-the-running-game department have cost their teams roughly 10 runs per season because of their inadequate arms. Here's a distribution of the catcher-seasons in the past quarter century (only catchers with significant playing time are featured).

Note: I prefer the convention of always looking at runs from an offensive point of view, so in the above charts (and others in this article), negative values represent runs saved by the catcher.

One could assume that a left-handed catcher would be the equivalent of the worst right-handed one, inflicting a roughly 10-run penalty to his team. However, like their righty counterparts, southpaw catchers would likely have their own bell-shaped distribution. We can only speculate about whether the best lefty would hardly be superior to the worst righty (as in the left-panel chart below) or the two distributions would have some degree of overlap (right panel).

Here’s a question for you: suppose that Yadier Molina were left-handed. How many runs would he provide/cost his team? Would he be Piazza-esque? Worse than that? Or maybe close to league average? (Since I mentioned Mike Piazza, it's worth noting that he doesn’t appear in the bottom three seasons of steal prevention, but does monopolize the fourth- through sixth-worst positions with his 1996, 2000, and 2001 seasons.)

The worst throwing season overall is an interesting example for our exercise. It belongs to Scott Hatteberg’s 2001. Hatteberg, then playing for the Red Sox, had a sore arm, and opposing teams noticed: he somehow gunned down only 12 runners while allowing 115 steals. The rest of the story makes for some of the more enjoyable moments of Moneyball, as Billy Beane A's made a useful first baseman out of him.

For our purpose, it’s probably safe to assume that a strong-armed lefty catcher would fare better than a dead-armed righty.

Gains on borderline pitches
Now let's look at the distribution of framing runs, again since 1988 (using the Retrosheet-based method I introduced some time ago).

Here we don't have any clue as to whether left-handed catchers would fare worse than right-handed ones (if any comes to your mind, don't hesitate to share your thoughts in the comments below). Supposing a similar distribution for lefties, I would lean toward letting the ones inclined to try the position do so, knowing they’d need to be good at framing to stick there. It’s likely that they wouldn’t have to be the best framers around to make up for their throwing disadvantage: just 1.5 standard deviations above average, assuming they’re at the 2001 Hatteberg throwing level.

My controversial hypothesis
As I mentioned in the introductory section, I suspect that a left-handed catcher might even have an advantage in framing pitches. And since the run-value distribution of framing is a lot wider than that of steal prevention, even a small edge could signify a net gain for the team on defense.

What makes me believe this hypothesis could be true?

Let's start with the catchers themselves. Since right-handed throwers wear their mitt on their left hand, they reach the inside corner against right-handed batters (and the outside corner against left-handed batters) easily. When they have to catch a pitch on the other side of the strike zone—that is, to their own right—they need to stretch their arm a bit across their body. Since framing is in part the art of convincing the umpire that you didn’t move, I’d speculate that it’s easier to display steadiness when the pitch arrives on your glove side.

Now, on to the umpires. Umpires make a slightly higher proportion of incorrect calls on the outside corner than they do on the inside corner. I believe the reason for this is that they usually place themselves on the inside corner, which gives them a better view there. Take a look at this plot:

Above you see how the umpire correctness (using the rulebook strike zone definition) varies on the horizontal plane. The chart is constructed using 2012 four-seam fastballs delivered at mid-height (so that vertical location should not be a factor in judging) that did not feature a swing by the batter.

As one would expect, umpires are close to 100 percent right on down-the-middle pitches, as well as on those far away from the plate. The highest rates of wrong calls occur closer to the edges (the vertical lines in the plot). And for both right-handed and left-handed batters, the outside corner features a greater proportion of miscues.

I would also like to note the difference between the two curves. While the wrong calls when righties are at the plate peak precisely on the plate corners, the line for lefties is shifted slightly to the left. Also, the difference between the outside and inside corners, while barely noticeable for right-handed batters, is huge for southpaws. (I'm not sure I have a good explanation for this, although eye dominance might have something to do with the phenomenon.)

Finally, a brief reminder about the batters: more of them swing from the right side than from the left.

So my speculation revolves around these points:

1. Catchers can exploit the umpires' fallibility, especially on the outside corner;

2. It's easier to look steadier and get calls when the ball is delivered to the catcher's glove side;

3. More right-handed batters than left-handed ones come to the plate, offering more opportunities to left-handed catchers for the favorable combination of the previous two points (outside corner pitch on the catcher's glove side).

The fact that we have zero left-handed catchers in the big leagues (and as far as I know, no trace of any further down the professional ladder) means that this is nothing more concrete than conjecture.

However, we can look for the plausibility of point no. 2 on our righty-only population.

When working on this article, my memory kept summoning sequences from Ben Lindbergh's weekly articles on framing featuring left-handed batters being called out on strikes on pitches just outside the strike zone. And when I started to browse several of Ben's articles, it looked like the lefty hitter/outside pitch combination was indeed dominant.

However, being a statistician, the confirmation bias bell started ringing inside my head, so I decided to go a bit more by the numbers rather than relying on memories that were likely distorted by my underlying hypothesis.

Let's look at the plot below, again featuring mid-height four-seamers from 2012 that weren’t swung at:

The curves displayed above don’t contradict my line of thought.

Catchers gain more extra strikes on their left side, where they don't have to stretch their glove-hand across their body. The difference is big when left-handed batters are at the plate and the glove-side effect compounds the umps-are-more-fallible-on-the-outside-corner one. It is hardly detectable when right-handers are hitting and the two effects nearly cancel each other out.

Let’s be cautious…
In the previous section I made every effort to support my point. However, there are ways to make it seem senseless.

First, the plot displayed last, while showing many gained strikes on the outside corner to lefty batters, also shows a good chunk of strikes lost in the middle-to-inside part of the plate. If a southpaw catcher has a symmetrical effect on right-handed batters, we have to account for the negatives as well as the positives.

Second, between switch-hitting and platoon, the right-handed batters do not outweigh their left-handed colleagues by a wide margin, at least when a right-handed pitcher is on the mound.

Third, I have only looked at fastballs, thereby completely ignoring the possible effect of catcher handedness on pitches with different trajectories.

…but not entrenched
However, while the hypothesis of an advantage in framing might be far fetched, I can’t find any reason for lefties to be at a disadvantage. And given the spread in framing talent, I would lean toward keeping a small door open for southpaw backstops.

Here’s how I would envision the ideal candidate for this out-of-the-box experiment: a lefty first baseman in the minors whose bat appears to be adequate for The Show, but not at an offense-first position, and who isn’t suited for a move to the outfield. Would an infielder-turned-catcher be able to put up better framing numbers than guys who have donned the tools of ignorance since day one? Just ask Russell Martin.