*Stats in this post are current up to right before the July 31, 2014 PIT-ARZ game.*

The MLB non-waiver trade deadline just passed. I’m not interesting in debating what teams should or should not have done except to say the price for quality players was very high this year. The whole supply & demand, free market thing really worked in the favor of teams that were already out of the post season race. It was suggested that the Pirates needed a right-handed batter (RHB), since they don’t do well against left-handed pitching (LHP). I had my doubts this was really true, and adding a good RHB won’t improve the team beyond what general improvements you could expect from that batter. MLB teams generally do better against LHP, since most batters are RHB and the RHB/LHP split favors the batter.

Before getting into this, LHP make up only 21% of the Pirates’ season-to-date plate appearances, out of all the problems the Pirates could have making a roster move to address this isn’t necessary unless you are looking to platoon. More on that later.

Looking at the team batting splits, the Pirates have an overall .722 OPS and a LHP .670 OPS. On the surface, it appears they are performing worse against LHP, and I will concede the argument the Pirates HAVE performed worse against LHP so far in 2014, but this shouldn’t continue going forward.

The Pirates have 4,152 plate appearances racked up thru July 30th, but only 867 of them have occurred against LHP (~21%). To put this in perspective, that is equivalent to less than one month of games. How accurate are batting statistics at the end of April? They aren’t. Put simply the Pirates ‘struggles’ against LHP can mostly be attributed to a small sample size.

I went and laid out all the outcomes (1B, BB, 2B, etc.) in a vector of plate appearances and had the computer randomly draw 900 samples from the entire Pirates season and computed the OPS 1000 different times. Then I plotted them below.

Due to the central limit theorem the mean should hover around .720 (the overall OPS) and the data should be normally distributed. Because of this I constructed the normal distribution curve and then used that to calculate the probability that a 900 plate-appearance sample can be drawn from the Pirates’ total plate appearances. It turns out 9% of the time the program will select plate appearances that total a < .670 OPS. 9% isn't that likely, but it is not outrageous to conclude the Pirates low vsLHP OPS is due to small sample size.
*This is not just applicable to LHP vs overall splits, but any low-count split including RISP. I wrote about this previously and came to a similar conclusion. *

The composite distribution curves below illustrate what happens with sample size increases and why small small sizes are problematic. The vertical line is the .670 OPS mark. On the 900-sample distribution (vs LHP) there is a 9% probability of drawing a .670 OPS from the Pirates’ total plate appearances. This is the area underneath the curve to the left of the red line. Using the 3000-sample distribution curve, it’s 0.0016%. There is barely any area under the 3000-PA curve at that point, and this is a huge difference. (3000 samples are approximately how many the team has against RHP.)

One more graph! This is a histogram of the differences between the LHP OPS and the overall OPS. The Pirates are on the low end of it. Not great, but there’s a lot of variation there.

Switching from statistics to baseball, the Pirates have the second fewest plate appearances against LHP in MLB. They are 11-9 in games started by a LHP. That alone should discount the poor-performance-against-LHP argument, but obviously the team batting stats suggests that they are and it has been woven into a narrative.

Looking closely at the Pirates’ roster there are many solid RHBs, McCutchen [their best hitter], Martin, Marte, Sanchez, and Mercer/Harrison are pretty good against lefties. Now, some of these player are underperforming against LHP this year, but this is where the small sample size comes in again. You wouldn’t determine any of these batters lost their platoon advantage after only 80 plate appearances. Going forward almost all of these bats should regress to their normal platoon splits.

Pedro Alvarez, Gregory Polanco, Ike Davis. Their platoon splits are pretty atrocious both for 2014 and career-wise. For example, Alvarez has a .787 OPS vs RHP and a .517 OPS against LHP this year. I don’t want to get into analyzing what’s wrong with the Pirates’ left-handed bats, except to say they are terrible against LHP. The argument should change from the *Pirates* don’t do well against LHP to the Pirates’ *left-handed batters* are terrible against LHP.

What can be done about this? The simple answer is to get better left-handed batters. Since that’s not really possible, the next best option would be platooning the left-handed batters. Ike Davis is already platooned with Gaby Sanchez, and Pedro Alvarez is barely starting any games. Polanco has regressed from his debut, but I think the best idea is for him to play everyday and deal with LOOGY relievers. I also don’t know how many fans actually want to see or are suggesting that he’s should be platooned. With all this in mind I’m not quite sure what acquiring a right-handed bat would accomplish. The Pirates are already trying to find a place for RHB Josh Harrison to play. He’s been having a good season, no matter what you think about Harrison. Furthermore, the Pirates have a guy who’s been killing LHP this year and has decent splits against them for his career. And that’s Jose Tabata.

Bottom line, adding a RHB wouldn’t help much because the team splits are still a small sample size against LHP. Beyond the statistics, the two big left-handed bats have terrible splits against LHP, and these problems have been already addressed by platooning and benching.