Investigating the Idea of Scarce Right-Handed Power

I want to put to rest the discussion about the lack of right-handed power in Major League Baseball today. There has been a lot of anecdotal commentary about how scarce right-handed power has become, but there haven’t been too many analytical articles supporting this idea. If anything, the handful of articles that have been written question if the problem even exists in the first place. There are two different arguments about this topic: the first is that right-handed power is scarce — that is to say left-hand power is bountiful — but right-hand power is not, while the second argument, which I won’t address today, is that relative to left-handed power hitters, right-handed power hitters have declined in number.

In a hypothetical choice between players of equal talent, you would almost always prefer a left-handed power hitter to a right-handed power hitter, since the lefty will have the platoon advantage more often and should be more productive as a result. There are valid arguments concerning rounding out line-ups, but right-handed batters are not scarce; good left-handed hitters are actually the scarce commodity.

For reference, the general population is estimated at having a left-handed rate of 10%, while baseball has a left-handed rate among batters is about 33%; lefties are overrepresented in baseball.

This is a box plot of the various player-seasons from 2010 until 2014. I’ve chosen this time span since it’s recent and it falls after the implementation of PITCHf/x, which improved the measurement of the strike zone. I’ve excluded switch hitters for simplicity, and set a floor at 200 plate appearances.

The player with the most home runs is a right-handed batter, Jose Bautista. The median home runs per season is 11 HR for right-handed hitters while the left-handed hitters have a median of only 9 HR. Even at the top — 30+ and 40+ HR — where the difference should be the easiest for people to notice, right-handed batters have the advantage.

Isolated power (ISO) is an efficient way to measure overall power of a hitter, and since it’s a rate stat instead of a counting stat, we can look at it across splits. The table below splits the entire league stats in a two-by-two square by batter and pitcher handedness.

As evidenced by the table, the lefty-lefty split is the worst out of the four combinations; I’ll address this split later. The righty-righty split almost has the same ISO as the left-handed batter platoon advantage, and right-handed batters have a significant advantage when facing a left-handed pitcher. These ISO splits would be enough to conclude that aggregated, right-handed batters have more power than left-handed batters. However, these splits include the entire league, we are more concerned about the top power hitters in the league.

The table below shows all the player-seasons from 2010-2014 where a player had 35 or more home runs, and it is order by single-season home runs. I’ve colored coded the table for quick visual analysis: red for right-handed batters and blue for left-handed batters.

The first impression is that there is a lot of red on the table. The second thing to notice is that right-handed batters occupy seven of the top 10 player-seasons and 23 out of the 33 (70%) spots on the entire table. These fractions roughly reflect the population of batters, which splits along the 33-67 lefty-righty line.

To investigate this further, I wanted to see what baseball would be like if the frequencies of platoons were changed. Left-handed hitters get the natural advantage of batting in their favored matchup more often. This should skew their stats higher than right-handed who are batting against their platoon advantage. To create this alternate universe, I took play-by-play data from Retrosheet and resampled it (with replacement – much like bootstrapping) so that the batters had an equal number of PA against both left-handed and right-handed pitchers. Resampling then averaging those samples is a technique for overcoming the small sample sizes present in season splits. For fun, I also inverted the player’s PA by pitcher handness. This gave a right-handed batter many more PA against left-handed pitchers than right-handed pitchers and vis-versa.

I created a boxplot to show the distribution of top HR hitters and the effect that resampling has on the hitters. The left-most boxplot is the same plot as the box plot above only but this plot show only the players who hit more than 30 HR in a season. It represents the actual home runs hit by players during a single season between 2010 and 2014. Outliers like Chris Davis’ and Jose Bautista’s 50+ HR seasons quickly disappeared when I resampled the data.

The middle graph represents an average of the results from the 70 resampled seasons. The top right-handed power hitters had a slight advantage using the actual statistics from 2010-2014, and then when I resampled to simulate seasons with equal number of PA against pitchers from either side of the rubber, the distribution of right-handed batters shifted upwards, separating themselves from left-handed batters, who shifted downward.

The right pair of box plots is the extreme, inverse resampling; it inverts the number of PA the batter faces against each type of pitcher. The results are a much more dramatic stretching of the distributions and right-handed batters getting more home runs at the top.

Looking on the lower end of the spectrum, Vernon Wells and Pedro Alvarez were the players who dropped to the lowest HR total. Wells, a right-handed batter, has a dramatic reverse split in 2010, with a 67 wRC+ against left-handed pitching and a 140 wRC+ against right-handed pitching. Alvarez has a historically terrible lefty-lefty split, but in 2013, he hit 36 HR; this was predominately from plate appearances against right-handed pitchers.

There have been many theories suggested for why the lefty-lefty split is so low relative to the other three handedness splits. These include the rarity of the match-up and difficulties picking up the ball from a certain arm slot. Admittedly, I’m not a hitting or pitching coach, so I’ll defer to those more qualified me for the details of those topics. However, I’d suggest that in addition to those reasons, a selection and survival bias exists for left-handed batters, since they take advantage of right-handed pitchers. Hypothetically, the platoon advantage would push a less talented left-handed batter to have equal stats with a more talented right-handed batter.

Using these results it can be shown there is more right-handed power than left-handed power in MLB. Right-handed power has more representation in the recorded stats, HR and ISO, and they are more talented when the platoon advantage is leveled. The distribution of left-handed power hitters is shifted lower than their right-handed counter parts indicating that left-handed power is the scarce commodity.

For those interested in the details of the analysis, I used play-by-play Retrosheet data to assemble every batting event of the players with more than 30 HR. That data set was split into different years, then into different players. The play-by-play data was then split again by pitcher-handedness creating two data frames for each player in R. I sampled with replacement from each data set using the total PA divided by 2 (rounded) as the number of sampled pulled from each data frame. This was done 70 times for each player-season, and then the results from that resampled season were averaged to obtain the values used in the box plot. Stats from resampled seasons formed a normal distribution before aggregation.