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"The Book" and the Royals - Part 1 Batter Platoon Splits

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Hat tip to B.C. for pointing out an error in my math.
I am going to run a little series here looking at how the Royals are run compared to being run strictly by the numbers. A few years back Tom Tango, Mitchel Lichtman and Andrew Dolphin wrote a book called, "The Book" that looks at several concepts (lineup construction, splits, butting, base stealing) and determines the ideal way to play a situation. I will be using their concepts in this short series.

Willie Bloomquist this season has batted 2nd in the lineup 4 times. These games were all against LHP and Pena was the catcher. Ned Yost was trying to get a right handed bat in against left handed pitchers. Historically, right handed hitters do better against left handed pitchers and vice versa. Willie is not the best hitter on the team, but does his platoon split make him a better choice against LHP than other players.

Note: In "The Book", they use wOBA to compare players. It is a value of how value a player contributes in both OBP and power. For those that need some additional information on wOBA, here is a nice writeup by Alex Remington.

According to "The Book", it takes 2200 plate appearances for a RHH to regress 50% away from the league average platoon split. In laymans terms, take the league split for 2200 PA and the player's split for their number of PA and combine a weighted value of these numbers for the player's true split.

Willie over his career has hit 0.313 wOBA vs LHP and 0.276 wOBA vs RHP with 793 PA vs LHP (link) for a platoon split of 0.039. The league average split from "The Book" is 0.017.  Here is the formula for determining Willie's true platoon split.

((2200 * 0.017)+(793 * 0.039))/(2200+793) = 0.023

Now that the split is know, it can be applied to Willie's true hitting ability. Finding this value is easier said than done, but I will quickly get a value for this example. Projections have him around a wOBA of 0.300 for this year and he has a wOBA of 0.296 lifetime, so a talent level of 0.300 wOBA is fairly close.

Now I need to weight the value by the number of PA against each type of pitchers

L = wOBA+split*(1-L%) = .300+.023*(1-.394) = .314
R = wOBA-split*(1-R%) = .300-.023*(1-.606) = .291

Using the preceding numbers, Willie should be a 0.314 hitter against LHP and 0.291 against RHP.

Now I will see if he should be hitting above a better, but left handed hitter like David DeJesus.

For left handed hitters, it takes only 1000 plate appearance vs LHP for the player's true splits to be weighted at 50%. The league average platoon split it 0.027 for LHH. Using these number and Davids lifetime platoon splits, of 0.318 wOBA vs LHP in 1175 PA and 0.356 wOBA vs RHP, his true platoon split can be found.

((1000 * 0.027)+ (1175 * 0.038))/(1000 + 1175) = 0.033

Looking at some projections and past numbers, it can be said that DeJesus is around a 0.350 wOBA hitter.

L = wOBA+split*(1-L%) = .350-.033*(1-.171) = .323
R = wOBA+split*(1-R%) = .350+.033*(1-.829) = .356

Using these numbers David should bat 0.323 vs LHP and 0.356 vs RHP.

Platoon splits are important, but the new batter needs to be near the ability of the player they are replacing in the lineup for there to be an advantage. I hope that explains how true platoon splits are figured and let me know if there are any questions.