Jose Tabata, lineup construction and double plays

Via Twitter, I had the following brief exchange this afternoon:

With my interest piqued, I set out to determine an answer. Jose Tabata has a history of producing ground balls on close to 60% of his balls in play. How many times would he hit into a double play over a full season if he batted second in the lineup, behind Andrew McCutchen?

To start, I attempted to establish the number of double play opportunities that Tabata would encounter. In his career, McCutchen has 140 singles and 93 walks in 840 plate appearances. Subtracting the 37 times he has stolen second base and the 10 times he has been thrown out attempting to steal second base leaves us with 186 incidences (22.1% of PA) in which he was standing on first base as the subsequent batter stepped into the box.

Next, I took a stab at determining the rate in which Tabata will hit double play ground balls. Tabata has yet to hit into a double play in his career, but I only count 11 occurrences in which he has batted with a runner at first and less than two outs. We can probably just throw out that small sample. In 107 career plate appearances, he has produced 50 ground balls. Eleven of those 50 ground balls have gone for base hits, so we can eliminate them as potential double plays. By examining his spray chart, I estimated that 18 of Tabata’s ground ball outs would not have been ideal for turning two with McCutchen and Tabata darting along the basepaths. Add it all up, and we have 21 ground balls (19.6% of PA) off the bat of Tabata with the potential for a double play.

At this point, we have McCutchen on first base (and staying put) after 22.1% of his plate appearances. Tabata hits a double play ball in 19.6% of his plate appearances. Multiplying those percentages together gives us a 4.35% rate in which Tabata will hit a double play ball with McCutchen on first base. But we also must adjust for the situations in which there are already two outs, and the double play will not be in effect. There would always be less than two outs in the first inning, so we can automatically include those situations as potential double plays. Assuming 600 plate appearances and 150 games in a season, that is a guaranteed 150 plate appearances. With the number eight hitter (.300 OBP), a pitcher (.150 OBP) and McCutchen (.370 OBP) hitting in front of Tabata, I think it is safe to assume that Tabata would bat with two outs in about 50%* of the other 450 plate appearances. Thus, Tabata would bat with less than two outs in approximately 375 plate appearances.

* [(0.7 * 0.85) + (0.7 * 0.63) + (0.85 * 0.7)] / 3 = 0.544
On average, at least two of those three hitters will make outs in 54.4% of all trips through the lineup, thus bringing Tabata to the plate with two outs. I subjectively rounded down to 50% to account for situations in which an inning ended due to an out made by either the #8, #9 or #1 hitter.

4.35% of 375 plate appearances gives us 16 double plays over the course of a typical season for Tabata. In 2009, the average major leaguer hit into about 12 double plays per 600 plate appearances. Thus, batting Tabata second is likely to have a counterproductive effect on the Pirates’ lineup. It would be more optimal to bat Tabata leadoff and McCutchen second. Tabata can pound the ball into the dirt with the bases empty and McCutchen, who generates far fewer ground balls, can bat with runners on base.

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