# Lineup Simulation That Uses Regressed Splits

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The Rays lineup is .06 runs per game better against RHPs with this man. (Photo by J. Meric/Getty Images)

A few days ago, Sky Kalkman, doubtless while taking a brief break from drinking milkshakes with missionaries, tweeted about projecting scoring using a Lineup Simulator and regressed lefty/righty platoon splits. The problem (and this is something I've run into before but never spent enough thought on) is that lineup simulators (or analysis of pinch hit decisions that want to include the effects sequencing) need their projections to be broken down into ratios of the different hit types. But lefty/righty regression, at least when based on the research from The Book, just uses a single number (usually wOBA).

So, if we know what wOBA to expect for a given hitter against pitchers of each handedness, the question then becomes, how do we arrange the components of that wOBA? The easiest method is to simply assume that the distribution of extra base hits is the same against either handedness, and I actually think that in this case the easy road is correct. I have seen no compelling evidence of predictable patterns in platoon splits (if you have some, please pass it along and I'll gladly remake this model). I've tried to find a pattern in the components of platoon splits myself, and gotten nowhere, but I did accidentally and unexpectedly derive something resembling the wOBA coefficients, which was pretty cool. Some players exploit the platoon advantage by getting on base more, others exploit it by hitting for more power. Some do both. It's a crapshoot, which is which. For some players, it changes year to year. In the absence of a well-defined pattern, I think it best to assume none.

And if we agree to spurn the obvious complexity, our task becomes quite easy. Here is a L/R split wOBA breakout tool (.xls version). To set my ratios of types of hits, I've used complete year ZIPS projections (I worry about ZIPS RoS diluting the sample size and giving back any advantage of increased accuracy with a loss of precision). To use the tool, just enter a hitter's name, and the wOBA you expect the hitter to post (which you can get from my L/R splits regression tool, updated yesterday). The spreadsheet will import all the components of wOBA (using FanGraphs 2011 coefficients) from the ZIPS projections, except for plate appearances, and then it will solve for plate appearances. This works, because the lineup simulator is interested only in ratios, not in counting stats, so this tool will see the desired ratios of hit types and stolen bases, and merely provide the correct number of outs so that the numbers work.

Two notes: Although the lineup simulator asks for "ABs," according to the FAQs, it actually means PAs. Also, while wOBA separates walks and hit-by-pitches, the lineup simulator only has one field, labeled walks. I'm simply adding projected HBPs to the walk total. I hope that's the right thing to do.

The lineup simulator can obviously provide hours of fun, so I'll just look at one example. Against Justin Verlander Luke Scott and his projected .332 wOBA against right handed pitching just returned from the DL and replaced Hideki Matsui and his .314 projected wOBA in the cleanup spot. What's the effect of this swap? Well with tonight's lineup against an average righty, the Rays would be expected to score 3.08 runs per game, or 498 runs over the course of a season. With Matsui instead of Scott, they would be expected to score 3.02 runs per game, or 488 runs over the course of the season. That's a difference of about one win on the season.

Just on a whim, I decided to run the simulation again assuming a healthy Longoria and Joyce came back and replaced Brooks Conrad and Will Rhymes. My dreamer's lineup of Jennings - Pena - Joyce - Longoria - Zobrist - Scott - EJ - Molina scored 3.46 runs per game, or 560 runs on the season. That's the equivalent of over six wins difference, just from the offensive side (we know how much the defensive side has been hurt by the injuries as well).

I'll leave you with one final thought. These projected wOBAs splits are assuming an average pitcher. To determine the run environment for a particular game, you would need to include the pitcher's skill and split as well. Pitchers often times have larger, better defined, and more varying splits than hitters, so the same simple regression we do for hitters doesn't work as well for them. It's actually better to take the career wOBA split for a pitcher at it's face value, as long as he's been around for awhile.

According to The Book, though, pitchers and hitters act evenly on the expected result of the batter/hitter confrontation, meaning that a .280 wOBA pitcher vs. a .320 wOBA hitter can be expected to yield a .300 wOBA over the long haul, just as a .320 wOBA pitcher vs. a .280 wOBA hitter would. If you want to calculate the expected runs in a single game, I'm comfortable averaging starting pitcher splits with regressed batter splits to get a single wOBA before feeding it into my wOBA chopper and eventually the lineup simulator. It's very imprecise, and ignores plenty of nuance, but I don't believe to do so would rock the boat in any meaningful way.

Enjoy, and let me know if my tool helps turn up anything interesting.

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