Birnbaum on Hirotsu's Markov lineup study

By Jason Wojciechowski on May 27, 2011 at 7:15 PM

Here, Phil Birnbaum, Everyone's Favorite Sabermetrician (at least until Colin Wyers knocks him off the spot when he blows up Ultimate Baserunning or something), summarizes the results of a study by Nobuyoshi Hirotsu that asks whether the lineup that scores the most runs is necessarily the optimized lineup in terms of winning games. My friend Migs emailed me the paper a few weeks ago, and I've been meaning to read it, in no small part because using Markov chains is significantly more attractive to me than simulations for a lot of baseball analysis.

But the main reason I was intrigued is that a major fret for me in baseball analysis has been that we might be too simplistic in our individual performance -> team runs -> team wins ideas. (For an example of the kinds of issues I have, see this lengthy comment I just left on a Steven Goldman piece at Baseball Prospectus. If you're not a subscriber but you're interested in the comment, let me know and I'll get it to you another way.) Lineups are one part of that -- we expect a lineup to score N runs in a game, but we know that in reality, that N comes from a distribution of runs throughout the season: M1 times the team scores R1 runs; M2 times, it scores R2 runs; ...; and Mn times, the team scores Rn runs. There could conceivably be a significant number of cases in which a team's run distribution causes it to underperform its total runs scored. (The trivial example is a team that is somehow designed to win one game 1000-3 and lose every other game in a shutout.)

But what Hirotsu found, as summarized by Birnbaum, is that a lineup that scores more runs overall is nearly always (as in 599,987 times out of 600,000) going to beat the lineup that scores fewer runs more than 50% of the time. (Note that Hirotsu did not compare relatively trivial examples, like a team's best lineup versus its worst lineup -- instead, he compared the best to the top 20,000 or so next-best.) I will still read the paper, mainly for its methods, but I am glad to put this small worry of mine to rest.