Mariano’s pitch sequences and game theory

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This is a nerdy subject, so I’ll keep it short and link-heavy. With pitch data freely available, we’re going to start seeing Game Theory used to analyze pitcher-batter matchups. Tommy at Beyond the Box Score touched on this earlier this week, and it’s a good read on pitch type game theory. Today at The Baseball Analysts, Dave Allen looks at Mariano Rivera’s pitch sequences. But, because Marino throws only one pitch, this sequencing deals with location rather than pitch type. An amazing non-game-theory note: Mo is insanely good when throwing to his glove side. Many pitchers have trouble controlling pitches on that side. Allen goes on to show how Mo fares when throwing inside to a lefty after an outside pitch, inside to a righty after an inside pitch, and so on.

As we know, Mo dominates lefties. He’s not quite as good against righties, and he’s particularly bad when going inside after an outside pitch — and is also not quite as good when going inside-outside. Tom Tango runs with that. In most cases with Game Theory, he says, we need to take the batter into consideration, because each batter has different strengths and weaknesses. With the outside-inside sequence, though, the difference is too pronounced to chalk it up to poor choices to certain batters. Mo throws this sequence 37 percent of the time (as in, throws an outside pitch 37 percent of the time after he throws an inside pitch). He would do well to cut down on that. Mo fares best against righties when going with the outside-outside sequence.

Just how long can you continue to throw righties outside cutters? I’m not sure. This is where longer pitch sequences would be helpful. For instance, if Mo goes outside-outside-inside, does he fare well? Or is that the sequence that hurts him the most? After all, he went inside after an outside pitch, which for him produces the worst result. But just prior to that he went outside after an outside. This also raises the issue of whether these sequences cover multiple batters. In other words, if Mo strikes out a righty with an inside cutter and opens the next righty with an outside one, is that counted as an inside-outside combination? Or are the sequences limited to single plate appearances? I would think you’d produce a bit of noise if you overlapped batters. Better to stick to single-batter sequences for these analyses.

This is the type of analysis that gets me excited. Even non-stat-heads can enjoy pitch sequencing and Game Theory. It’s an attempt to break down the most fundamental game in baseball, that between the pitcher and batter. Analysis doesn’t get any better than that.

ALDS and ALCS tickets go on sale Monday
Game 160: This could have been a meaningful series
  • The Three Amigos

    Mo’s game theory is he wins.

    • tommiesmithjohncarlos a/k/a Ridiculous Upside

      Mariano is the exception to the Nash Equilibrium. Even if you accurately predict his actions, the decision you make will not be your best decision. Whatever Mariano does harms your position.

      • Marcus

        (googles Nash Equilibrium)

        (scratches head, forces a smile)

        Heh heh! Oh, I get jokes. Jokes are funny. Heh heh!

        (scratches armpits, lumbers away)

        • tommiesmithjohncarlos a/k/a Ridiculous Upside

          Yeah, that one was pretty esoteric, eh?

          Go ahead, I’ll wait.

          • Marcus

            Takes one to know one!


  • Ivan

    Doesn’t he throw a 2 seamer to righties to get em off his cutter away? And also he still goes to that 4 seamer for the K too.

    • whozat

      If so, it is indistinguishable from the inside cutter by speed, spin and movement.

    • DF

      I don’t think he goes with the 4-seamer much at all anymore. I feel like he used to throw it up in the strike zone, but scrapped it in favor of an all-cutter approach.

      • DF

        And had I read the article, I would have learned he throws it 15% of the time to righties, and essentially never to lefties.

        On a tangentially related note, it amazes me that managers ever allow lefties to face Rivera. That they remove right-handed hitters in favor of lefty-swinging pinch hitters, in pursuit of an alleged platoon advantage, is just madness. Seems like it happens a lot less now than it did earlier in his career, but you still see it happen sometimes.

        • Accent Shallow

          Well, it’s not like they’re removing A-Rod to let him face Hinske. The pinch hitters are generally superior to the hitters they replace.

          Whether Mo’s reverse platoon split negates that entirely or only partially is another matter.

  • tommiesmithjohncarlos a/k/a Ridiculous Upside

    This is the type of analysis that gets me excited. Even non-stat-heads can enjoy pitch sequencing and Game Theory.

    I think you overestimate non-stat-heads.