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know what he’s doing out there, he may throw 140 pitches—but of the 140, he’s only maxing out on 40. The other 100, he’s taking a little off, putting a little on. But when the slop is flying, he’ll reach back and make his best pitch. 12
    This impacts the hitting externality in an interesting way. While having a good on-deck batter may help the current hitter see more pitches in the strike zone, the pitches he does see may be tougher to hit than if he had a stiff hitting behind him. When there’s more to lose from letting up, that’s when we expect a pitcher to reach back for more. In the language of La Russa, a better on-deck batter creates more “slop.” And more slop for a hitter ought to make it more difficult for him to hit the ball.
    If pitchers do vary their effort according to the game situation— and we have good reason to think that they do—then we need to modify the traditional protection argument. The externality of a good on-deck hitter may not be positive, but negative. If the good on-deck hitter causes the pitcher to ratchet up his effort, the batter might actually have a tougher time hitting. Having a poor on-deck hitter may cause the pitcher to be less fearful of the hitter reaching base, and therefore save his effort for a more crucial situation. In this case, a poor on-deck hitter would provide a positive externality. I can easily see a pitcher letting up on an eight-hole batter in the NL, because there is a weak-hitting pitcher on deck. The pitcher may say, “If I don’t get this guy, I’ll just get the pitcher.”

A Scientific Test
    While, theoretically, it’s easy to see why the traditional view of protection might be wrong, we don’t know this. This is a problem that we can examine, but it requires some advanced statistical techniques. My math professor colleague, Doug Drinen, and I pondered the existence of hitting externalities over several lunches and decided the subject warranted further investigation. So we designed a test that would measure hitting externalities if they existed.
    Using individual plate appearances of batters, we were able to observe how the hitting prowess of the on-deck hitter affected the hitting outcome. We had to be especially careful because there are many other factors that could impact the hitting of a batter. Therefore, we used a multiple regression technique to “hold constant” these other factors. As long as we could include in the model other factors that might influence the hit probability of the batter, we could isolate the impact of the on-deck hitter on the outcome. These were the outside factors we controlled for:
    • The hitting ability of the current hitter and pitcher— measured by OPS and OPS allowed for that season (See Appendix B for definition of OPS)
    • The handedness of the pitcher and hitter, to control for the “platoon advantage,” which is that opposite-handed batters and pitchers increase offense
    • The situation of the game (the number of outs, the base runner configuration, the inning of the plate appearance, and the score of the game)
    • The park in which the game was played (parks substantially affect run production)
    For data from 1984 to 1992, we measured the influence of on-deck-hitter quality (measured by OPS) on the likelihood that a batter would walk, get a hit, get an extra-base hit, or hit a home run. Doug and I were a bit shocked by what we found. Though the conventional baseball wisdom—a better on-deck hitter does protect a batter from being walked—is partially correct, the hitter also lowers his ability to hit for average and power. Therefore, a good hitter imposes a negative externality and a bad hitter imposes a positive externality on the batter who
precedes him in the batting order. This is completely counter to the conventional baseball wisdom.
    However, there is one crucial caveat. Though we found the impact to be real—it’s more than a product of random chance—the size of the effect is