The proper batting order, mathematically speaking

I’m not very good at math, but paradoxically, I’ve always loved statistics — in a very sort of casual, lay statisticians way. Stats is one reason baseball is so appealing to me. I have two fantasy teams because I like the numbers of baseball. I used to play simple game when I was a kid called Dice Baseball (it used, no surprisingly a dice and baseball cards), and I kept all my own stats.
So the idea that the time honored tradition of the clean-up hitter is not statistically sound is of profound interest to me.
The New Scientist article argues that, mathematically speaking, you should bat your best hitter second in the line up rather than 4th because the number 2 spot will get more at bats than the number 2 spot. And the weakest hitter should hit 7th or 8th to put him the furthest number of batting spots from the best hitter.
There is some logic to that, but here’s my problems with the story.

  • Well, the first one is easy — there’s no home base in baseball. It’s called home plate;
  • But, how do you define best hitter? On the Yankees, who is the better hitter? Jose Vidro, who is hitting .321 with only 10 home runs, or Cliff Floyd, who has 19 home runs but is hitting only .284 (We’ll ignore the fact, for the moment that Montreal has Vladimir Guerrero, who has 26 HRs and is hitting .332)? Traditionally, you put your biggest HR threat in the clean up spot, not necessarily your “best” hitter. Tony Gwynn was the Padres best hitter for 20 years, but he never batted 4th (he often batted second, but that didn’t seem to help the Padres win more). So the study offers a false dichotomy of sorts. To return to Montreal’s line up, there are few hitters like Guerrero who combine power and average, so he would seem a natural to hit second, but what happens when you don’t have a Guerrero? Who, then, is the best hitter?

It’s worth noting that it was quite revolutionary when Tony LaRussa started batting Mark McGwire #3 in the line up. Here was the strongest power hitter of his generation, and through he hit for good average, he was never a threat to winning a batting crown. But he maintained such a high HR to at-bat ratio, it made sense to get him as many at bats in a game as possible. So he hit third. The Giants do that with Barry Bonds now, and the Cubs follow suit with Sammy Sosa. The day of the high-average, low power #3 hitter, such as the prototypical Rod Carew, seem to be over. Will moving the Bonds and McGwires to the #2 hole be next?

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