Even More HBP

It just dawned on me that, implicit in my arguments is that there’s some idealized rate at which a pitcher “should” be hitting batters. Here’s a little thought experiment:

Imagine a baseball league in which nobody ever hits anything but singles. Logically, pitchers in such a league would never want to walk a batter or hit him, because those ALWAYS lead to baserunners; whereas a pitcher who makes the batter put the ball in play will get him out two-thirds of the time. And even if he does get a hit, you're basically no worse off than if he'd taken a base on balls or a HBP.

Conversely, imagine a league where EVERY hit goes for extra bases. In this slugging league, pitchers might decide that they're better off pitching inside and risking a walk or HBP, rather than giving up a double, single, or homer. You can't score the runner on first with a walk.

So, it seems logical that the more extra base hits there are, the more willing a pitcher should be to pitch to the inside of the plate and risk either walking or hitting the batter. What that exact rate should be, I don't know. But it seems like isolated power and HBP would go up and down together. And they do!