My theory: Since most people are righthanded, their dominant leg is also their right one. As such, when righthanders run counterclockwise, they need to push harder on the right leg, the outside leg, when making turns, and this is most naturally done by pushing on their dominant leg.

When learning to ski and skate, I always felt more comfortable stopping and turning by pushing on my right leg.

I imagine that proficient skiers and skaters are ambidextruous as far as their feet are concerned. I imagine the lefties who have spent a lifetime playing baseball are the same and don't find running counterclockwise unnatural, the way we righties might feel running clockwise.

Any lefthanders out there to contradict my hooey? How would you react to running and turning clockwise? My gut tells me that it would be more natural for you than for us righties.

I think it would have something to do with passing.  Baseball pre existed cars (I think) but whether walking or driving in North America you pass an oncoming object on the right.  It seems natural to pass the pitcher on the right.

Maybe if you figure out why we drive on the right side, you might get a clue?  I am guessing its because railways had their signs on the right side.

As well, I expect the fact that being left hander was frowned upon (you were punsihed if you wrote LH) and LH gloves were likely rare, encouraged most to throw RH.  As you say, this meant infielder would have an easier throw across the diamond.

In the end, it was just likely happen stance.

They play that way on our mirror image planet in an alternate universe.  At least that what the voices tell me.

The universe where Roy Halladay, the crafty young lefty, wears a beard? (Required Star Trek reference in alternate universe talk now fulfilled.)

That alternate universe - that must be the one where I'm young, sober, and refined.

Three attributes I may have possessed in passing, but certainly not at the same time.