I think there must be a missing variable, such as excess water whisking off more quickly, greater evaporation due to heat transfer or maybe something else.

(Yes, sometimes that exposure time can result in you coming out ahead, but it's not really answering the question)

EDIT: What the hell's with the downmods? What is this, reddit?

For a given amount of time, running in the rain makes you more wet.

For a given distance, running in the rain makes you less wet.

Running reduces your exposure time by more than the increase in rain_per_time.

Perhaps I've simply mis-understood you.

My point is that reducing your exposure time is basically altering a different variable in the equation.

If you control that variable by not running to a place where the exposure to rain stops, it becomes clear that by running you will get more wet than if you were simply walking.

And yes I understand that practically, running to a dry spot is the whole point.

You originally said:

    In other words, running in the rain gets
    you more wet, given that all running is
    doing is reducing your exposure time.

What have I misunderstood?

Um, the "exposure time" variable is exactly that. The act of running causes you to increase your rain exposure, so unless I'm missing something, at some point the "exposure time" will become long enough that the act of running is rendered ineffective, and then actually becomes worse. (For example, if you ran around in a circle for a set time, instead of from point to point).

Like I said, I do get that by that point it may not functionally matter, and that if you ran from your car to the store you will not be as wet as if you walked, but it is important to understand the subtleties in order to properly understand why.

Maybe others will understand you and gain something from it, but I doubt there's much to be gained by you continuing to explain to me, and me trying to understand.

Thanks for trying.