Always run.
You can break the problem down into parts. One part is what falls on you during motion, mostly on your head. The other part is the stuff you walk into.
The stuff that falls on your head is a function of the rate of rain and how long you’re in it. This value will always be lower if you run,
The second part is a bit more difficult to explain. Think of what would happen if gravity turned off and all the raindrops suddenly stoped in mid-flight. If you walk through that, the number of drops that hit you is a function only of your size and the density of the rain. It’s like you’re punching a hole through it, that hole doesn’t change if you run or walk.
Now turn gravity back on. What changes? Nothing. Running will not increase the density of the drops.
So one of the two will not change and the other will go down if you run. So run!
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