If the rain is "continuous", or pours, it's meaningless to compare whether running or walking is a better strategy because either way you would end up like a drowned rat.So only discontinous model is worth discussion in this context.

Imagine the rain drops are actually gold coins.

A moving man can grab more coins than those who just stand dumb because after he gets the coin overhead, he would rather rush ahead to catch the coins flying in front of him than wait for the drop of the coins overhead.