Because you are generally taller than your surface area from above, running forwards will sweep a path collecting all the rain falling in an area matching your frontal area.
Walking slowly, you just pick up the rain that would be falling onto your head and shoulders, the surface area from above.
There’s a lot more variations on this, angle of the rain, how much, how fast you are going to be moving (eg standing still isn’t going to be smart)
Mythbusters did a test on this with people wearing paper suits that were weighed afterwards to see how much rain they soaked up.
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