Just adding my $.02
When I was punished for things like lack of focus, repeated ticks, depending on which rehearsal block we were in I either dropped and did push-ups or ran with my section. But as I ran or pushed ground, I was thinking about how to get back into rehearsal. Getting worked up physically as a brass player with an elevated heart rate and shortened breaths were the opposite of what my staff wanted so I tried to take enough time to settle down my breathing and heart rate as possible.
The point? So that when I'm hauling across the field (rehearsal or otherwise), horn in a 'pop' position and playing full out, I'm able to relax and play how I was instructed to do.