[DS]

Let's look at it in this (admittedly simplistic) example.

Let us assume you have a 100 sq km search area, with one search asset that can scan a 1 sq km region at a time. I takes 5 minutes to complete the scan of 1sq km.

Let us also assume that when you are stationary, your noise signature gives a searcher a 50% chance of detecting you in the space of that 5 minutes before the searcher moves on. If you are moving, and thereby making more noise, the searcher has a 66% chance of detecting you.

With those constants, let's run the calcs:

If you stay still, you have a 0.5% chance of being detected on the 1st search grid. If you move from one grid to another, you have a 1.2% chance of being caught (66%/100 grid squares x 2 grid squares occupied during search phase 1).

If we assume this calc runs 100 times for the 100 squares searched one at a time, you have a 50% chance of being detected if you stay still, vs, a 120% (apparently statistically certain detection) chance of being detected if you kept moving.

Know, I am NOT a statistician, nor am I a real word tactician. Still, if you acknowledge your chances of detection are smaller the quieter you are, and you have no way of knowing if you are actually moving TOWARDS a searcher instead of away from one, it seems to me you are better off staying still. That said, in the real world, you almost always have some information, but never all information, so if I hear active sonar ranging to the south, I may choose to move away, even though I may be unwittingly moving towards a silent enemy in wait to the north.