Can't catch deer - they run away

Tip: never run unless you are shooting, go straight ahead using binoculars to scan the undergrowth. You need perks - for vertical position and for crouching, but they reduce the speed by only 15%.

With such advice, you will constantly run into animals that will stand and look at you. They are alert, but they are not so easily frightened off. You just need to freeze and let them calm down.