Going after your deer right away is not always the best thing to do, I lost a deer(nice buck) that way. It is better to wait atleast 20-30 minutes, once you spook that deer and he/she runs sometimes you will loose site of them(including any signs). If you see the deer go down, watch it, give it a few minutes, if there is no movement then chances are it's dead, either way it is still better to sit and wait. Let me ask this, is it better to have a wounded animal running around or is it better that it is shot and killed(even if it is by another hunter)? Then there is the point of safety, you shoot the deer, you instantly go after it, it runs, another hunter see's it(doe), but he hears you comming after it, so he figures must be a BUCK, next thing you hear is baaaa. You don't hear "aam" because he nailed you. It is up to you how you hunt, but it has been proven that it is better to wait, usually the deer will run a short distance, lay down and die.