For me, yes the training miles make a difference, to a certain extent. It was more of a difference a few years ago when I started running, less so now.
What seems to affect me more is making sure I'm properly (Not over or under) hydrated for the few days leading up to a race, make sure I'm eating correctly for the few days leading up to a race. Controlling and reducing my adrenaline, especially immediately before the race and the first miles. You can take a lot out of your legs by them working harder than they should be, not neccessarily going fast, just that your legs are tense, run relaxed, loose shoulders, loose legs. On a flat mara I'll even aim for a negative split just to make sure I don't put all the effort into the first half.
Thought they'd moved the finish when I first came round the corner. Would love to know if it was a timing mate, just to see what the actual speed of me was, as opposed to Mr Garmin. Always was more of a sprinter than a distance runner!