A quote from Denis Waitley, author of The Psychology of Winning, states the positivity of visualizing success:
"Winners say, Of course I can do it! I've practiced mentally a thousand times"
The thousands of repetitions in your mind end up paying off when it comes time to perform. You feel like you've done it a thousand times because you have in mental rehearsal. It's a very comfortable spot to be in and that comfort really relaxes your muscles, your mind, and allows peak performance to flow forth.
UFC light-heavyweight James Te Huna takes similar stance to his fighting game. Visualization of hundreds of techniques going well improves the odds that they do when the Octagon door shuts. There's no surprises and fears, and the brain is used to the scenarios which pop up in a fight because they have already been rehearsed mentally. There's less stress and anxiety regarding your performance when it's a familiar situation.