On the whole taper thing. I'm going to come at it from a running perspective. When one ( trains for a marathon they typically run their longest run (about 20 miles) 3 weeks before the race. Two weeks before they run about 12 miles and the week before 8. This has been tested over the years. Tapering is a relatively new concept in sports. In the old days people would run 20+ miles a few days before the race. And over the last couple of decades people started experimenting with tapering and found they felt better, and ran better and faster when they "took it easy" for about two weeks before the big event.
And even if it is in your head once you get to a competition there is very little separating the top athletes, being mentally more prepared, more focused, and more determined becomes a deciding factor.
Ask the US swimmers why Phelps is so dang good, and they will all say it's because of his mental state and ability to be so tough.
Most sports, swimming included, after a point become more mental than anything else. It's more about how much you want it, and how hard you are willing to push yourself than it is about your physical state.
Sorry this was so long, hope it makes sense.