There's no doubt that perception relates to sports performance in a very important way. Perception is the mechanism in our brain that determines how we experience everything.
Athletes having a good day may experience the same conditions in a different way than athletes having a bad day. However this might be difficult to measure in a reliable way.
Jessica Witt has been studying perception in athletes for some time. Her latest study shows that good golfers see the hole as larger than bad golfers. Tiger Woods sees a golf course differently than you do.
Naturally the same sort of effect would apply for other sports. A succesful basketball player on a good night might experience the basket as an ocean into which he is simply throwing rocks.
Similarly, a great runner might not have any problems at all during a race, while a weaker runner might complain of this and that. It could be almost like they didn't run on the same course.
Most runners have experienced a tough moment when even a tiny hill seems like a steep mountain. That's when we try to think of mental tricks to change the limiting perception.
Hopefully further research will be able to suggest practical solutions. In the meantime, let's keep on experimenting.