Sometimes in the second half of games athletes start making dumb mistakes. I don't imagine players would lose their ability to see plays developing, but they do lose the ability to execute.
I noticed the same thing while working. I used to get so tired by the afternoons that I'd sometimes zone out and lose chunks of time because I wasn't my most productive. But now that I'm working out almost every day, I'm feeling great and feel mentally sharper at work.
It's a good reminder that a tired body leads to a tired mind. The people who think they can eat poorly, not work out, and stay in front of a computer for 18 hours a day don't realize the disservice they're doing themselves from multiple perspectives.