So how does experience work? Here is my idea.
What if stamina means you perform less well after X minutes played? What if the decrease was exponential?
Now what if experience meant that, the more you have of it, the less exponential the decrease in performance becomes for X minutes played, and the more linear it becomes. That would mean an experienced player would perform the same way as his inexperienced twin at the beginning of the game.
However at the end of games and X minutes played, he will perform significantly better than his twin (but still not as good as he did at the beginning of the game) because his performance will have decreased, but the inexperienced twin's level of performance will have been decreasing at an (increasingly) higher rate.
After all, experience is all about knowing how to take possessions off during the course of a game without affecting your team, in order to save energy for when it matters most!
"Air is beautiful, yet you cannot see it. It's soft, yet you cannot touch it. Air is a little like my brain." - Jean-Claude Van Damme