I think it works like this. The coach considers which player will perform better when deciding whether to make a substitution. A player's performance deteriorates throughout the game, with players with worse stamina tiring quicker. So your starter probably has better skills, but his performance deteriorates and the sub may then be comparable in performance. I don't know whether resting on the bench replenishes skills, or simply stops the deterioration.
When I first started, I did train stamina for a couple of weeks.
Before I trained it, I was getting better balance in playing time. Apparently the starters were tiring quicker.
After I trained it, my starters were getting more playing time. But more importantly I might be fairly even during the 1Q, and then start pulling away in the 2nd Q. So stamina is important in determining substitutions among your players, but it is also important vs. the other team's stamina as far as winning games.