Stamina doesn't make your players play better, per se. It simply allows them to play at their highest level for longer... Basically, as the game goes on your players get tired, and as they get tired they begin to play worse. They'll miss more shots, they'll commit more fouls, allow more offensive rebounds, etc. If you increase their stamina, you increase the amount of minutes they can play before that happens.
Also, as was previously mentioned, trainer level does not affect any of the team training options.
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