"Perhaps it would have been different, but let us be thankful that this isn't war," Patroclus smiled a little when Achilles seemed to calm. He was definitely in need of a bath or a shower (and what a wonderful invention indoor plumbing was, truly) after his fights but Patroclus had no intention of straying from his side just yet. Even if it was only his pride that was wounded he was mindful that this probably did mean a lot to Achilles in terms of it being his first true loss, even if it was not strictly a real loss. Nobody died and nobody was hurt because of it, but still. It mattered.
Yes, perhaps he would surprise him. Join the Fight Club, as it was called. Achilles was taking an interest in what he did despite not caring much for medicine or how it was applied other than whether or not it could heal a wound, Patroclus would... try and fail to fight, he supposed. After his death, he had been considering it as a useful skill to learn purely so they could never be separated by death again. "I hope you don't have any ridiculous notions that I could ever think less of you for something like this."