I’m not an athlete but I think most people engaged in sport wouldn’t be inclined to drink wine in the middle of it, not if they were trying to win.
There are lot of great places for wine drinking: parties, weddings, funerals, showers, watching shows, even watching sports – but I’ve never seen anyone stop in the middle of a fight or game or duel or race to take a sip of wine. Marathon runners will stop for some water or Gatorade but wine? Nope. It’s interesting that Claudius thinks this wine poisoning bit is going to work – because almost anyone would be likely to refuse it in the midst of a bout.