If you predicate your logic on a ~50% win rate, then yes.
If you flip a coin a bunch of times, you get all kinds of streaks and patterns.
Man, I swear more people *NEED* to read Innumeracy by John Allen Paulos. If more people had a good grasp on the likelihood of "unlikely" events, we'd be better off.
EDIT: Brings to mind a line from one of my favorite movies "Moneyball". Goes something like "You could play this season over again forever and never get that same 20 game streak." There are tons of ways to get the same win record for the A's at the end of the season, and a streak only stands out because we put emphasis on the smaller picture instead of the full record. Same in your case. There are billions of win/loss combinations and streaks that will get you that same record. That same streak and win/loss for any 20 game set is just as likely as any other. Just like a Royal Flush is just as likely as getting a 3, 8, 10, J, K of non-matching suits. We just put emphasis on that one hand.