Sean I think you have to do the math. I love looking at baseball teams to do this kind of math because you get a decent sample size (162 games) and you get the randomness you would get in a typical betting year as well. I looked at the TB Rays. They won 56% of their games for the year but had plenty of ups and downs. They only play one game a day, obviously, so you don't have to deal with multiple bets each day but it's all the same.
If you started with a $100,000 bankroll and wagered 2% on each wager, recalculating after each day, you ended up at $124,932. If you just wagered 2% on each play, you ended up at $125,800.
I also took the Cleveland Indians who won 49.4% of their games figuring if you have a losing season betting it's probably around the 49% number. When looking at their games, readjusting the wagers left you with $78,668 and betting the same amount left you with $79,600.
Both situations left you with about a 1% higher return by leaving the bets the same amount.
Let me know if you think there is an error in my math but pretty sure this is correct.