Every game he didn't place a bet, he was signaling to the bookies that he thought his team would lose. I don't think he threw any games, but he certainly didn't have the same incentive to win that game. If he knows he's going to place a bet tomorrow, he's going to manage the team differently today when there isn't any money at stake.
There are so many reasons not to honor Pete Rose with a spot in the Hall of Fame. Off the field, he's a pathological liar, a convicted felon, and a statutory rapist. On the field he corked his bat and probably used steroids. Oh, and he bet on baseball games as a player and as a manager.