I'm sure bookies watch interviews with coaches/managers before games and parse what they say to figure out how confident they are. "But they're doing that to signal to their players and the other team what they want them to believe." And couldn't that also be true of betting patterns?

So he didn't bet when certain pitchers were up. Probably because he knew they didn't win as often. Don't bookies have access to won/lost records, too?

The one possible accusation is that he would schedule a stronger pitcher in a mathematically unimportant late-season game rather than saving him for a division rival later in the week. But considering the bonuses teams usually get for post-season appearances, those would have to be pretty big bets to change his scheduling.