Doggieinvestor - let me ask the question in another fashion.
Could you see Terry Francona, just before the game starts tonight, say to his team, "Alright fellas, Yanks lost today. Let's go out there and play hard - let's gain some ground on 1st place!" Something to an effect to spark a fire under thier asses.
Because if you think that is a reasonable hypothetical, if that is not too far-fetched to imagine, then the Yanks losing today has some effect on the Boston game.
I certainly agree that the Yankees loss could influence the Red Sox game by maybe 3 percentage points in either direction. But, in no way could it alter the odds enough to make it smart to risk ten times more (or whatever) on the game. The games are largely independent events.