For the first game the star is out, the other players on the team rally to the rescue, playing with extra effort to compensate for the star's absence. In addition, the opponent often lets down - thinking it may be an easy game with the star out. Also, if the star's absence is announced the day of the game, the betting market tends to over-adjust; bettors betting the game at any price, with a sense of processing insider information, is a common phenomenon. The fact is, the injury is almost immediately accounted for in the point spread, the momentum of betting creates an over-reaction. These factors combine to make betting ON the team with the star player out in the first game a generally profitable approach.

In following games, it's hard for the short handed team to match the extra effort - in fact, the extra effort from the first game tires out the healthy players for future games. And, because of the surprisingly good performance in the first game, the oddsmaker decreases the adjustment for the injury. Plus, the future opponent is less likely to underestimate the short-handed team.  These factors combine to make betting AGAINST the team with the star player out in follow-up games a generally profitable approach.

Others questions to consider:

How important is the absent player to the team chemistry. If highly important, his absence can have more effect that stats might indicate.

How good is the back-up?