Will Justices Recuse Themselves Because They Are Baseball Fans?

An interesting question has been posed in anticipation of the Supreme Court deciding on whether or not to hear a case regarding fantasy baseball. The issue in the case is as to who owns the statistics for baseball players. Is it Major League Baseball, or are they owned by nobody and therefore, free to the world. It is known that Justices Alito and Stevens are big baseball fans, but do they also participate in fantasy baseball? If they do, it would be interesting to see if they recuse themselves because the league they play in would be affected by the decision. If the Court finds for MLB, then others who provide fantasy leagues (such as Yahoo, ESPN, CNNSI) would either have to pay for the statistics or would be forced to no longer host these leagues. If they pay for the statistics then users will likely have to pay for leagues that are now free. Users will also likely have to pay in MLB is the exclusive provider of these leagues. So, it would appear that the Justices have a rooting interest in the outcome and may have to recuse themselves, similar to what they do when they have stock ownership in a company that argues before them.