In NCAA Division I football (FBS), the "BCS paradox" occurs when a conference simultaneously wins and loses the BCS National Championship game. Despite not winning the conference division and playing one less game while the other team competes for the conference championship, the 2nd-in-division team still competes for the MNC (Mythical National Champion) title.
The resulting game is 100% guaranteed to top any previous games labeled as "The Game of the Century", and ensures that the record of "Most Viewers Falling Asleep" will be shattered.
Note that the "BCS paradox" only applies to the $EC, because no other conference can bring in the same amount of money...er, produce the two greatest teams in the nation.
Despite losing the snoozefest against LSU in the regular season, Alabama's week of rest (while LSU was battling Georgia for the conference title) paid off as the Crimson Tide beat the Tigers in the most boring game in the history of football. The fact that the SEC both won and lost the BCS National Championship resulted in the first-ever "BCS paradox".