An even more elegant solution to the overtime problem was proposed in 2002 by Chris Quanbeck, an electrical engineer (and Green Bay Packers fan). Quanbeck's idea was to auction off possession of the ball in the natural currency of the game: field position. The team that was willing to begin closest to its own goal line would receive the privilege of possession.
Football's number crunchers reckon that this "privilege" turns dubious about 15 to 20 yards away from your own goal line. That is, the expected value of having the ball so far back is negative—it's more likely that your opponent will score before you do. But it's not clear that the same would be true in overtime, when teams would be attempting to get within field-goal range rather than trying for touchdowns. If this system were implemented, it might take a couple of seasons for a consensus to develop about how far back is too far back. Still, everyone would be trying to work that out from a position of equal ignorance.
I like it. He also mentions MDS's pizza-splitting solution, but claims the auction is fairer still, as the "splitting" solution still conveys an advantage to the team that picks second. In an auction, the decision is simultaneous, and no team has an advantage.