…[in] the "Field Position Auction" proposal we submitted to the N.F.L. at the end of the 2002-3 season. In it, the loser of the overtime coin flip decides the yard line where the offense starts, and the winner chooses between taking the ball or starting on defense. We would also like to present an alternative method that achieves the same result, but eliminates the coin flip.
At the start of sudden-death overtime, the teams engage in a silent auction to decide possession. Each team writes down the yard line at which it would be willing to start its offense. The numbers are given to the referee in sealed envelopes; the team that picks the lower yard line gets the ball first. The first team to score wins. There is no coin flip. Each team has an equal chance to take possession, and the team willing to give up more field position gets the ball.
Otherwise the coin flip winner ends up triumphant sixty percent of the time. Here is The New York Times link, and thanks to Robert Schwartz for the pointer.