February 3, 2011
Super Bowl XLV will be the first played under the NFL’s new overtime rules, in which each team gets a possession, unless the extra period’s initial possession results in either a touchdown or a safety. Previously, though no Super Bowl has ever gone into overtime, the team winning the coin toss could take home the Lombardi Trophy by merely driving for a title-clinching field goal.
But is either of these rules truly fair? Even under the new rules, the team that wins the coin flip has an advantage over its opponent, because it has the opportunity to score a touchdown, and win the game, before the other team’s offense gets possession of the ball.
Steven Brams, a professor in New York University’s Wilf Family Department of Politics, and James Jorasch, founder of Science House, an organization that brings together science and business, have devised a rule that is more equitable than both the old and new overtime rules, because it takes the randomness out of which team gains the initial possession and neutralizes the advantage of being the team to receive the ball.
Brams and Jorasch’s overtime rule rests on an on-field bidding process in which the kicking team kicks off from a more advantageous position—farther from its goal line so its opponent needs to cover more yardage to score.
Here’s how it would work.
Dispensing with a coin toss, the teams would bid on where the ball is kicked from by the kicking team. In the NFL, it’s now the 30-yard line. Under Brams and Jorasch’s rule, the kicking team would be the team that bids the lower number, because it is willing to put itself at a disadvantage by kicking from farther back. However, it would not kick from the number it bids, but from the average of the two bids.
To illustrate, assume team A bids to kick from the 38-yard line, while team B bids its 32-yard line. Team B would win the bidding and, therefore, be designated as the kick-off team. But B wouldn’t kick from 32, but instead from the average of 38 and 32—its 35-yard line.
This is better for B by 3 yards than the 32-yard line that it proposed, because it’s closer to the end zone it is kicking towards. It’s also better for A by 3 yards to have B kick from the 35-yard line, rather than from the 38-yard line, it proposed if it were the kick-off team.
In other words, the 35-yard line is a win-win solution—both teams gain a 3-yard advantage over what they reported would make them indifferent between kicking and receiving. While bidding to determine the yard line from which a ball is kicked has been proposed before, the win-win feature of using the average of the bids—and recognizing that both teams benefit if the low bidder is the kicking team—has not. Teams seeking to merely get the ball first would be discouraged from bidding too high—for example, the 45-yard line—as this could result in a kick-off pinning them far back in their own territory.
“Metaphorically speaking, the bidding system levels the playing field,” Brams and Jorasch maintain. “It also enhances the importance of the strategic choices that the teams make, rather than leaving to chance which team gets a boost in the overtime period.”
They add that bidding in the first and second halves could also be used to determine who kicks and who receives in each half, rather than simply alternating. For example, a weak kicking team might bid in the first half so that it is likely to receive. But if it jumps substantially ahead in the first half, it might bid so that is likely to kick in the second half.
“As this example illustrates, the situation a team faces in the first and second halves may be quite different, which will alter its strategic calculation, making its choices more intriguing to fans,” they note. “It is surely more exciting to anticipate the bids of each team in each half, and possibly overtime, than to observe a coin flip at the beginning of a game—no matter which celebrity is doing the ceremonial toss. The strategic skill and ability of a team, which should count in deciding contests, is largely lost in the coin flip.”
Brams and Jorasch add that the idea of teams bidding, and then averaging the bids to achieve a win-win solution, is applicable to other sports and games. In chess, for example, the players could bid on how much less clock time would be allocated to the player of the white pieces, offsetting white’s advantage in moving first. The player who bids less would get the white pieces, but at the average of the two bids.
In football and other sports, as well as games like chess, the principle is the same: The players or teams bid numbers that would make them indifferent—that is, give them no advantage—between two states. Then an intermediate value would be chosen, which puts each player in a position that, according to its expressed preferences, is better than that of its opponent.
“The players start from a level playing field and cannot cry ‘unfair,’ whatever the outcome, because each had a say about the course of play,” Brams and Jorasch conclude. “Skill and strategic acumen come to the fore when the outcome can no longer be attributed to the luck of the draw—or a coin flip.”
Brams is the author of Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures (2008), among other works, and innovation expert Jorasch is a named inventor on more than 350 issued U.S. patents.
Type: Press Release
Press Contact: James Devitt | (212) 998-6808