Steven Brams and James Jorash propose a system for reducing the advantage that comes from winning the coin flip in overtime:
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.”
This seems like a good idea. Also fun for the fans–another way to second-guess the coach.
Cute idea, but the flaw in this proposal is the touchback rule. After a certain point on the field the odds of a kick going into the end zone and getting placed on the 20 yard line go asymptotic. In this system the smart coach would bid their own 1 yard line. They get the ball and are likely to get it at the 20 given a standard kick. A better variant would give the kicking team the option of punting the ball, that way if someone bids deep into their own territory the "winner" of the right to kick can punt the ball and put it out of bounds deep in the opposing side of the field without any chance of a return.
I was suggesting something similar for cricket several years ago (surely got the general idea from somewhere else, it's certainly not new). In cricket, winning the toss is frequently critical, as the game is strongly asymmetric and the condition of the wicket can strongly favour either batting or bowling first. Splitting the difference between sealed bids is an interesting idea though – I was just thinking of an open auction.
What were they bidding on for criket – an advantage in the number of runs or an advantage in the number of wickets.
I don't know that I like this type of inteference in the game. It might make betting easier but it seems to take away some of the randomness of game play and the "fighting against the odds" mentality that sport can generate. If we just aim to make it as fair as possible so that the outcome only depends on the strength of the team then we might as well just simulate it and not even play.
These guys definitely aren't economists: the proposed mechanism isn't even a truthful one! In the example (38 and 32), if you believe the other guy will bid 38, you should bid 37.9999. There is a truthful version of precisely this mechanism, which is essentially just a second-price auction: the low bid kicks from the high bid's yard line.
I think the most obvious option for cricket would be to bid in runs which are added to the total made by one team or the other. The problem with the status quo is that the toss really can be critical, and in extreme cases make the whole game a bit of a farce. That's especially disappointing when it's an important game, like the final of a competition. It's supposed to be a game of skill!
Is this different from Che and Hendershott (2009) "The NFL Should Auction Possession in Overtime Games"? They reference a Tim Harford column in Slate. Anyone figured out the priority of these ideas? On cricket, I agree the toss is asymmetric. I thought maybe what they could do would be to let the team losing the toss be in charge of how the roller is used during the game. Alternatively, you could let the team losing the toss make a substitution after the toss, but before the start of play to allow them to adjust the composition of their team slightly to the conditions (whereas the team winning the toss would have to stick with their named 11).
I've been trying to argue for a system that I think is better. You still do a coin flip. The coach that wins gets to place the ball on the field (or defer). The other coach decides who gets possession there. First score still wins. The most important feature of this system is that any 8 year old appreciates its basic fairness, it's usually known as the "I cut and you choose" system.
I wasn't clear on how the Brams/Jorash system handles ties. I assume that many coaches would be perfectly happy (rationally or not) with the ball at their own 20, especially if the score is 45-45. So I imagine a common situation would have both coaches bidding the other team's 1 yard line. How is this handled by Brams/Jorash?
How big, in points, is the average advantage for the team winning the flip?
There is a similar system used in chess (!) tournament tiebreaks.
The "armageddon" tie-break system gives the players an unbalanced amount of time for time controls, with White getting more (typically 5 minutes vs 4 minutes for Black), but Black gets draw odds — he is deemed the winner if the game is drawn.
The variant is intended to allow for longer time controls while still giving someone draw odds. Both players bid on how much time they will receive, subject to being less than some reasonable longer time interval (say less than 60 minutes). The players get the amount of time they bid, but the one with the shorter bid plays Black with draw odds.
As most players prefer to play Black in the 5 vs 4 minute versions, it turns out most do in these too. The strategy is to get lower than the opponent, but hopefully not too much lower. The balance is between getting undercut and having to win the game outright, vs. being at a huge time disadvantage.
I am pretty sure the 2010 US championship was decided in such a fashion.
A similar idea was actually proposed by someone within the NFL (coach would bid on what yard-line they would start on with the ball – no kickoff) but dismissed by the competition committee. I still think it's a great idea.
A second price auction is better, but it still runs into the problem of the touchback. I say make them play overtime XFL style, which if anyone remembers was to place the ball at the 50 yard line and make the teams race out to dive on the ball.