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The NFL Should Auction Possession in Overtime Games Yeon-Koo CHE anD TERRence HenDERSHott uper Bowl XLIII of 2009 featured an auction method to eliminate the coin flip’s DIAGNOSING THE PROBLEM one of the closest contests in Super randomness by letting the teams bid to deter- art of the issue with the current NFL over- Bowl history. If not for the miracu- mine the initial possession. Ptime rule is its sudden death format; name- lous catch by Santonio Holmes in ly, that an overtime game is won by the first the waning seconds, the Steelers WHY THE CURRENT OVERTIME PROCESS STINKS team to score. Sudden death, however, keeps Smight have kicked a game-tying field goal uppose that at the end of tie games, the the playing time manageable in light of the and the Super Bowl would have gone into Sreferee simply flipped a coin to determine physical nature of the sport and the network’s overtime. who won. Everyone would scream that this broadcasting constraints. Also, sudden death In a sense, however, overtimes can ruin was unfair, or, if unfair is the wrong word, it is not unfair by itself, as before the coin flip great games, because, with all too high prob- would certainly be silly. What would be the neither team has an advantage. It is only unfair ability, whichever team gets the ball first wins. point of calling this winning? to the extent that the possession, or receiving Instead of one of the best, the game might have And yet, what happens is not so far from an opening kickoff, confers a significant advan- been remembered as dubious, maybe even ig- that. From 2000 through 2007, in 37 of the tage, as it now does. nominious, with many ‘what ifs.’ We propose 124 overtime games, the team that won the A clue to the nature of the problem and initial coin toss won on its initial possession. to its solution is found by asking what hap- Could overtime outcomes be made more pened in 1994. That year, the NFL moved the Yeon-Koo Che is the Kelvin J. Lancaster Professor of Economic ‘fair’—by which we mean, could random- kickoff spot from the 35 to the 30-yard line Theory in the Economics Department at Columbia University. Terrence Hendershott is a tenured Associate Professor at Haas ness be reduced to increase the role skill and where it remains today, which ensures that School of Business, University of California, Berkeley. execution play in determining the outcome? the receiving team gets good field position. © The Berkeley Electronic Press The Economists’ Voice www.bepress.com/ev October 2009 -1- Field position is everything, as any watcher of Figure 1 football knows and as David Romer has exten- 1 ... ............ sively documented. ............. ............. ............... ................... .......................... A has ball ............................................. .......................................... .................................. ........................ ..................... ECONOMICS BUT NOT ECONOMISTS TO THE ..................... ( ) ................. ............. ............. ......... ............. Probability ................... ............. RESCUE ................. ............... ............ ............. ............ ........... .............. ........... ............. of team A ............ .............. ne lesson of economics is that markets or ............ ............... ............. ..................... ............. ..................... ........... .................... ..............B... has ball auctions produce fairer and less random winning ............... ........... O ........... ..... ................ ................ outcomes. To minimize the impact of luck, it ............ ........... ........... ........... ............ ............ must be the case that the team that receives ............. ................... ..................... ..................... .................... the opening possession has no real advantage. .................... .................... To accomplish this: Why not let the teams trade on who receives the opening possession x∗ 1000 with the starting position used as currency? Yardage from own endzone Although the idea is an economic one, it came first from those who care about the the chance to have the first possession 100 Say team A will win with probability p(x) problem most—not from economists. Chris yards from its own goal, ready to score. They against team B if A has possession x yards from Quanbeck, an electrical engineer and a Green would each grab at the chance, so it wouldn’t A’s goal line, and with probability q(x) if B has Bay Packers fan, was the first to suggest the be fair to give it to either. What about 90 yards? possession x yards from B’s goal line; p(x) is idea of auctioning off the possession, accord- Well, again they would both want the ball. On the upward sloping line and q(x) is the down- ing to an article in Slate. According to his idea, the other hand, neither would want the ball ward sloping line in Figure 1. As x rises, p(x) the team offering to start at a position closest backed up against their own goal. So is there a will go up because it gets easier for A to score, to one’s own end line would win possession at distance x* in between where it wouldn’t mat- at least from a field goal, as one gets close to that position. ter to either team whether A started with the the other team’s end line. Likewise, q(x) will How can opening a market help make the ball x* yards from its goal line or B started with fall with x because B too is more likely to win overtime game less random and, therefore, the ball x* yards from its goal line? Typically, the farther from its own goal line it takes pos- more fair? Imagine that you offered each team there will be, as illustrated in Figure 1. session, which makes A less likely to win. The Economists’ Voice www.bepress.com/ev October 2009 -2- Consider the x* that equates p and q, the its bid. Remarkably, team B will also want to ger of 1 – p(x) and 1 – q(x), thus leaving it with x* such that p(x*) = q(x*). Both teams must lower its bid as well because 1 – q(x) > 1 – p(x), the ‘shorter end of the stick,’ team A will equal- be indifferent to possession at x*. For exam- and 1-q(x) is the probability that B wins if B ize p(x) and q(x) by proposing x*. ple, it might be that the Steelers are just as takes the ball x yards from B’s goal line, and likely to win if they get the ball at their own 1-p(x) is the probability that B wins if A takes COMPLICATIONS 18 yard line as if the Cardinals get the ball at the ball at x yards from A’s goal line. Thus, he theory above is all very elegant, but it the Cardinals’ 18 yard line; that is, p(18) = bids will go down until x falls to x*. Tis unlikely that the teams will have a com- q(18). But then Cardinals should be indiffer- In fact, any standard auction could be used mon and accurate understanding of the prob- ent to possession at precisely 18 yards since to achieve the same result. The point is that abilities of each team winning starting at each 1 – q(18) = 1 – p(18). the auctions will force the teams to bid so that position, as we have implicity assumed. Each But how would we find such an x*? Easy. opening possession yields no real advantage. team presumably knows more than its oppo- Hold an auction. This outcome increases fairness by eliminat- nent about the status of its own offense and Consider an auction in which each team is ing the randomness of the coin flip: The team defense units, and more importantly, its own bidding for possession of the ball. The auction losing possession at the bid of x* does not kickers, at the start of overtime. We argue in is descending in field position which means ‘envy’ that possession. Further, if two teams a paper in Economics Letters that in such a re- that x begins at 100 yards, which means tak- are equally strong or skilled, as is likely giv- alistic setting, auctioning off the possession is ing the ball at 100 yards from ones own goal en the game is going into overtime, then they fairer than divide and choose. line. Each team would love that opportunity! will win with the same likelihood; that is, if Suppose, for instance, that each team Teams successively bid lower numbers, x, in an p(x)=1 – q(x) for all x, then p(x*) = q(x*) = ½. ‘guesses’ x* with some error and that two teams’ attempt to win the auction and get to start with Instead of an auction, one could apply guesses combined are more accurate than one the ball x yards from their own goal line. The another classical idea, namely the ‘divide-and- team’s guess. In divide and choose, the divider lowest bid wins. choose’ method, to achieve the same outcome. will likely propose his best guess on x*, and Suppose that the current bid is at x and One team (divider), selected by, say, coin flip- this may ‘tip off’ his information. The chooser team A is more likely to win if it starts with ping, proposes ‘x’ and the other team (chooser) may exploit this by acting on even better infor- the ball x yards from its goal line than if B chooses between gaining and ceding posses- mation than either team has. This means that starts with the ball x yards from B’s goal line: sion at the chosen x. Say team A is the divider. coin flipping is again necessary to settle the im- that is p(x) > q(x). For such an x, A will lower Then, fearing that team B will choose the big- balance, which brings us full circle. The Economists’ Voice www.bepress.com/ev October 2009 -3- Auctions avoid coin flipping altogether NFL commissioner Roger Goodell suggest- REFERENCES AND FURTHER READING since they treat both teams symmetrically.

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