Reminder: NFL (and College) Overtime is Still Not "Fair"

I don't mind tie games. If two teams are evenly matched and play equally well, a tie is the logical way for a game to end (outside of elimination games, of course).  Ties also make for more interesting playoff races as more teams remain in playoff contention later into the season.  Most football fans, however, disagree with me, and see ties as unsatisfying cop-outs that should be quarantined in the world of soccer.  Overtime reliably serves to break a tie, but it has to be designed carefully or it may reward the wrong things.  In football today, no level of football can claim an overtime system that is totally "fair," but there are fair alternatives to the current systems.

The NFL changed its overtime rule before the 2012 season to require a team scoring a field goal on its initial possession to kick off, to reduce the advantage gained from winning the overtime coin flip.  Since that change, 38 games have gone to overtime. Two of those ended in ties (SF-STL in 2012 and GB-MIN in 2013) and 19 were won by the team receiving the ball first in overtime, with five of those 19 winning with a touchdown on their first possession.  Eliminating the ties from the discussion, 19 games out of 36 (52.8%) were won by the team who won the coin toss and received the ball first.  That sounds pretty fair - but is it?  If you flipped a fair coin 36 times, what are the chances you would flip 19 or more heads?  There are 2³⁶ combinations of coin flips, and the number of those that include 19 or more heads is equal to the sum of 36!/(n!(36-n)!) for all n from 19 to 36.  Dividing the second number by the first shows that 43% of the ways you could flip a coin 36 times include 19 or more heads, so there is a 43% chance you'd get 19 or more heads by chance when flipping a fair coin 36 times, or in other words there is a 43% chance that teams receiving the opening overtime kickoff are winning the game 52.8% of the time by nothing more than random chance.  So, clearly 19 wins out of 36 is within the margin for randomness, though we'll need many more years of overtime games to determine whether that pattern holds up.

Still, it stands to reason that the team that receives the opening kickoff in overtime has some advantage - they can still win the game outright with a touchdown, and even if they settle for a field goal on their first drive, they win the game if they can hold the opposition for a single series.  Even if they kick a field goal and then allow the other team to tie it up again, they can still win with a second field goal.  All of these advantages add up; Advanced NFL Stats' Win Probability Calculator estimates that a team starting overtime at its own 22-yard line, which was the average starting field position after kickoff in 2011, has a 54% chance of victory.  In fact, they have a greater than 50% chance of victory as long as they return the opening kick past their own 5 yard line.  Is it fair that either team should get any advantage at all from something as random as a coin flip?  Well, yes, in a sense.  Both teams have the same likelihood of winning the coin toss before it happens (ex-ante in economics speak), so in that sense the coin toss is fair to both teams.  But after the toss (ex-post), the chances of victory are not equal, and the team with an advantage has done nothing to deserve it - they just won a coin toss.  So the NFL system is not fair because it gives one team an ex-post advantage based on something other than being good at football.

The overtime format used by NCAA football is arguably even worse.  Not only does the team winning the coin flip (who will choose to play defense first in that format) have an advantage (estimated at 52%), but by starting each overtime period at the 25 yard line, the overtime rules create a game that is significantly different from the one played during regulation.  A team with a low-variance offensive strategy designed to punch it in from the 25 has an advantage in overtime over a team with a risk-taking offense designed to create big plays to change field position, even if both are evenly matched in a full-field game.  Similarly, a blitzing, risky defense that can sack a team out of field goal range is an advantage over a risk-averse, bend-don't-break scheme, since the likelihood and consequences of allowing a big play are reduced with a smaller field to defend.  In short, NCAA overtime changes the rules of the game at the most critical time, deciding a game of football with a game of red-zone football.  It's not quite as bad as deciding a hockey game with a shootout, but it's bad, especially since it doesn't even remove the coin-flip advantage.

There are better ways.  Electrical engineer Chris Quanbeck was the first to propose an auction system for determining overtime position.  The idea is simple but brilliant: play full-field sudden death overtime, but let the two head coaches bid on the starting field position, with the team that bids the worst (lowest) starting yardline beginning on offense at that spot.  Each team has its own particular strengths and weaknesses, and therefore each team has some point on the field where it would rather be on defense than offense.  The field position where one coach stops bidding and lets the other team have the ball is the break-even point where there is no remaining advantage to either team.  Fairness!

Quanbeck proposed three possible forms of auction:

1. The standard, live auction.  An auctioneer, hopefully with a big hat and a fast voice, starts the bidding at some yardline and each coach bids a lower number until one side stops bidding, e.g. "alrightnow whowantsthisball at the 25, 25, 25 yardline, yes! 25 do I hear 24, 24 yessir! 23, 22, 21, 21, 21 going once, 21 going twice, 20!..." etc.  I'd love to see Bill Belichik forced to participate in this.
2. Dutch auction.  Give each coach a buzzer, and start a counter at 1, with the count increasing by one per second.  The first coach to buzz in stops the count and starts on offense at that yardline indicated on the counter.  The strategy here is obviously to wait as long as possible while still buzzing first.  No auctioneer or big hat, but this could still get exciting as the tension builds in the crowd, waiting to see who will blink first.
3. Sealed bids.  Each team writes on a slip of paper the yardline where they would be willing to take the ball and gives their slip to the umpire in a sealed envelope.  The low bid wins and starts on offense at the yardline they bid. This method would be less exciting than the other two, but would probably be the quickest.

There are two other ways of choosing that are along these same lines.

1. I cut you choose. Familiar to anyone who has ever had to share a piece of food with a sibling.  One coach names a yardline, the other decides whether to go on offense or defense at that spot.
2. I cut, random choice.  In this variation, one coach names a yardline, then a random process (coin flip, pull from hat, etc.) is used to determine whether he starts on offense or defense.

Economists Yeon-Koo Che and Terrence Hendershott of Columbia University and UC Berkeley, respectively, compared the auction method to the "I cut you choose" method, finding that the two methods are essentially equivalent if both sides have equal knowledge of their own and each others' preferences, though this isn't a realistic assumption in practice.  In reality, both sides have imperfect information, so under "I cut you choose," the coach who "cuts" by naming the starting field position actually tips his hand somewhat, and the coach who then "chooses" offense or defense has some additional information that wasn't available previously.  They concluded that auctions are therefore the fairer method in the realistic scenario where each team has incomplete information about both teams' likelihoods of winning when starting from any position on the field.  Option 2 above, the random choice, is another way of eliminating the chooser's advantage, though the risk there is that the coach who "cuts" could pick an extreme field position one way or the other and hope to win the coin flip, which just brings the random coin flip advantage right back.

As much as I'd like to see coaches bidding for overtime field position like contestants on Storage Wars, or sweating through a game of chicken with panic-button buzzers, the "sealed bids" auction seems like the best choice.  It's quick, it's fair to both teams, it adds a little drama and strategy while removing the randomness of the coin flip, and it lets the game be decided with full-field football instead of goalline football.

One final note: the team receiving the opening kickoff of the game also has an advantage, which the Advanced NFL Stats calculator estimates at 52%, just less than the advantage for the receiving team in overtime.  So the opening possession of the game should also be decided by sealed bids, in addition to the beginning of overtime.