The field trials to the women’s 100 meter dash for the London olympic games had a little unusual twist: Allyson Felix and Jeneba Tarmoh had the same result of 11.068 seconds. Three runners will represent the US in this event. The problem is that Felix and Tarmoh finished together at the third place. I read contradicting articles regarding whether the USA Track and Field, who is in charge of the procedure of choosing the representatives, did or did not have a rule to handle such a case. In any case, it was decided that both athletes will be given the choice of a run-off or a coin toss to determine the final representative.

I will let the poor runners and the USATF solve the issue of who will represent the US in the women’s 100 meters in London. What interests me is what Bobby Kersee, coacher of both Felix and Tarmoh, thinks of the suggested solution of flipping a coin.

Yahoo reports that Bobby Kersee told the Associated Press that “Nine times out of 10, most athletes aren’t going to want to flip a coin. Would you go to the Super Bowl and after two overtimes or what have you, have the referees take both coaches to the middle of the field and say, ‘We’re going to flip to see who wins the Super Bowl?’ I don’t see that.”

Why not? Suppose that a game does not end, like the three-month long quidditch game or the 6 overtimes basketball game between Indianapolis Olympians and the Rochester Royals in 1951. Does driving the players to death make more sense than flipping a coin? After all, the way players play when exhausted does not resemble their usual play, and it might well be that eventually the result is as random as a flip of a coin. It is easy to make a case for play-until-the-end. But sometimes, as in the Felix-Tarmoh case, such a solution might not be feasible due to various constraints, like deadlines and other races. In that case, why not flip a coin?

## 4 comments

June 26, 2012 at 1:10 pm

Zlati PetrovNow consider this question: why isn’t every Super Bowl decided by a coin flip?

Maybe we can argue that because the two teams at such an event are both so good and evenly matched, it is quite likely that the outcome is about as random as a coin flip in almost every Super Bowl.

I add this question because I think it helps us find the answer to yours.

One theory may turn on legitimacy. If the two Super Bowl teams resolve to flip a coin, they may worry that if they win their victory will not be recognized as legitimate after the fact.

This means that the value of victory does not depend only on the fact of victory but on the way it was achieved (I think you can see that- fans oftentimes say that some win was a “fluke”, for example, which robs the win of some of its value).

But if fans know that the outcome is as random as a coin flip, why would they not find a coin flip’s outcome just as legitimate?

One answer is that they don’t know it- they think that the two teams have unequal chances of winning an actual game so a coin flip is unfair (in this case, we define unfairness as the extent to which the coin flip’s mean outcome deviates from an actual game’s mean outcome).

But that’s too easy. A more complex answer may be that players and coaches are psychologically biased to think they have a greater than 50% chance of winning every game.

This psychological bias may be evolutionary. If you don’t believe that you have a greater than 50% chance of winning any given game, regardless of the opponent or at least on average, you may prefer not to compete at all (iff the utility function is such that if a game is a 50/50 lottery you would actually prefer to sit at home and not go through the rigors of training and investing huge amounts of sweat in preparation).

In other words, the psychological bias is a prerequisite to the very existence of a sport altogether.

Thus, even if in reality each Super Bowl team has a 50/50 chance of winning, the two sides both believe they have a greater than 50% chance of winning because if they didn’t they wouldn’t be there, on the field.

July 1, 2012 at 11:04 pm

Jonathan WeinsteinEilon,

Though it does not surprise me that they chose to re-race, you are right in the following formal sense: The first race was not *actually* a tie. Someone was first, we just can never know who it was. Furthermore (this would require some assumptions) no tiebreak procedure will tell us who won with accuracy greater than 50% (within a tiny epsilon). So we might as well use the one with lowest cost, a coin flip. The re-race has the same 50-50 chance of picking the “correct winner” as a coin flip. But it feels better to them, obviously!

July 2, 2012 at 11:01 pm

Darren WillisIn the case of Felix and Tarmoh there is statistical evidence to suggest that Felix has a better than 50/50 chance of winning the rematch. She has, on average, produced better times than Tarmoh over the course of the season.

Confidence is also another key factor in performance. Felix will have been supremely confident after qualifying in the 200m with the fastest time in the world in 14 years. Tarmoh, thinking she had already secured the spot, will be questioning everything and everyone, including herself.

For the fan it is about the spectacle and the unknown. Overtime or a tiebreaker that requires an athletic conclusion is bonus time. The Wimbledon tennis match between Nicolus Mahut and John Isner in 2010 was history; a moment that will live in the annuls of the sport.

Sometimes an efficient conclusion just isn’t that interesting.

July 6, 2012 at 5:10 am

Manthos Kallios (KGSM 2000)I disagree that “the first race was not *actually* a tie. Someone was first, we just can never know who it was.” Within the limits of our ability to measure, it was a tie.

Also, questions of probability (the fact that Felix, on average, is the better athlete and therefore “ought to” or “would” have won a rematch) are, I believe, irrelevant in this or any other *sporting* matter. The existence of a “greater-than-50% expectation” is contradicted by history. One need only look at Greece’s winning of the 2004 Euro football championship when nobody at the beginning of the competition (including the team itself) seriously believed that we would make it past the quarter-finals…but miracles happen.

The nature of sporting competition is quite clear and covers both legitimacy and brutal reality. The winner is whoever is better on the day on some *relevant* sporting dimension, regardless of past form and whether this dimension changes with circumstances. Even with a “driving the players to death” strategy and accepting the fact that “the way players play when exhausted does not resemble their usual play”, the win would be based on endurance, a sporting dimension. In international football, after extra-time has been played, the game devolves to penalty kicks. Nobody likes it (especially the English who lose consistently in this phase) but at least it does rely on some level of sporting skill and not on something as random as a coin toss.

Finally, a home-grown example: At the 1999 Thunderbird MBA Rugby Championship, the Kellogg team won 3rd place via a beer-drinking boat race because neither of the two teams involved (I think that the other one was Duke) could be bothered to play a full game. Beer-drinking is, of course, a valid sporting dimension in rugby.