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Olympic badminton / the downside of group stages in competitive sports

Source: http://en.wikipedia.org/wiki/Badminton_at_the_2012_Summer_Olympics_%E2%80%93_Women%27s_doubles

News articles:
http://www.huffingtonpost.com/2012/08/01/badminton-olympics-disqualified-lose-matches_n_1727640.html
http://www.bbc.co.uk/sport/0/olympics/19072677

For a bit over two weeks, people all around the world gathered in London to watch the athletes of the 2012 London Olympic Games. Not everyone was cheering every moment; one of the most notable moments of the games occurred in badminton women’s doubles, when four doubles teams were disqualified for poor sportsmanship during the group stage. (This was the first time in Olympic badminton that the competition format began with group play followed by knockout stages.)

The 2 teams primarily discussed here are:
*1. Wang Xiaoli and Yu Yang (China), who played
Jung Kyung-eun / Kim Ha-na (South Korea)

*3. Ha Jung-eun and Kim Min-jung (South Korea), who played
Meiliana Jauhari / Greysia Polii (Indonesia)

* the numbers 1 and 3 in front of these two teams mean that they were seeded first and third, determined from ranking and past performance.

As their two matches progressed, the teams each made numerous errors (such as serving incorrectly into the net and making long or wide shots), and the crowd reacted badly, booing at what they saw. The result was that the four teams from both groups were disqualified, later being found guilty of “not using best efforts” and “conducting oneself in a manner that is clearly abusive or detrimental to the sport”.

The question related to our class is: why did they throw their matches anyway? Is the objective in competitive sport not to overcome your opponent and win? Besides, winning at this group stage generally guarantees better placement (to play competitors ranked lower) in the knockout stage. To start, we begin by examining how this group stage transitions into the knockout stage.

The rules were simple: the winner of Group A (A1) played the second-best of Group C (C2) in the quarterfinals; the winner of Group C (C1) played the second-best of Group A (A2) in the quarterfinals. In this situation, we have two highly-ranked teams (Wang/Yu ranked 1st and Ha/Kim ranked 3rd) in two different Groups vying for a comfortable spot in the quarterfinals. Let’s call them Team A and Team C.

We can construct a payoff matrix for these highly-ranked teams:

		Team A
		Win	Lose
Team C	Win	For both: face a weaker opponent (+), but play a team from their country(-)	For A: play C (-), but do not play a team from their country(++) / For C: play A (the stronger team)(–)
	Lose	For A: play C (-) and face a team from their country (–) For C: play A (the stronger team) (–)	For A: face a weaker opponent (+) and do not play a team from their country (++) For C: do not play A (++) but face their team from their country (-)

Note that while the two teams do not really want to play each other, they also realize that they do not want to play a team from their team from their country later in the quarterfinals or semifinals (so that they maximize their country’s chances at a medal). From this matrix, and from the outcomes, we can probably conclude that Team A had the reasoning to lose its match. The objective of team A was to avoid playing another team from their country that already advanced. In the case for Team C: they do not want to play Team A, the higher-ranked, stronger team. (Assuming team A wins, team C wants to win, and visa versa). Both teams are, nonetheless, still attempting to eventually win the tournament.

So, re-writing this payoff matrix with values:

		Team A
		Win	Lose
Team C	Win	For both: +5-10 = -5	For A: -5+10 = 5 For C: -10
	Lose	For A: -5-10 = -15 For C: -10	For A: +5+10 = 15 For C: +10-5 = 5

Here, we see that it is nothing but beneficial for Team A to lose its match: to avoid playing another team from their country. We should also take into account that Team C’s match occurred an hour after Team A’s match. There is the possibility that Team C played accordingly after knowing team A’s result (that it lost). As long as we believe the payoff matrix and its results for teams A and C, we can then conclude that, after Team A threw its match, Team C would realize this and throw its match as well: to avoid a confrontation with team A. The matches to determine A1, A2, C1, and C2 happened on July 31, one after the other. The payoff matrix above provides a possible explanation about why both of these highly-ranked teams were trying to lose: they were maximizing their country’s chances in getting the most medals (and avoiding playing each other).

In the aftermath, the teams were accused of throwing their matches in an attempt to get a better placement in the knockout stage. The incident here is ugly, unsportsmanlike, and should always be frowned upon. But it’s interesting to note the dynamics in play here, especially during a group stage, when teams can attempt to engage in match fixing. Such occurrences would not happen if Olympic badminton reverted to its original format: let every match be a knockout match (if you lose, you’re out), and the placement of teams is determined only beforehand, with rankings.

— Andy W.

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