The Tao of Gaming

Boardgames and lesser pursuits

Olympic Losing to Win

Slate has an article on the Badminton thing at the Olympics. (Short Form — Several teams deliberately lost matches and were disqualified by the World Badminton Federation).

The article proposes  the “Let the best winner pick their opponent” method, but any bridge player who follows the world championships knows that isn’t a Panacea. You won’t tank to go from 1st to 2nd, but you’ll tank from 4th to 5th.

The bridge system advances 8, with the 1st seed getting the pick of 5th-8th. Suppose that the teams are rated on strength (higher number is better). In theory, that means that you should have:

  1. 100
  2.  95
  3.  90
  4.   85
  5.   80
  6.   76
  7.   73
  8.   70

after the qualifying. But bridge has some element of luck. (Presumably, so does Badminton). Suppose that we say that the #3 team did poorly (but well enough to qualify) and the #7 team did great.

  1. 100
  2.  95
  3.  73
  4.   85
  5.   80
  6.   90
  7.   76
  8.   70

Now, assuming rational selection (you always want to pick the weaker opponent), The favorites pick the #8 seed (as before) but now the #2 picks the 7th seed and the #3 picks the 5th seed. Poor #4 seed (skill=85) is
playing up!. So they tank and lose a match, now look at it

  1. 100
  2.  95
  3.  73
  4.   80
  5.   85
  6.   90
  7.   76
  8.   70

Now (because they lost a match) they get to play the lucky #3 (skill 73), and the new #4 seed gets to play the #90. None of which isn’t to say that the Badminton idea is terrible, just that this isn’t as easy to solve as you’d expect.

Letting the #1 seed pick any opponent (not just 5-8) does solve this a bit, but brings up some hard feelings when the #2 seed picks the #3 seed, and the 3rd seed doesn’t get to pick.

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Written by taogaming

August 3, 2012 at 6:48 pm

Posted in Game Theory, Misc

3 Responses

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  1. A solution would be to let #4 decide (before any pick is done) whether they want to be “pickable” by #1-3 or not. Now the 85-rated team gains little by losing on purpose as the 80-rated team can decide to be pickable, and thus be the ones to get to play 73.

    Antony Lee

    August 3, 2012 at 7:55 pm

    • And once the 4 seed decides, the 3 gets to, then the 2. There will still be some artifacts. Probably better is to have some seeding committee seed the teams subjectively after qualification, then randomize 3-4, 5-6, and 7-8. Or even better, beforehand and secretly. That’ll make it hard even to game the committee. Real carryover also helps prevent this “sportsmanlike dumping.” Intentionally losing to someone to KO someone else is all well and good until you play them down 40.

      JeffG

      August 5, 2012 at 9:39 pm

  2. The disadvantage of an open pick system is that the lowest rated team will always play the #1 seed regardless of how well they do (as long as they make the cut and don’t get the #1 seed). They have very little to play for once they make that cut. The second worst rated team only cares about their seeding if they get to the #1 or #2 seed (and the worst rated team doesn’t seed higher) and so on up the line.

    If you have the top four seeds picking from the bottom four there’s several wonky things that occur around the 4/5 breakpoint. Low rated teams have a lot more incentive to get into the top half, to avoid being picked by the top seeds. Higher rated teams, if they can’t get a high pick, may not care too much about their ranking or as shown may actually prefer to be picked instead of picking.

    All of this gets messier if particular teams match up better or worse with particular opponents. Then the importance of angling for position takes on a lot more significance.

    In general i prefer single or double elim (with best 2/3, 3/5 for shorter/random contests) brackets to avoid just this type of finagling within the tournament. It won’t stop potential seeding shenanigans before the tournament, but for sports like badminton where current performance is more important than past I don’t think it matters as much.

    frunk

    August 6, 2012 at 5:09 pm


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