Tag Archives: Olympics

when is the optimal strategy is to throw a badminton match?

I’ve been following the badminton scandal in the news. First, let me say that I never thought I’d hear the words “badminton” and “scandal” in the same sentence. I thought that this was one of those rare cheating events that sometimes happens. The evidence suggests that the optimal strategy may sometimes be to lose on purpose.

In previous Olympics, the entire set of badminton matches were in a tournament with knockout rounds. A team could apparently not chance their seed or path to gold. In this Olympics, there was a new preliminary pool round with the performance in the pool leading to seeds in the later single elimination tournament with 16 teams. This introduced a wrinkle to the optimal strategy. Now a team might want to think about how they could optimize their seed/path in the single elimination rounds. Obviously, introducing a path to the gold by doing something other than winning every possible match potentially invites trouble. However, the badminton rounds of play with a preliminary pool and later tournament is like what happens in volleyball, basketball, soccer, and other sports. I haven’t seen “lazy” players obviously throwing a match. Usually, winning more in the preliminary round only makes it easier later on.

Apparently, there is a huge incentive in badminton to throw matches. The badminton magazine Badzine conducted a study about throwing matches, since it is common knowledge that the Chinese throw matches. They found that matches were won by “walkovers” or early retirements in 20 of 99 (20%) of all-Chinese matches [link to article]. Walkovers/retirements occured in 5.3% of matches when non-Chinese athletes played their compatriots and in 0.74% of the matches between Chinese athletes and non-Chinese athletes. So the Chinese “throwing” rate is an outlier, which suggests that the Chinese badminton players are all in cahoots with each other. The Olympics scandal, however, included two Chinese teams, one Indonesian team, and one South Korea team.

Here is why the players’ strategy changed from winning all preliminary games to throwing a match:

The attempt to throw the two matches in the women’s doubles had it roots in a surprise result earlier in the day when the Chinese second seeds, Tian Qing and Zhao Yunlei, were beaten by a Danish pair. The result meant that Yang and Xiaoli had to lose to avoid meeting their compatriots before a potential showdown in the final.

A similar desire to avoid the hot favourites seemed to have cross-infected the second match, between  South Korean third seeds Ha Jung-Eun and Kim Min-Jung and Indonesian pair Meiliana Juahari and Greysia Polii [link]

And yes, the cheating was so obvious that people in the audience booed the athletes’ lack of effort:

Lori Halford, 35, who had paid £40 along with her husband for tickets to the evening session, told The Independent: “It was immediately clear that something wasn’t right. The first shot went into the net, then the next shot went into the net. The next return went under the net. There was no speed or strength to their play. There was a complete contrast to the others playing in different games who were giving it everything they could.” [link]

Throwing a badminton match is not dissimilar to sumo wrestlers throwing matches, which was discussed in detail in Freakonomics.

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beach volleyball and game theory

I played volleyball from junior high until when I finished my PhD.  I mostly played traditional 6-on-6 inside volleyball, but I was happy to play just about any type of pickup game. In all those hours on the court, I learned a few things about volleyball strategy.  6-on-6 volleyball highly specialized. A team usually has a setter, two outside hitters, two centers, a weak side hitter, and a defensive specialist that plays in the back row usually for the centers. The team uses their three hits to set up an offense, and no player can touch the ball twice in a row.  Usually, the setter is shielded from the first hit so that she can handle the second hit, accurately passing the ball to a hitter for the best possible offensive attack.

Beach volleyball is a bit different, and the strategy is worth discussing. Clearly, both players have to be good at everything (defense, passing, hitting, blocking, and anticipating the other team’s move).

Less obvious is the role of game theory.  Here, there are two players per team, and a team has three hits to get the ball over the net. It is almost always best to use all three hits to properly set up the offense to maximize the chance of winning the point.

The opposing team, however, wants to minimize the chance of this team getting the point. Every team has a stronger hitter. Usually it’s the tallest person on the team. A team’s goal is to get the best hitter the ball on the third hit. This means that the best hitter needs to get the ball on the first shot. The strategy here is less complicated with a deterministic route of hits between the two players (i.e., if player A gets the ball first, then only player B can get the ball next).

The opposing team is aware of who should not get the ball first, and generally serve or hit to the shorter player. This is like a zero-sum game with perfect information. During the US beach volleyball games with Misty May-Treanor Kerri Walsh Jennings, I noticed that teams almost always served to Misty (the shorter of the two) than to Kerri, despite how good Misty is at serve receiving and defense. This was not a coincidence. This is also not the same strategy as in indoor volleyball, where tall players are usually less skilled defensively, and as a result, often are the target of serves and spikes.

Have you noticed other Olympic sports that have a strong game theory aspect? I’m sure there are lots!


Are you looking forward to the Olympics?

I am looking forward to the Olympic games starting tomorrow.

I am happy to announce that there will be at least one operations research major at the Olympics: Quanitra Hollingsworth, who has a B.S. in Mathematical Sciences/Operations Research from VCU will be competing in the Olympics for the Turkish women’s basketball team. I am so proud of her!

Aside from watching Quanitra compete, I am most looking forward to seeing sports that I don’t normally follow in between Summer Olympics, including:

  • men’s and women’s gymnastics
  • all swimming events
  • badminton
  • marathon
  • volleyball (I prefer indoor to beach, but I’ll settle for either).

I am planning to blog about the Olympics. Please recommend some topics that you’d like to learn about. In the mean time, check out my other Olympic-inspired posts:

  1. Is London ready for the Olympics?
  2. Olympic scheduling
  3. Curling and OR
  4. Olympic scoring systems

What are your favorite Olympic sports?


is London ready for the Olympics? A post on passport check queues at Heathrow

I hate waiting in line, even for a minute.

This post expands upon a great post in The Operations Room blog on passport/immigration waiting times at Heathrow. The queues to clear passport control at Heathrow have become quite political (see this article). The reason is that the UK have increased security (read: slower server service rates) and are anticipating a large number of new passengers when they host the Olympics this summer (read: larger customers arrival rate).

I had the misfortune to travel to and from London via Heathrow in mid-April. (London was a pleasure, the queue at Heathrow was a misfortune). It took me nearly two hours to get through  immigration. I had plenty of time to think about queuing and logistics while I waited. Here are some of my observations.

  • There were two large queues: one for EU residents and one for the rest of us. The wait at Heathrow was much shorter for EU residents. Residents should have a shorter wait. The Operations Room notes that the goal is to get EU residents through the queue in 25 minutes and non-EU residents through in 90 minutes.
  • The problem at Heathrow was staffing too few people. There were 3-6 booths open for non-EU residents at any given time.  They could have maxed out to ~15 booths. There were two people at the front of the queue that would tell us when a booth became available.
  • My service time was about 30 seconds, but 15 seconds to walk over to the booth. Some of the open booths were a long walk from the front of the queue. There wasn’t much inefficiency in the system except for the long walks to open booths.
  • The system is not at steady state. International arrivals come in bunches. It was very busy when I arrived at immigration and less so later.  This makes it challenging to staff the booths. If you are a passenger, your wait is a bit of the luck of the draw. If you arrive at the wrong time, you may have to wait for awhile. Clearly, scheduling >6 people to work the non-EU booths is a bare minimum. I’m not sure if it was possible. One cranky member of the Heathrow staff was unsympathetic because she claimed to have been working for 14 hours at that point.

How could queue waits become shorter? It’s easy: open more booths! In reality, that may be easier said than done: manpower was recently reduced by 18%.  Here are some other suggestions.

  • Having an “on deck” area near each immigration booth where the next person in line could wait would eliminate most of the walking time from the front of the queue to the booth (15 seconds per passenger). The walking time was large relative to the service time, since most service times are short.
  • Some passengers, however, require a long service time. The problem with an “on deck” area is that passengers would get irate if they get stuck behind someone who takes a long time. It’s all about managing expectations.
  • Heathrow in particular needs to find the right mix of staff in the booths vs. directing queue traffic. For the Olympics, it’s probably a good idea to have lots of people directing traffic since they’ll have fewer passengers who are familiar with the airport. People in the UK do this very well, so I expect that those who come for the Olympics will not be lost in the airport.
  • When I entered the queue, there was a sign that said “45 minute wait from here.” The sign was clearly bogus, since it depends on how many booths were open. My wait was more than an hour longer than the posted sign. I would recommend against signs that raise service expectations. People will get even more impatient if they are promised a shorter wait.
  • Centralized immigration booths are efficient (if run properly!). Therefore, I would advise against something like mobile agents who could do the passport checks at the gates. This would only introduce new inefficiencies. The agents would need extra time to move from gate to gate and then set up. Passengers may view a less efficient mobile agent system as “fair” or “preferable” since they are first-come-first-serve and they have shorter lines. But I’m not so sure about this.
  • When all else fails, they can take a cue from Disney and install video projectors where they can show Beatles footage and play famous movies set in London. Or if they can’t find the overhead to install new equipment, they could hire street performers like jugglers to perform for those waiting in line (although I’m not sure if there will be enough room for juggling).

Do you fantasize about optimizing queues while waiting in a queue?


Curling and OR

I discovered two articles (via Jeffrey Hermann of Bethlehem Road) by Kostuk and Willoughby about curling using operations research.  The first paper addresses the “age old debate in curling about whether it is better to be down one point with last shot, or ahead by one point without.”  The answer: it depends.  An earlier paper by the authors (using data from the Canadian men’s championship games) concludes the opposite, namely, that “it is better for a team to be ahead by one point without the last shot.”

Are you hooked on curling?

Has OR been used to analyze other Olympic sports?

Related post:


Olympic scoring systems

A couple of changes on 2/20/10.

I have been having a lot of fun watching the Olympics.  Part of the fun is learning about the scoring systems for the various sports.  There is a lot of variation in scoring, and I have been particularly interested in the objective scoring systems.  It seems that many of the sports require athletes to be consistent over several attempts, either through qualifying rounds or through multiple runs.  A single bad attempt takes an athlete out of the competition. In some of the summer Olympic sports, athletes can toss out low scores, keeping only the best score (such as the longest shot put or javelin throw). So far, this is what I have come up with.

Objective scoring

1. Fastest overall time in one attempt, no qualifying rounds (one great performance is needed for a medal)

Speed skating, downhill skiing, Nordic

2.  Best overall time/score after qualifying rounds in which an athlete must finish in the top two of four to advance (one bad attempt takes the athlete out of medal contention)

Short track skating, snowboard cross,

3.  Best total (average) time/score in multiple attempts (one bad attempt takes the athlete out of medal contention)

Luge, Skeleton

4.  Best overall score over a set of attempts (thus throwing out all but the best score)

Are there any winter Olympic events for this score?  I can only think of summer events, such as shot put.

Halfpipe (see below) uses the best of two scores, although it is subjective.

Subjective scoring

The subjective scoring systems get a lot of attention, particularly for ice skating.  Most of the subjective scores are based on multiple attempts, which means that the athletes must be consistent.  However, extreme judge scores are discarded.  Figure skating is scored as follows:

A panel of twelve judges then award a mark for grade of execution (GOE) that is an integer from -3 to +3. The GOE mark is then translated into a value by using the table of values in ISU rule 322. The GOE value from the twelve judges is then averaged by randomly selecting nine judges, discarding the high and low value, and averaging the remaining seven. This average value is then added to (or subtracted from) the base value to get the value for the element.

The halfpipe uses five judges who each give a score from 0-10, resulting in a total of 50 points (all scores are used). However, only the best score (of two) is used for the score. There is a qualifying round in which only the top twelve athletes move to the final. On a related note, students at Westminster college used simulation to predict that Shaun White would win the halfpipe (he did!).

Olympic gymnastics is scored differently.  The scoring system was changed in 2004, but they keep the tradition of the judges scoring a gymnast separately, and then working together to find consensus.   I always liked that system, since it is like an instant peer-review, in which a gymnast is not penalized or rewarded if a judge misses something.  Gymnastics scoring works as follows:

The new system is heavy on math and employs two sets of judges, an A panel and a B panel, to do the computations. Two A-panel judges determine the difficulty and technical content of each routine. Six B-panel judges score routines for execution, artistry, composition and technique.

The A-panel judges’ scorecards start at zero, and points are added to give credit for requirements, individual skills and skills performed in succession.

The A panel counts only the gymnast’s 10 most difficult skills, which are ranked from easiest to most difficult (from A to G for women and from A to F for men). An A-level skill, like a back handspring in the floor exercise, is worth one-tenth of a point. The value increases by one-tenth of a point for each subsequent level, meaning a B-level skill is worth two-tenths and an F-level is worth six-tenths.

Required elements add a maximum 2.5 points to the score. Extra points, either one-tenth or two-tenths, are given for stringing skills together.

Each judge adds the marks, then the two reach a consensus.

There are many Olympic sports, so I’m missing a lot here.  What has been your favorite Olympic scoring system?  Which is the most fair (or unfair)?

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