Some in the west might deem sumo a freak show in which obese children and even more obese adults are paraded to an admiring audience, but is it any more freakish than seven foot basketballers or 300 pound gridiron footballers who can run even time? It is one of the oldest martial arts, perhaps dating back to 23BC (if descriptions written eight centuries later can be so accurate!), but certainly it can be traced to 821 AD when, along with archery and equestrian archery, it formed one of the great annual tournaments at the Japanese imperial court. All modern sumo wrestlers belong to a training stable, the oldest of which date back to the late eighteenth century, and, similar to the WWE, are given new names when they begin their career. There are six sumo wrestling tournaments a year, each lasting 15 days with each wrestler participating once a day. Rankings which determine a wrestler’s social status and monthly income are revised after each tournament taking into account each wrestler’s win/loss record. It was results at some of these tournaments that exposed corruption in the form of match-fixing.
Of course successful match-fixing is covert: no one boasts about it at the time. However, if there is sufficient data on actual results over time, possible patterns of match-fixing (as opposed to individual instances) can be identified by the use of probability theory. One example where data were available led to an investigation by American economists Mark Duggan and Steven Levitt into possible historical corruption in sumo wrestling. Duggan and Levitt had information on tournaments from January 1989 to January 2000, covering 32,000 bouts involving 281 wrestlers and their examination revealed overwhelming evidence of match rigging in the final days of the tournaments. Each additional victory was worth about three ranking points except the eighth win which offered over 11 points. This non-linearity of rewards meant that in the crucial bout when a wrestler had seven wins he stood to gain much more than his opponent stood to lose, a situation which provided an opportunity for possible match fixing. An examination of the data showed that approximately 26.0% of all wrestlers finished with exactly eight victories and only 12.2% with seven, whereas the statistical expectation would have been for a frequency of 19.6% in both cases. Moreover on the last day of the tournament wrestlers with seven wins were victorious roughly 25% more often than would have been predicted.