Hi people, Having suffered some serious bad beat recently, I decided to push the boundaries of bad faith a little further by using the power of science to justify my lousy badminton play . The question I asked myself was: considering two hypothetical players with identical abilities, what would be a typical score at the end of a 21 points game. For the sake of simplicity, I took the simplest model possible by making the assumption that the result of each rally is given by a coin flip (50% chance of winning for both players). This ignores the numerous psychological or physical effects of winning or losing points and as such doesn't reflect the real world, but I suppose the results are slightly surprising and I thought I might share them with you, fellow bad players. I first wrote a tiny program simulating millions of games on my computer and then actually realized it was not very difficult to derive the exact mathematical probabilities. Both the “experimental” and theoretical results are compatible so I am quite confident with my numbers. I can give details if requested but don't want to bother you too much. The probabilities of various scores (point differences) and the cumulative probabilities (prob. of winning or losing by n points or less) are given on the two linked images. The probability of a 2 points difference is also high because of the tie-break system and a 1 point difference is unlikely (only when reaching 30). The other probabilities follow a half-bell curve. The average point difference is 5.3. I think it is quite interesting because, I would tend to consider any below 21-15 to be a clear win or defeat. In the hypothetical case of identical players I considered, it will happen nearly one third of the time ! Even more surprising, 7% of the time, there will be more than 10 points of difference. This means that a score of 21-11 or less would not be be unlikely to happen once for a single player playing 5 matches in a row during a tournament. From these simplistic results, I would emit the hypothesis that we (or I, at least) often underestimate the influence of luck alone when we play badminton. While I don't know much about that, there might be a case for a cognitive bias that make us think that the “best player should win the match” more often than it would really be the case. So next time you get beaten 21-12 21-13, just claim that, actually, you were stronger, it's just math that made you lose Olivier http://img24.imageshack.us/i/pointdifferencedistribu.png/ http://img851.imageshack.us/i/ulativedistribution.png/
