Evaluate Decathlon Current Scoring System

In decathlon the athletes’ performances are recorded in meters, centimeters, minutes and seconds. These performances from different events are converted into points to make them comparable. However, how to convert results into points is a difficult and controversial issue. In this thesis, it is believed that points of a performance should be rewarded basing on its difficulty, the quality of a performance. At first, We test sample’s departure from normality by Anderson-Darling test and P-value combination test. The tests results confirm that the results of decathlon in top level competition follow normal distribution. Then, the parameters μ and σ2 are estimated by calculating the original data’s mean and standard deviation. Furthermore, we define difficulty through the cumulative distribution function and evaluate the current scoring system. The evaluation is focused on checking the property that the performances with same difficulty should be rewarded same points. The result shows that, according to the current scoring system, the points for combinations of two events with same product of difficulties differ significantly. The more difference of the two difficulties is, the more points will be rewarded. In the end, Yigal Garchak’s algorithm is discussed, and after comparing with the scoring system using today, it is found that his proposal lacks of sensitivity of level of difficulty.