Sequential Prediction of Table Tennis Games Using Sequential Probability Ratio

Background/Purpose: Sequential prediction refers to the prediction method in sequential analysis where the sample size or test length is not fixed in advance. In sport games like table tennis and badminton, scoring points occurred sequentially. The Wald's sequential probability ratio test (SPRT) is a specific sequential hypothesis test, and the decisions are made with regard to a continuation of scoring. The SPRT reduces the amount of time making decisions compared to a “fix-length” situation. The purpose of this study is to model a sequential prediction of results in table tennis games using SPRT algorithm. Method: A total of 30 sets of 5 games between Ryu and Hao, the top professional table tennis players, were analyzed in this study. Bayesian model based on expert systems of SPRT (EXSPRT) by Welch & Frick (1993) was used to calculate posterior Bayesian probabilities. The difficulty parameters of the SPRT were calculated for each service and receive situation, taking into account winning (theta0) or losing (theta1) games. The alpha and beta parameters of the SPRT were set at .10 (conservative decision on winning/losing), .20 (centrist decision on winning/losing) and .30 (liberal decision on winning/losing), respectively. If posterior probability (PR) is higher than (1-beta)/alpha and lower than beta/(1-alpha), sequential prediction of results (i.e., conservative, centrist, or liberal decision on winning/losing) was made. Ryu was set as the reference player for this model. Analysis/Results: Gaining score ratio of Ryu's winning game sets (theta0) showed .59 to service and .63 to receive, and gaining score ratio of Hao's winning game sets (theta1) were calculated as .41 to service and .48 to receive. In 30 sets, liberal decision on winning or losing game was 78% accurate with only 6 points needed. For centrist and conservative decisions on winning or losing games, the accuracy were 85% and 97% with only 13 points and 17 points needed, respectively. Conclusions: The SPRT algorithm for sequential prediction of results in the table tennis games appears to be useful. Information can be used in sport media and communication.