概率论在预估网球比赛决胜盘局数中的应用

The Application of Probability Theory in Estimating the Number of Games of Final Set in Tennis Matches

在采用长盘决胜制的网球比赛中,决胜盘的局数有多有少,不易预估.首先基于概率论在选手发球局的胜球率一定的情况下,理论计算了决胜盘局数的期望值,然后利用蒙特卡洛方法,数值模拟了网球比赛决胜盘的局数,结果表明,随着模拟次数的增多,理论值和数值仿真结果完全一致.最后统计了10场的发球局胜球率为86%的实际比赛记录,并计算了10场网球比赛的决胜盘的平均局数,对比分析发现,理论、仿真、实战等三者结果非常一致.

In the tennis match with the advantage set,the number of games in final set is difficult to predict.In this paper,based on the theory of probability,the expected value of the number of games in final set is calculated theoretically under the condition that the winning rate of the player′s serve is certain.Then,using the Monte Carlo method the number of games in the final set of the tennis match is numerically simulated.The results show that the theoretical values are completely consistent with numerical simulation results while increasing the number of simulations.Finally,the actual game records of ten games with winning rate of 86%in service games are counted,and the average number of games in the final set of ten games are calculated.The comparative analysis shows that the three results of theory,simulation and actual matches are very consistent.