基于蒙特卡洛模拟算法的欧冠淘汰赛抽签概率的研究  

Research on the draw probability of Champions League knockout matches based on Monte Carlo simulation algorithm

作　　者：潘素娟 丁杰[3] PAN Sujuan;DING Jie(Department of Information Engineering,Fujian Commercial College,Fuzhou 350012,China;Key Laboratory of Financial Mathematics of Fujian Province University(Putian University),Putian 351100,China;School of Economics,Xiamen University,Xiamen 361005,China)

机构地区：[1]福建商学院信息工程学院,福建福州350012 [2]金融数学福建省高校重点实验室(莆田学院),福建莆田351100 [3]厦门大学经济学院,福建厦门361005

出　　处：《延边大学学报（自然科学版）》2020年第4期344-351,共8页Journal of Yanbian University（Natural Science Edition）

基　　金：福建省中青年教师教育科研项目(JAT190502);金融数学福建省高校重点实验室开放课题立项项目(JR201802);国家自然科学基金资助项目(11001142)。

摘　　要：为研究欧冠淘汰赛抽签概率问题,以欧冠2017—2018赛季淘汰赛的抽签规则和抽签流程为例,利用蒙特卡洛模拟算法建立了一种新型的抽签概率模型,并通过计算得出了对阵概率的数值解.利用置信区间和分位点对模型所得的对阵概率进行验证表明,该模拟方法具有较好的可信度.对抽签概率进行模拟显示,巴萨队对阵切尔西队的概率约为40%(该结果与实际对阵结果相符),由此再次表明该模拟方法具有可靠性.In order to investigate the draw probability of the Champions League knockout tournament,a new draw probability model is established by using Monte Carlo simulation algorithm,and it is used in the draw rules and process of the 2017-2018 Champions League knockout round,thus the numerical solution of the match probability is obtained through calculation.The confidence interval and quantile are used to verify the match probability of the model,the proposed method exhibit good reliability.The simulation of the draw probability of Barcelona versus Chelsea is about 40%,which is consistent with the final actual result,therefroe the simulation results once more indicate that the proposed method is reliable.

关 键 词：抽签概率 蒙特卡洛模拟 区间估计 置信区间 分位点 

分 类 号：O212.2[理学—概率论与数理统计]