마코비안 도착과정을 이용한 축구경기 득점결과의 예측 = Predicting the Score of a Soccer Match by Use of a Markovian Arrival Process

다국어 초록 (Multilingual Abstract)

We develop a stochastic model to predict the score of a soccer match. We describe the scoring process of the soccer match as a markovian arrival process (MAP). To do this, we define a two-state underlying Markov chain, in which the two states represent the offense and defense states of the two teams to play. Then, we derive the probability vector generating function of the final scores. Numerically inverting this generating function, we obtain the desired probability distribution of the scores. Sample numerical examples are given at the end to demonstrate how to utilize this result to predict the final score of the match.

목차 (Table of Contents)

• 1. 서론
• 2. 마코비안 도착과정을 이용한 축구경기의 모델링
• 3. 축구경기 득점확률분포의 분석
• 4. 모수추정과 수치예
• 5. 결론
• Acknowledgement
• 참고문헌

참고문헌 (Reference)

1 Srinivas R. C, "The Batch Markovian Arrival Process : A Review and Future Work, In Advances in Probability and Stochastic Processes" Notable Publications, Inc 21-49, 2001

2 Lucantoni, D. M, "The BMAP/G/1 queue : A Tutorial" 330-358, 1993

3 Dyte, D, "Rating Based Poisson Model for World Cup Soccer Simulation" 51 (51): 993-998, 2000

4 Lee, H. W, "Queueing Theory" Sigma Press 2006

5 Lucantoni, D. M, "New Results on the Single Sever Queue with BMAP" 7 (7): 1-46, 1991

6 Dixon, M. J, "Modelling Association Football Scores and Inefficiencies in the Football Betting Market" 46 (46): 265-280, 1997

7 Neuts, M. F, "Matrix Geometric Solutions in Stochastic Models" The Johns hopkins University Press 1981

8 Dixon, M. J, "A Birth Process Model for Association Football Matches" 47 (47): 523-538, 1998