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Team's seasonal win probabilities

Published online by Cambridge University Press:  02 July 2021

Sheldon M. Ross Open the ORCID record for Sheldon M. Ross [Opens in a new window]
Sheldon M. Ross*
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. E-mail: smross@usc.edu
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Abstract

We consider a competition involving $r$ teams, where each individual game involves two teams, and where each game between teams $i$ and $j$ is won by $i$ with probability $P_{i,j} = 1 - P_{j,i}$. We suppose that $i$ and $j$ are scheduled to play $n(i,j)$ games and say that the team that wins the most games is the winner of the competition. We show that the conditional probability that $i$ is the winner, given that $i$ wins $k$ games, is increasing in $k$. We bound the tail probability of the number of wins of the winning team. We consider the special case where $P_{i,j} = {v_i}/{(v_i + v_j)}$, and obtain structural results on the probability that team $i$ is the winner. We give efficient simulation approaches for computing the probability that team $i$ is the winner, and the conditional probability given the number of wins of $i$.

Keywords

Applied probabilitySimulationStochastic modeling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 988 - 998
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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