SCENE EVALUATION OF A BALL GAME FOR SOLVING LINE-UP OPTIMIZATION

Abstract

Since baseball has been a big business that produces a large amount of money, it becomes important for baseball teams to compose an optimal batting order that maximizes expected runs, Using "markov chain model to estimate the expected runs (Covers et al. 1977)", an expected runs of a certain batting order will be computed. However, it takes an O(n^9) time to reach an optimal batting order in the case of n-batters set. Therefore, we adopt a kind of heuristic method to find a near-optimal batting order instead of finding an optimal one by modeling this problem as a matching problem. To define it as the matching problem, which assigns players to proper line-up positions, we need to quantify "required function of each line-up position", "ability of each player", and "degree of conformity of each line-up position with each player". In this paper, we focus on quantification of "required function of each line-up position". In our quantification method, the required function of each line-up position is quantitatively extracted for giving an evaluative to find a near-optimal batting order. In addition, we evaluate our method in two steps. First, we evaluate the valid of "our quantification method of required function". Second, we evaluate "our matching problem" from the following four viewpoints: 1. Accuracy of expected runs; 2. Computational Effort; 3. Scalability of the method; 4. Conviction of the method; by comparing existing methods.