- 學位論文
運用Copula-based Regression Model預測中華職棒賽事結果
Applying Copula-based Regression Model to Forecast the Outcomes of Chinese Professional Baseball League.
摘要
由於棒球是二個球隊互相較勁的比賽，若以卜瓦松分配為個別球隊的邊際得分模型來預測棒球比賽結果可能存在個別球隊得分與勝負不一致的問題，因此必須考慮雙變量而非單變量的卜瓦松模型。由於傳統研究雙變量卜瓦松模型是不允許有負相關結構的，且常限制其與個別單變量模型為同一分配族，例如一個多變量常態模型，其各別單變量亦為常態。相較之下Copula允許有負相關，且Copula是一個能將雙變量的聯合分配函數與各自的邊際分配連接在一起的函數。 本論文之目的即在利用Copula函數的優勢，尋找一個雙變量卜瓦松模型來預測中華職棒之賽事結果。 本研究參考了 Govan (2009)的Offense-Defense model為中華職棒球隊的進攻及防守建立Rating，做為得分模型的自變數之一，再加上其它棒球統計變數後，為每一個中華職棒球隊配適一個卜瓦松廻歸的得分模型，再以兩兩球隊的卜瓦松廻歸模型代入Frank Copula及Clayton Copula函數中，以二階段最大概似估計法求得新的邊際模型參數估計值及Copula參數，以得到各球隊得到各種分數的機率值，取最大機率值所對應的分數為所預測的分數。 本論文為球隊建立進攻及防守的排名，結果發現進攻及防守排名變數在模型中佔有重要的地位；在比賽分數的預測上，本研究以Clayton Copula模型的在「大小盤」的預測正確率略高於Frank Copula模型。
並列摘要
Baseball is played by two teams, and it is problematic to fit each team a poisson model for its marginal distribution since the success or failure of a game may be inconsistent with the fitted scores of each individual team. Therefore, bivariate model should be considered rather than univariate model. Conventionally, a negative dependence structure is not allowed in bivariate poisson models, and it restricts the univariate marginal distributions has to be the same family as the bivariate joint distribution, On the contrary, copulas allow negative dependence structure and marginal distributions and bivariate distributions of different families . The objective of this study is to forecast the outcome of the baseball game by using the advantage of Copula function. We consider Govan’s Offense–Defense model to ranking the offensive and defensive capability of Chinese professional baseball league, and treat it as one of independent variable. With other baseball statistics variables, we fit the scores of each team with a poisson regression model and substitute poisson regressions models of pairs of teams into Frank Copula and Clayton Copula models. The parameters of final bivariate poisson models and Copula function can be estimated by maximum likelihood. The probability distribution of fitted scores can be constructed. The fitted score with the maximum probability is assumed final predicted score. This study establishes ratings for each team which can be used to make game predictions. The result showed rating of offense and defense are important variables. We found the Clayton Copula model has a better accuracy in over/under betting market.