The Comparison of the Cold and Hot Hand Models

[[abstract]]運動一直是人類最為普遍的休閒活動之一，在各個地區或國家中，皆有其最為盛行的運動項目。此，學者紛紛著手研究與運動相關的議題，其中”冷熱手感”更為重要的研究之一。 本文之目的在於二項模型、二狀態馬可夫轉換模型與三狀態馬可夫轉 模型之比較。研究中採用美國職業棒球聯盟(MLB)中五位選手的資料，以上述三種模型進行每場比賽打率的配適；並進而採用AIC法作為配適效果的評斷標準。 分別以二項模型、二狀態馬可夫轉換模型與三狀態馬可夫轉模型進行配適，並依AIC法判斷這三種模型配適的優劣性發現，二狀態與三狀態馬可夫轉換模型對於這五位選手的打擊資料配適的優劣性差異不大，其中又以Javy Lopez的冷熱手感模型配適較優的比例高於二項模型，然而其餘四位選手以二項模型的配適為較佳。藉由模型的配適，Javy Lopez選手可能有冷熱手感的存在。[[abstract]]Exercise is one of the most common leisure activities of human beings. In each country or regions all over the world, there is most popular sport activity. Researchers are therefore exploring sports related issues. Of all the related issues, one import research is focusing on ”Hot hand and cold hand” or ”streakiness” phenomena of sports. The objective of this study is to compare the binomial model, two-state Markov switching model and three-state Markov switching model that are used to fit the baseball batting data. In this study, we use game at-bats and hits data of five players of the U.S. Major League Baseball (MLB). The three models have been fit to the data of hitting probability of each game respectively. Furthermore, the AIC method is used for model selection. Binomial model, two-state Markov switching model, and three-state Markov switching model have been fit respectively. According to the AIC method to judge the three models, we find that the two-state Markov switching model and the three-state Markov switching model do not present significant difference in model fitting for the five players. Among, the rate of fitting streaky models is better than fitting binomial model for Javy Lopez’s data. However, the remaining four players better fit binomial models. By model fitting, Javy Lopez may exist streakiness