運用線性迴歸模型預測運動賽事勝率

本論文希望藉由相對簡易的線性迴歸模型，進行NBA例行賽的勝率預測，資料使用2015-19年度NBA例行賽資料，模型選擇線性迴歸模型，主要實驗方法針對在建立線性迴歸模型上的資料拆分以及變數挑選，勝率預測方式我們藉由迴歸模型所預測出的信賴區間做為預測分數區間，並藉由每場比賽兩隊的分數區間分佈作為基準去計算勝率，驗證計算出的勝率方法使用binomial分佈，代入各別不同的對戰組合次數以及預測勝率的機率值，並選出最高機率所代表的事件與實際情況比對，作為最後驗證預測勝率是否準確的方法，最後在針對單一場比賽不考慮特定對手的情況，模型預測準確度為83.64%，若是針對特定對戰組合以及對戰次數，實驗結果模型準確度為48%，若在允許一場勝負誤差的情況下，模型預測準確度為92.2%，主要造成預測誤差的情況在於NBA賽制上不平均的對戰次數，以及各種不同對戰組合上樣本的不足而導致。

關鍵字

線性迴歸模型； NBA ；勝率預測

並列摘要

This study uses the relatively simple linear regression model to predict the winning percentage of the NBA regular season. The dataset uses NBA regular-season results from 2015 to 2019. The prediction model uses linear regression models. The main methods are data splitting and variable selecting. We used the confidence interval predicted by the regression model as the predicted score interval. And we used the score interval distribution of the two teams to calculate the winning percentage. We used the binomial distribution to verify the estimated winning percentage. Substitute each match combination and the predicted winning rate, and finally select the highest probability event as the predicted result and comparing with the actual situation. The final prediction accuracy is 83.64% in a single match without considering the specific opponent, and the prediction accuracy is 48% in a particular match. If we tolerant the prediction results having one game error, the prediction accuracy becomes 92.2%. The main reason for the prediction error is the imbalance of competition and the insufficient number of sample size.