評估NBA球員表現的統計方法

Abstract

由於籃球比賽相較於棒球是團隊合作成分較大的球賽類型，在評估球員個人的表現時會變得比較困難。使用正負值為基礎的方法可以將球員對球隊及隊友的各種可能影響考慮進去，而不是只有參考球員個人的表現。本篇文章使用貝氏的加權回歸線性迴歸模型(BWLR)，找出個別球員以及個別球隊對每次球權結果的影響，包含了進攻以及防守兩部分，並且利用實證資料估計在不同比分及比賽時間之下，每次球權結果的變異，進而將”垃圾時間”效應加入我們的模型。交叉驗證的結果顯示貝氏加權線性迴歸模型在每次球權及每場比分差的均方根誤差均較未加權的模型小，而預測每場比賽比分差的相關係數以及比賽勝負的準確率也提高，代表此模型有抓到垃圾時間的分數變異。另外我們將BWLR與Lasso, Ridge, Elastic net的表現作比較，發現BWLR雖在每次球權及每場比分差的均方根誤差較大，但其預測最後比分差的相關係數以及最後比賽勝負的準確率較高。 同時我們也可以利用BWLR找出在球隊之中，哪個球員才是貢獻最大的，我們發現在2014’-15’賽季中，冠軍隊伍金州勇士隊中對球隊在攻守兩端幫助最大的是Draymond Green，而不是名聲較高的Stephen Curry。

Comparing to baseball games, basketball games are more about team works. It makes evaluating the performance of an individual player or individual team more difficult. The plus-minus based models could take every possible influence of a player on his team or teammates into account, rather than only considering the player’s personal performance. In this thesis, we applied Bayesian Weighted Linear Regression (BWLR) to evaluate the player performance and team effect on the points per possession (PPP), including both offensive and defensive parts. In addition, we tried to consider the garbage-time effect into this model by estimating the variance of points per possession of empirical data under different points differential and game time. The cross-validation results showed that root-mean-squared-error (RMSE) of possession and game points of BWLR were smaller, and the correlation of predicted game points and accuracy of predicted winning results were higher than the unweighted model, which meant that the BWLR model did catch the variance of the points per possession in garbage time. We also compared BWLR to shrinkage methods including lasso, ridge, and elastic net. Although the RMSE of possession and game points of BWLR were larger, the correlation of predicted game points and accuracy of predicted winning results were higher than shrinkage methods. We can use BWLR to find which player has the most important contribution in a team. We found that in 2014’-15’ season, the most contributed player in the champion team, Golden State Warriors, was not the most famous one, Stephen Curry, but Draymond Green, who performed well in both offensive and defensive ratings.