Normal-Based Multivariate Statistical Techniques And Its Application To NBA Player Analysis

In this paper I utilize multivariate statistical techniques to analyze NBA player. I focus my attention mainly on two interesting issues—to rank the outstanding players by their season performance and hence to predict MVP of the season, to distinguish those who are qualified to enter the Naismith Memorial Basketball Hall of Fame. In the first part, Ⅰ try to refine many NBA technical statistics into three common factors—offensive factor, assist factor and defensive factor. Ⅰ sum factor scores into a composite score by weights after they are estimated. Ⅰ also propose an adjust method to adjust the composite score from the point that MVP is not only for personal performance but also for team achievement. Ⅰ consider the ranked first player to be MVP. The decision that how many common factors to retain is critical, so Ⅰ use a variety of method to aid the process. In particular, Ⅰ introduce AIC (Akaike information criterion) and it works well.In the second part, Ⅰ investigate some player’s probability to be admitted into Basketball Hall of Fame by discriminant analysis. Because NBA technical statistics were improved step by step, statistics of many retired players are incomplete. Ⅰ manage to solve the problem by cluster analysis. Classical discriminant analysis can’t handle nominal or ordinal nominal variables. Ⅰ design a questionnaire to consult among experts and hence to sum up all the honours into a continuous honour index which can be directly handled by model. Ⅰ also introduce EDDA—a family of discriminant models which merge classical LDA and QDA into the family. Ⅰ adopt CVE (cross-validation error) and AIC to guide the choice of the best model among EDDA family. Ⅰ also compare the pros and cons of both principles. Last but most important, Ⅰ propose a method to choose a subset of variables which is based on multivariate mean compare hypothesis test. Ⅰ call the method p-value selection method.Through out this paper the idea of normality test and transformation has been emphasized. Ⅰ use a variety of methods to assess normality of samples. Whenever there seems a significant departure from normality box-cox transformation is employed to make data more normal-like.