Are the "Four Factors" indicators of one factor? An application of structural equation modeling methodology to NBA data in prediction of winning percentage - Baghal, T. (Journal of Quantitative Analysis in Sports, 2012)
Significant work has gone into the development of team and individual statistics in the NBA; for example, the team measures of the "Four Factors." Less work has been conducted using multivariate analyses of these metrics, including identifying possible new statistical techniques to analyze these data. In particular, this research examines the feasibility of using structural equation modeling (SEM) for multivariate analyses of NBA Four Factors data. SEM consists of both confirmatory factor analysis (CFA) and path modeling. Before SEM is employed, this research first examines the effects of offensive and defensive Four Factors in a linear regression model, expanding previous research and providing a baseline for the SEM. In doing so, the data show the importance of effective field goal percentage. Next, structural equation modeling is employed. The CFA finds that offensive Four Factors are indicators of a single latent factor, labeled "offensive quality." The "defensive quality" latent factor is estimable when replacing opposing teams` free throw rate with steals per possession. The SEM is extended to regress winning percentage on latent offensive and defensive quality as well as salary. Salary is an important and often overlooked part of multivariate models examining team statistics, but it is easily incorporated in SEM. The explained variance for the regression in the SEM is similar to that of the linear regression model and indicates the importance of both offensive and defensive quality, with offensive quality having a larger effect. Team salaries are related to offensive quality, but not defensive quality or winning. As such, a second structural equation model is proposed where the effect of salary on winning is mediated by its relationship with offensive and defensive quality. Since salary is related to offensive quality but not defensive quality, and offensive quality is more important to winning percentage, this suggests that money spent is done so for offensive performance and affects winning through the performance paid for. These results suggest potential team strategies, as well as the applicability of SEM to sports analytics, not only to NBA data, but to other sports data as well.