三分球出手對投籃犯規影響

Abstract

本文以 National Basketball Association (NBA) 的半場統計資料，檢視在三分球被視為贏得比賽或總冠軍重要因子的時代，過多的三分球出手是否會反而減少球隊被犯規而能站上罰球線的機會。如何適當地進行出手選擇的分配，關係到球隊是否能極大化贏球的機會。 在籃球這項運動中，扣除特殊的技術犯規，又分成投籃犯規(shooting foul)和非投籃犯規(personal foul)。由於非投籃犯規造成的原因，並不直接和球員的出手選擇相關，並非我們關注的主要變數。因此，本文主要估計三分球出手比例對投籃犯規的影響，且主客場球隊是否有差異。 我們發現，使用 OLS 估計的結果，顯示三分球出手比例對於投籃犯規的確有顯著的負向關係，無論為主場球隊或客場球隊。為了解決內生性的問題，我們也嘗試使用工具變數法進行估計。使用前幾場比賽的三分球命中率當作本場比賽的三分球出手比例的工具變數。估計結果顯示，整體而言，客場球隊的三分球出手比例對於投籃犯規有顯著的負向關係，且估計的係數大於 OLS 的結果。此外，上下半場和不同的球隊有不同的顯著效果。

Using National Basketball Association (NBA) half time aggregated data, this article examines whether too many three-point shots would reduce a team's chances of getting to the free-throw line after being fouled in an era when three-pointers are a major factor in winning games or championships. The proper allocation of shot attempts has a lot to do with maximizing a team's chances of winning. In the sport of basketball, except for special technical fouls, there are two types of fouls, shooting foul and personal foul. Since the cause of non-shooting foul is not directly related to the player's shot selection, it is not the main variable we are concerned about. Therefore, in this paper, we estimate the effect of the percentage of 3-point shots on shooting fouls and whether there is a difference between home and away teams. We found that the results using OLS estimation showed that the percentage of 3-point shots made did have a significant negative relationship with shooting fouls, both for home and visiting teams. To address the endogeneity issue, we also attempted to estimate using the instrumental variable method. The percentage of 3-pointers made in the previous games was used as an instrumental variable for the percentage of 3-pointers made in the current game. The estimated results show that overall, the percentage of 3-pointers made by the visiting team has a significant negative relationship with shooting fouls, and the estimated coefficient is larger than the OLS results. In addition, there were different significant effects in the first and second halves and by team.