Shrinkage estimation of NFL field goal success probabilities

[摘要] National Football League (NFL) kickers have displayed improvement in both range and accuracy in recent years. NFL management in turn has displayed a rather low tolerance for missed field goals, particularly in game-deciding situations. However, these actions may be a consequence of a perceived appreciable variability in NFL kicker ability. In this paper, we consider shrinkage estimation of NFL kicker field goal success probabilities. The idea derives from the literature on estimating batting averages in baseball, though the classic James-Stein shrinkage approaches there do not apply to independent binary field goal attempt trials. We study a variety of weighting schemes for shrinking model-based kicker-specific field goal success probability estimates to a league-wide estimate, as a function of distance. As part of the development, we briefly detail collecting NFL play-by-play data with the R statistical software package, identify the complementary log-log link function as preferable to the more commonly applied logit link function in a generalized linear model for field goal success, and demonstrate the desired variance-reduction, both in and out of sample, enjoyed by our proposed shrinkage estimators. We illustrate our methods by ranking NFL kickers from 1998 to 2014, analyzing individual kicker success at mid-range and long-range field goal attempts, and studying kicker ability over the last decade. Stadium effects are added to the model and found to be highly significant and to have an impact on the kicker rankings.

[关键词] NFL kicker rankings;generalized linear models;weighted average;big leg kickers;web scraping;stadium effects