Game, Site, Match: Topics in Causal Inference and Sports Statistics

Abstract

This thesis presents three self-contained chapters: a dynamic linear model for rating athletes using their game scores (Game), new perspectives power analysis for multisite trials (Site), and a synthetic matching method for observational causal inference (Match). Matching is the most transparent strategy for conducting causal inference with observational data. In Chapter 1, we generalize Coarsened Exact Matching (Iacus et al, 2012) and augment it with local synthetic controls (Abadie et al. 2010). We demonstrate how our method improves performance while preserving the spirit of exact matching, leading to theoretical and practical benefits. Chapter 2 turns to the analysis of game data. Athletic organizations often want to rate athletes’ abilities based on their past performances. For sports with multiple competitors in each event, Bayesian dynamic linear models (DLMs) provide a natural framework for doing so. In Chapter 2, we extend DLMs using monotone transformations to account for non-normality in game scores and illustrate the use of our method on Olympic athletes. Multisite trials, where randomized experiments are conducted within each of many sites (e.g., schools), are popular in education. In Chapter 3, we consider the problem of power analysis for these trials. We clarify common misunderstandings in this setting and propose a new approach using average margins of error.