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Sports analytics -- broadly defined as the pursuit of improvement in athleticperformance through the analysis of data -- has expanded its footprint both inthe professional sports industry and in academia over the past 30 years. Inthis paper, we connect four big ideas that are common across multiple sports:the expected value of a game state, win probability, measures of team strength,and the use of sports betting market data. For each, we explore both the sharedsimilarities and individual idiosyncrasies of analytical approaches in eachsport. While our focus is on the concepts underlying each type of analysis, anyimplementation necessarily involves statistical methodologies, computationaltools, and data sources. Where appropriate, we outline how data, models, tools,and knowledge of the sport combine to generate actionable insights. We alsodescribe opportunities to share analytical work, but omit an in-depthdiscussion of individual player evaluation as beyond our scope. This papershould serve as a useful overview for anyone becoming interested in the studyof sports analytics.

Big Ideas in Sports Analytics and Statistical Tools for their Investigation