One of the most important tasks in sports analytics is the development of models for game outcomes or within-game performance to estimate team and player strength. We discuss a variety of commonly used probability models for game outcomes, including Gaussian models for high-scoring games like basketball, correlated Poisson models for low-scoring games like hockey and soccer, paired comparison models for head-to-head games, and ranking models which are often used for races. We consider dynamic extensions to these models to account for the evolution of team and player strengths over time. Full analyses of these time-varying models can be simplified into rating systems, such as the ubiquitous Elo rating system. We further discuss methods for assessing player strength within team games inferred from play-by-play data using the "plus/minus" approach and its variants, and summarize alternative approaches to evaluating player contributions from within-game performance. Applications of the discussed methods are demonstrated using sports data examples throughout the talk.