Beyond the Yard Line: Accommodating Rounded Sports Data in Statistical Models

In American football, rushing, passing, and receiving yards are recorded as whole numbers, but using a unique method of rounding, even though the true yardage is continuous and recorded precisely on the field. This rounding introduces measurement error that is systematically ignored in most statistical analyses of these data. Beyond rounding, football yardage presents additional challenges: it can take on negative values and is strongly skewed. These characteristics complicate distributional assumptions and propagate rounding effects. We illustrate the consequences of these issues using data from running backs during the 2023 National Football League regular season. We show that appropriately modeling play-level yardage as a discrete, skewed, and possibly negative quantity, without access to the true values, is important to reconcile the approach with the data generation process. We compare candidate models that correctly incorporate rounding from a model checking and validation perspective. Our findings underscore the broader importance of accounting for discretization and asymmetry in sports analytics and other fields, where recorded data may mask the underlying measurement process in ways that meaningfully affect statistical conclusions.