The problem of distinct value estimation has many applications. Being a critical component of query optimizers in databases, it also has high commercial impact. Many distinct value estimators have been proposed, using various statistical approaches. However, characterizing the errors incurred by these estimators is an open problem: existing analytical approaches are not powerful enough, and extensive empirical studies at large scale do not exist. We conduct an extensive large-scale empirical study of 11 distinct value estimators from four different approaches to the problem over families of Zipfian distributions whose parameters model real-world applications. Our study is the first that \emph{scales to the size of a billion-rows} that today's large commercial databases have to operate in. This allows us to characterize the error that is encountered in real-world applications of distinct value estimation. By mining the generated data, we show that estimator error depends on a key latent parameter --- the average uniform class size --- that has not been studied previously. This parameter also allows us to unearth error patterns that were previously unknown. Importantly, ours is the first approach that provides a framework for \emph{visualizing the error patterns} in distinct value estimation, facilitating discussion of this problem in enterprise settings. Our characterization of errors can be used for several problems in distinct value estimation, such as the design of hybrid estimators. This work aims at the practitioner and the researcher alike, and addresses questions frequently asked by both audiences.