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Benchmark experiments are the method of choice to compare learning algorithms empirically. For collections of data sets, the empirical performance distributions of a set of learning algorithms are estimated, compared, and ordered. Usually this is done for each data set separately. The present manuscript extends this single data set-based approach to a joint analysis for the complete collection, the so called problem domain. This enables to decide which algorithms to deploy in a specific application or to compare newly developed algorithms with well-known algorithms on established problem domains. Specialized visualization methods allow for easy exploration of huge amounts of benchmark data. Furthermore, we take the benchmark experiment design into account and use mixed-effects models to provide a formal statistical analysis. Two domain-based benchmark experiments demonstrate our methods: the UCI domain as a well-known domain when one is developing a new algorithm; and the Grasshopper domain as a domain where we want to find the  best learning algorithm for a prediction component in an enterprise application software system.