There is great interest in producing effectiveness measures that model user behavior in order to better model the utility of a system to its users. These measures are often formulated as a sum over the product of a discount function of ranks and a gain function mapping relevance assessments to numeric utility values. We develop a conceptual framework for analyzing such effectiveness measures based on classifying members of this broad family of measures into four distinct families, each of which reflects a different notion of system utility. Within this framework we can hypothesize about the properties that such a measure should have and test those hypotheses against user and system data. Along the way we present a collection of novel results about specific measures and relationships between them.