There has been a long-standing conceptual debate over the legitimacy of assigning components of offspring fitness to parents for purposes of evolutionary analysis. The benefits and risks inherent in assigning fitness of offspring to parents have been given primarily as verbal arguments and no explicit theoretical analyses have examined quantitatively how the assignment of fitness can affect evolutionary inferences. Using a simple quantitative genetic model, we contrast the conclusions drawn about how selection acts on a maternal character when components of offspring fitness (such as early survival) are assigned to parents vs. when they are assigned directly to the individual offspring. We find that there are potential shortcomings of both possible assignments of fitness. In general, whenever there is a genetic correlation between the parental and direct effects on offspring fitness, assigning components of offspring fitness to parents yields incorrect dynamical equations and may even lead to incorrect conclusions about the direction of evolution. Assignment of offspring fitness to parents may also produce incorrect estimates of selection whenever environmental variation contributes to variance of the maternal trait. Whereas assignment of offspring fitness to the offspring avoids these potential problems, it introduces the possible problem of missing components of kin selection provided by the mother, which may not be detected in selection analyses. There are also certain conditions where either model can be appropriate because assignment of offspring fitness to parents may yield the same dynamical equations as assigning offspring fitness directly to offspring. We discuss these implications of the alternative assignments of fitness for modelling, selection analysis and experimentation in evolutionary biology.