Both construct specification equations (CSEs) and entropy can be used to provide a specific, causal, and rigorously mathematical conceptualization of item attributes in order to provide fit-for-purpose measurements of person abilities. This has been previously demonstrated for memory measurements. It can also be reasonably expected to be applicable to other kinds of measures of human abilities and task difficulty in health care, but further exploration is needed about how to incorporate qualitative explanatory variables in the CSE formulation. In this paper we report two case studies exploring the possibilities of advancing CSE and entropy to include human functional balance measurements. In case study I, physiotherapists have formulated a CSE for balance task difficulty by principal component regression of empirical balance task difficulty values from Berg’s Balance Scale transformed using the Rasch model. In case study II, four balance tasks of increasing difficulty due to diminishing bases of support and vision were briefly investigated in relation to entropy as a measure of the amount of information and order as well as physical thermodynamics. The pilot study has explored both methodological and conceptual possibilities and concerns to be considered in further work. The results should not be considered as fully comprehensive or absolute, but rather open up for further discussion and investigations to advance measurements of person balance ability in clinical practice, research, and trials.