A critical measure of the quality of a mixed-integer programming (MIP) model with fixed data is the difference, or gap, between the optimal objective value of the linear programming relaxation and that of the corresponding MIP. In many contexts, only an approximation of the right-hand sides may be available, or there may be multiple right-hand sides of interest. Yet, there is currently no consensus on appropriate measures for MIP model quality over a range of right-hand sides. In this thesis, we provide formulations of optimization problems that represent the expectation and extrema of both absolute and relative MIP gap functions over finite discrete sets. In addition, we provide the conditions under which absolute MIP gap functions are periodic. Thus, we provide a framework by which to determine a MIP model's quality over multiple right-hand sides.