The study of cosmology is entering an era of higher quality and higher quantity data that shifts us from limitations due to raw statistics of our data to limitations due to the accuracy of our underlying physical models. A specific set of models where this problem is prominent is the use of halo models to connect the invisible world of dark matter to the visible world of stars and galaxies. Most of these halo models make their predictions by taking the mass of dark matter halos as the sole parameter. The literature has demonstrated that secondary halo properties can have enhanced clustering compared to the general population of dark matter halos, in an effect that is referred to as ``halo assembly bias.'' Neglecting halo assembly bias from our models can result in severe biases. I add to the literature by making the first detailed study on the choice of halo definition on common measures of halo assembly bias. I utilize non-traditional halo definitions seeking a choice that minimizes the impact of environmental effects which may drive halo assembly bias. I find that halo assembly bias is a strong function of halo definition for the properties of halo concentration, halo shape, and halo spin. I demonstrate that the impact of halo redefinition is primarily caused by the changing host halo populations, as neighboring halos are demoted to substructure. I further show that these results are consistent with those of the ``halo splashback radius''; however, halo splashback radius does not increase halo sizes sufficiently to remove halo assembly bias for most scales or masses. I discuss how these results give us insight to the relevant scales of what might be driving these relations and how they give a better understanding of galaxy formation and galaxy evolution. I conclude by laying out a course for the future with multiple paths to better understanding halo assembly bias and constraining how it impacts the models as well as utilizing it as a probe of galaxy formation
