Cellular reprogramming is a source of induced pluripotent stem cells, but this process remains incompletely understood. The current theory of equipotency during reprogramming, in which all cells are equally inducible, argues that clone size distributions arise only from stochasticity in the system. However, large variability is seen in experiments. Our null, stochastic model, does not agree with barcoding experiments and shows that the equipotency theory may not be correct. To better explain these distributions we introduce multiple populations with different reprogramming parameters. Reprogramming is driven by a few dominant clones, a feature that will be captured by this mixed population model. Furthermore, barcoding experiments show correlation in clone sizes in repeated trails, indicating that there is heterogeneity in the reprogramming potential of clones. We will develop a stochastic model informed by experimental evidence that the cells that are derived from the neural crest have a proliferative advantage. This approach also introduces heritable reprogramming potential into our model. An accurate model of the reprogramming process can inform our understanding of the path to pluripotency, and increase the yield of reprogramming protocols.