Napoleonic France won a great many of more than 150 battles in which it engaged. There has been much dispute about which, if any, of the many qualitative theories as to why it was so successful is correct; many of them centered on the personal characteristics of Napoleon himself. However, none of these theories appears amenable to statistical analysis. To examine this question quantitatively we take a new direction. We leave aside questions of generalship and instead analyze the sizes of both of the opposing armies in battles of the Napoleonic Wars, analyzing French wins and losses separately. We find the best-fit linear models for these data sets using the Geometric Mean Functional Relationship. The coefficients of determination for both of these results were 71%, implying that our best fits model the data unexpectedly well. The difference between these two models has high statistical significance. Napoleonic France won even though outnumbered on average by 9%, whereas their opposition won only when they outnumbered the French by typically 83%. We conclude that absolute sizes of armies -- and not just their relative size -- are important factors in determining the result of a battle, and that Napoleonic France and its opponents were very different in their ability to win for given army sizes.