The effect of battle circumstances on fitting Lanchester equations to the Battle of Kursk

Lanchester equations and their extensions are widely used in calculating aggregate attrition in models of warfare. However, due to a lack of high-quality battle data, few validation studies have had strong findings. In particular, there are only a few data sets containing detailed, two-sided, time-phased information. This study uses the Center for Army Analysis's recently compiled Kursk Data Base to examine how well the various Lanchester laws fit the southern front of the Battle of Kursk. The Kursk Data Base is unique in that it records the daily combat status of all of the division-level units as: (1) all combat forces in the campaign; (2) all combat forces within contact; and (3) combat forces within contact that are actively engaged. We find that much more of the variation in casualties during the Battle of Kursk is explained by the status of the forces considered and the phases of the battle than by the Lanchester variant used. Specifically, we obtain substantially better fits when we use only the forces that are actively fighting. An additional improvement in fit is gained by breaking the battle into its natural phases. Finally, when comparing fits among the basic laws, we observe that Lanchester's linear law fits these aggregate data better than the logarithmic law does and much better than the square law does.