Lanchester models of the Ardennes campaign

A detailed data base of the Ardennes campaign of World War II (December 15, 1944 through January 16, 1945) has recently been developed. The present article formulates four Lanchester models of the campaign and estimates their parameters for these data. Two-sided time histories of warfare on battles and campaigns are very rare, so Lanchester models have seldom been validated with historical data. The models are homogeneous in that tanks, armored personnel carriers, artillery, and manpower are weighted to yield a measure of strength of the Allied and German forces. This weighting is utilized for combat power and for losses. The models treat combat forces in the campaign (including infantry, armor, and artillery manpower) and total forces in the campaign (including both combat manpower and support manpower.) Four models are presented. Two models have five parameters (Allied individual effectiveness, German individual effectiveness, exponent of shooting force, exponent of target force, and a tactical parameter reflecting which side is defending and attacking.) The other two models remove the tactical parameter, which is not generally known prior to warfare, and estimate the other parameters without the tactical parameter. The main results of the research are (a) the Lanchester linear model fits the Ardennes campaign data in all four cases, and (b) when combat forces are considered Allied individual effectiveness is greater than German individual effectiveness, whereas when total forces are considered Allied and German individual effectiveness is the same. The interpretation of the latter result is that the two sides had essentially the same individual capabilities but were organized differently-the Allies chose to have more manpower in the support forces, which yielded greater individual capabilities in the combat forces. The overall superiority of the Allies in the campaign led to the attrition to the Allies being a smaller portion of their forces.