Fitting Lanchester equations to the battles of Kursk and Ardennes

Abstract

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good-fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition.

Mass action models of Falklands War battles

“…The sample size is very small but these results are consistent with most of the variance being between battles with high and low offensive support. Figure 2 is consistent with the log law best fit, frequently seen for fits of combat datasets [23,24,17], being an artefact of more voluminous offensive support for a number of battles with slightly less favourable force ratios for the attackers; but the sample size is too small to test this hypothesis.…”

“…Situational force scoring seeks to correct some of the employment oversights by scoring a force against its enemy in a terrain, for example tanks are less useful in urban settings than open country or anti-tank weapons do not add much to a force score if the enemy has no tanks. This approach requires enormous numbers of cases to span the space of possibilities and is, essentially, overfitting which makes it very hard to generalise [17]. Linear systems of mass action models with separate force numbers specified for each of the combined arms are commonplace.…”

Putting the art before the force

“…The significance of the log law has been a matter of speculation and the search for information to explain that significance has been a major driver for this article and its companion [9]. When time phased data, covering the daily numerical force strengths and numerical casualties for each force, became available for the Battles of Kursk and the Ardennes it caused renewed interest in discriminating between Lanchester laws [1,5,4,7,6]. Bracken [1] (1995) defined a generalised form of Lanchester equations which includes the square, linear and log laws as particular cases, and applied it to the Ardennes dataset.…”

“…Lucas and Dinges [7] developed their fcud data (about those actually fighting on each day) from the Kursk database [2] and found, for the homogeneous case, that the linear law worked best R 2 = 0.622 , followed by the log law R 2 = 0.535 and the square law R 2 = 0.289 . Lucas and Turkes [6] (2004) used a weighted sum of people, armoured personnel carriers, tanks and artillery to calculate the force strength for each side and undertook a complex analysis of the data from the Battles of Kursk and Ardennes. For the Ardennes, the force strengths gave R 2 of around 0.3 but with little to distinguish the three models, while a simple homogeneous approach using the numbers of soldiers gave R 2 < 0.1 .…”

When do armed revolts succeed: lessons from Lanchester theory

“…Although Lanchester models are stylized and highly abstract, they have been extensively used for analysis for almost a century because they provide profound insights regarding conditions that affect the outcomes of military conflicts. Examples of such analysis using Lanchester models include studies of the Battle of Britain (Johnson and MacKay, 2011), the Battle of Kursk (Lucas and Turkes, 2004), the Ardennes Campaign (Hung et al, 2005), the Battle of Iwo Jima (Engel, 1954), and the Battle of Inchon (Hartley and Helmbold, 1995). For further information on the analysis and applications of Lanchester models please refer to Washburn and Kress (2009)…”