Validating Lanchester's square law and other attrition models

Abstract

This article addresses the question of validating the homogeneous Lanchestrian square law of attrition by the use of historical data (and by extension, other attrition models). Validating an attrition model means testing that model against reality. In this case, Lanchester's square law is tested against the data from the Inchon‐Seoul campaign of the Korean War. The data are examined using three analysis techniques: linear regression, the Akaike Information Criterion (AIC), and Bozdogan's Consistent AIC (CAIC). The data do not fit the assumption of a single, constant coefficient, homogeneous square law battle. The data do fit a set of three such battles (a new one every six or seven days); however, the data fit three constant‐casualty‐model battles just as well. The homogeneous Lanchester square law cannot be regarded as a proven attrition algorithm for warfare; however, the square law cannot be regarded as disproved either. Data on more battles are required to validate the square law or any other proposed attrition law. © 1995 John Wiley & Sons, Inc.

Efficient Employment of Non-Reactive Sensors

“…Just as the Gurkhas appear to have achieved higher levels of performance than the British benchmark, so it seems reasonable to suppose that yet other forces may be expected to perform at a lower standard. Hartley & Helmbold (1995) in their analysis of the Inchon-Seoul campaign showed that, although the average numbers of US and N Korean personnel involved were very similar, US forces inflicted more than five times as many casualties on their opponents than did the N Koreans. These figures are garnered from US sources only and there may also be biases due to weapon lethality.…”

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)…”

An Inverse Problem of the Lanchester Square Law in Estimating Time-Dependent Attrition Coefficients

“…More recently, Hartley and Helmbold (1995) examined the validity of Lanchester's square law using historical data on the Korean War Inchon amphibious landing and the ensuing capture of Seoul. They concluded that Lanchester's square law with constant coefficients does not adequately fit the data on this three-week-long operation but might do so if each week were considered separately.…”

“…The technique in Hartley and Helmbold (1995) could perhaps be used for this if accurate data at closely spaced times are available. However, a more general approach to such problems has been developed in the engineering literature (Huang andChao 1997, Huang andChen 1999).…”

“…Here we call this the nonparametric conjugate gradient method (NP-CGM) to distinguish it from the possibly better-known parametric conjugate gradient method (P-CGM). In contrast to the method used in Hartley and Helmbold (1995), the NP-CGM does not require any assumption about the constancy or piecewise constancy of the attrition coefficients. Nor does it employ a particular functional form for the time-varying attrition coefficient, characterized by a finite number of adjustable parameters, as would be needed to apply the P-CGM.…”