Putting the art before the force

Adrian Pincombe, Brandon Pincombe, Charles Pearce

Abstract


We use a dataset from the Battle of Kursk to test three estimators of attrition: linear, quadratic and log dependence on the number of soldiers in each force. Data giving force numbers per day show significant collinearity, so we use force and loss ratios for our tests. We demonstrate that the strongest correlate in the dataset for a sides attrition is its own force strength. This supports the log estimator, and we evaluate the proposition that this counterintuitive connection is a product of the pre-battle art of war, where commanders attempt to balance their forces to their expectations of threat. Thus expected losses generate actual force numbers whereas we seek information on the ways that force numbers generate actual losses, and both processes are based on the same correlation information. We argue that the dataset must still contain information on the mechanisms of attrition, so we widen our search criteria and uncover some remarkable facts.

References
  • J. Bracken. Lanchester models of the Ardennes campaign, Naval Research Logistics, 42, 1995, 559--577.
  • W. J. Bauman. Kursk operation simulation and validation exercise---phase II. CAA-SR-98-7. US Army Concepts Analysis Agency, 1998.
  • C. von Clausewitz. On War. Edited and translated by M. Howard and P. Paret. Princeton University Press, 1984.
  • R. D. Fricker, Attrition models of the Ardennes campaign, Naval Research Logistics, 45, 1998, 1--22.
  • D. S. Hartley. A mathematical model of attrition data. Naval Research Logistics, 42, 1995, 585--607.
  • T. W. Lucas and T. Turkes. Fitting Lanchester equations to the Battles of Kursk and Ardennes. Naval Research Logistics, 51, 2004, 95--116.
  • T. W. Lucas and J. A. Dinges. The effect of battle circumstances on fitting Lanchester equations to the Battle of Kursk. Military Operations Research, 9, 2004, 17--30.
  • M. Osipov. The Influence of the Numerical Strength of Engaged Forces in Their Casualties. Voennyi Sbornik, 1915, no. 6 (June) 59--74, no. 7 (July) 25--36, no. 8 (Aug.) 31--40, no. 9 (Sep.) 25--37, no. 10 (Oct.) 93--96. Translated by R. L. Hembold and A. S. Rehm. Naval Research Logistics, 42, 1995, 435--490.
  • A. H. Pincombe, B. M. Pincombe and C. E. M. Pearce. A simple battle model with explanatory power, ANZIAM Journal, 51(E), 2010. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/2585
  • R. H. Peterson. On the `logarithmic law' of attrition and its application to tank combat, Operations Research, 15, 1967, 557--558.
  • L. R. Speight. Lanchester's equations and the structure of the operational campaign: between campaign effects. Military Operations Research, 7, 15--43, 2002.
  • H. K. Weiss. Lanchester-Type Models of Warfare. Proceedings of the 1st International Conference on Operational Research, Amsterdam, 82--99.
  • S. Wrigge, A. Fransen and L. Wigg. The Lanchester Theory of Combat and Some Related Subjects: A Bibliography 1900 -- 1993. FOA Rapport-D--95--00153-1.1,1--SE. National Defence Research Establishment, 1995. http://handle.dtic.mil/100.2/ADA302237

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2584



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.