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Combat Models and Historical Data: The U.S. Civil War

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  • Herbert K. Weiss

    (Palos Verdes Estates, California)

Abstract

Doubt has recently been cast on the applicability of mathematical models in general and Lanchester-type equations in particular to real combat. A comparatively small amount of effort has been spent in the past in testing theory against data, and so the general validity of such modeling largely remains to be demonstrated. In this paper, combat data on the U.S. Civil War is examined to determine the extent to which it can be explained by-simple mathematical relations, and some support, as well as problems, for such modeling is developed. A model for probability of winning is developed, depending solely on the ability of each force to continue to fight after sustaining specified fractional losses. Distributions of parameters describing battles, force ratios, and loss ratios are derived. Limited applicability of Lanchester-type equations is indicated. It is concluded that although these hundred-year-old battles may have limited application to future combat, the possibilities of deriving improved combat models by analyzing real life data are essentially unlimited, and that fact differs sufficiently from theory to make it unlikely that pure conjecture will hit upon the proper form for a combat model structure.

Suggested Citation

  • Herbert K. Weiss, 1966. "Combat Models and Historical Data: The U.S. Civil War," Operations Research, INFORMS, vol. 14(5), pages 759-790, October.
  • Handle: RePEc:inm:oropre:v:14:y:1966:i:5:p:759-790
    DOI: 10.1287/opre.14.5.759
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    Cited by:

    1. Jesús Fernández-Villaverde & Mark Koyama & Youhong Lin & Tuan-Hwee Sng, 2023. "The Fractured-Land Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(2), pages 1173-1231.
    2. Daewon Chung & Byeongseon Jeong, 2024. "Analyzing Russia–Ukraine War Patterns Based on Lanchester Model Using SINDy Algorithm," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    3. Anderton,Charles H. & Carter,John R., 2009. "Principles of Conflict Economics," Cambridge Books, Cambridge University Press, number 9780521875578, December.
    4. Kendall D. Moll & Gregory M. Luebbert, 1980. "Arms Race and Military Expenditure Models," Journal of Conflict Resolution, Peace Science Society (International), vol. 24(1), pages 153-185, March.
    5. Dean S. Hartley & Robert L. Helmbold, 1995. "Validating Lanchester's square law and other attrition models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 609-633, June.
    6. Pettit, L. I. & Wiper, M. P. & Young, K. D. S., 2003. "Bayesian inference for some Lanchester combat laws," European Journal of Operational Research, Elsevier, vol. 148(1), pages 152-165, July.
    7. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
    8. Jack Hirshleifer, 2000. "The Macrotechnology of Conflict," Journal of Conflict Resolution, Peace Science Society (International), vol. 44(6), pages 773-792, December.
    9. Hausken, Kjell & Moxnes, John F., 2002. "Stochastic conditional and unconditional warfare," European Journal of Operational Research, Elsevier, vol. 140(1), pages 61-87, July.
    10. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.
    11. Ian R. Johnson & Niall J. MacKay, 2011. "Lanchester models and the battle of Britain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 210-222, April.
    12. M.P. Wiper & L.I. Pettit & K.D.S. Young, 2000. "Bayesian inference for a Lanchester type combat model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 541-558, October.

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