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Series:   Elements in Defence Economics

How Important are Superior Numbers?

A Reappraisal of Lanchester's Square Law

Published online by Cambridge University Press:  06 February 2021

David L. I. Kirkpatrick
David L. I. Kirkpatrick
Affiliation:
University College London

Summary

A century ago Frederick Lanchester formulated a mathematical model of combat which suggested that the combat power of a military force was proportional to the product of the individual effectiveness of the units in the force and the square of the number of units deployed. This model reinforced a long-established faith in the importance of superior numbers. However, successive historical studies failed to identify any clear relationship between the numbers and losses in opposing forces. This Element analyses American Civil War battles, and shows that the ratio of losses incurred was inversely proportional to the ratio of numbers effectively engaged. This result demonstrates that the numbers of fighting units in a military force are less important than the ability of those units to get into action and inflict losses on the enemy. This result demonstrates the limitations of the Square Law, and should prevent it from being applied indiscriminately.
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Keywords

American Civil Warsuperior numbersLanchester’s Square Lawquality versus quantitydefence policy
Type
Element
Information
Series: Elements in Defence Economics
Online ISBN: 9781108973458
Publisher: Cambridge University Press
Print publication: 04 March 2021

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How Important are Superior Numbers?
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