Lanchester Revisited
To refine my earlier critique of Lanchester, his model applies to combat situations where the limiting factors to one’s destructive firepower are mass and weapon efficiency. Such situations do arise in war, and therefore Lanchester’s model is an appropriate tool for this narrow subset of military engagements.
Iwo Jima offers a classic example of a battle that fit the assumptions of Lanchester’s model. The small size of the island led to concentrated, firepower-based combat. J.H. Engel studied the recorded casualty rates to demonstrate that attrition during the battle for Iwo Jima closely followed the rates predicted by a Lanchester-style model [1].
Other historical studies show varying results, some demonstrating support of Lanchester’s linear law, others finding inconclusive results.
While the coefficients of attrition rates can be modified to account for training, terrain, moral and the host of other factors Lanchester does not explicitly consider, these modifications do not change the fact that Lanchester chose to make these factors exogenous to his model. This says a great deal about his assumptions regarding what dynamics would be interesting to study, and the implicit assumptions accepted by subsequent analyses using his models. My concern is that while it accurately describes a relatively rare type of military engagement, Lanchester’s model became the de facto standard for all combat.
[1] Engel, J. H. “A Verification of Lanchester’s Law,” Operations Research, 2, 163-171 (1954).
