RAND described the combat system from their hex boardgame as such:

The general game design was similar to that of traditional board wargames, with a hex grid governing movement superimposed on a map. Tactical Pilotage Charts (1:500,000 scale) were used, overlaid with 10-km hexes, as seen in Figure A.1. Land forces were represented at the battalion level and air units as squadrons; movement and combat were governed and adjudicated using rules and combat-result tables that incorporated both traditional gaming principles (e.g., Lanchester exchange rates) and the results of offline modeling….”

Now this catches my attention. Switching from a “series of tubes” to a hexagon boardgame brings back memories, but it is understandable. On the other hand, it is pretty widely known that no one has been able to make Lanchester equations work when tested to historical ground combat. There have been multiple efforts conducted to test this, mostly using the Ardennes and Kursk databases that we developed. In particular, Jerome Braken published his results in Modeling Warfare and Dr. Thomas Lucas out at Naval Post-Graduate School has conducted multiple tests to try to do the same thing. They all point to the same conclusion, which is that Lanchester equations do not really work for ground combat. They might work for air, but it is hard to tell from the RAND write-up whether they restricted the use of “Lanchester exchange rates” to only air combat. I could make the point by referencing many of these studies but this would be a long post. The issue is briefly discussed in Chapter Eighteen of my upcoming book War by Numbers and is discussed in depth in the TDI report “Casualty Estimation Methodologies Study.” Instead I will leave it to Frederick Lanchester himself, writing in 1914, to summarize the problem:

We have already seen that the N-square law applies broadly, if imperfectly, to military operations. On land, however, there sometimes exist special conditions and a multitude of factors extraneous to the hypothesis, whereby its operations may be suspended or masked.



Share this:
Christopher A. Lawrence
Christopher A. Lawrence

Christopher A. Lawrence is a professional historian and military analyst. He is the Executive Director and President of The Dupuy Institute, an organization dedicated to scholarly research and objective analysis of historical data related to armed conflict and the resolution of armed conflict. The Dupuy Institute provides independent, historically-based analyses of lessons learned from modern military experience.
Mr. Lawrence was the program manager for the Ardennes Campaign Simulation Data Base, the Kursk Data Base, the Modern Insurgency Spread Sheets and for a number of other smaller combat data bases. He has participated in casualty estimation studies (including estimates for Bosnia and Iraq) and studies of air campaign modeling, enemy prisoner of war capture rates, medium weight armor, urban warfare, situational awareness, counterinsurgency and other subjects for the U.S. Army, the Defense Department, the Joint Staff and the U.S. Air Force. He has also directed a number of studies related to the military impact of banning antipersonnel mines for the Joint Staff, Los Alamos National Laboratories and the Vietnam Veterans of American Foundation.
His published works include papers and monographs for the Congressional Office of Technology Assessment and the Vietnam Veterans of American Foundation, in addition to over 40 articles written for limited-distribution newsletters and over 60 analytical reports prepared for the Defense Department. He is the author of Kursk: The Battle of Prokhorovka (Aberdeen Books, Sheridan, CO., 2015), America’s Modern Wars: Understanding Iraq, Afghanistan and Vietnam (Casemate Publishers, Philadelphia & Oxford, 2015), War by Numbers: Understanding Conventional Combat (Potomac Books, Lincoln, NE., 2017) , The Battle of Prokhorovka (Stackpole Books, Guilford, CT., 2019), The Battle for Kyiv (Frontline Books, Yorkshire, UK, 2023), Aces at Kursk (Air World, Yorkshire, UK, 2024), Hunting Falcon: The Story of WWI German Ace Hans-Joachim Buddecke (Air World, Yorkshire, UK, 2024) and The Siege of Mariupol (Frontline Books, Yorkshire, UK, 2024).
Mr. Lawrence lives in northern Virginia, near Washington, D.C., with his wife and son.

Articles: 1516


  1. They don’t specify whether they are using the linear or the square law.

    And they do say “e.g.”, so possibly they have some other “traditional” methods in their bag of resolution mechanisms. As I am not aware of any definitive method of calculating loss exchage ratios or advance rates that is well supported by historical data, “traditional” methods may be the best on offer. At any rate, the important thing from a model valdation perspective is to be clear about the mechanism used.

    I have long harboured a fond beleif that ground combat could be quite well modelled by applying Lanchester’s linear law to area fire (including most direct anti-personnel fire), the square law to point (mostly anti-vehicular) fire, and breaking engagements down into “mini-battles” along the lines suggested by Rowland, depending on the degree ofcompartmentalisation of the terrain.

    All it needs is a massive research grant to let me poke about with the idea for a few years…

  2. Yes, a massive research grant … presumably RAND has this from the defense dept. In this game format, I’m tempted to take this to kickstarter or the like to get a broad popular public mandate to take an independent look at this, perhaps produce a follow-on game. How many video gamers and data science geeks would want to play, or at least support the development?

    Does Lanchester apply to air combat? Or for that matter maritime combat? If you’ve got references, or models (battle of Britain, perhaps) that prove this, please share so that I might read. Air power and how it enables and unlocks friendly ground forces, while depressing the possible activities of enemy ground forces is a fascinating topic. We see the Syrians claiming now that Russian air support has made the difference in their fight against the rebels – part propaganda, part truth?

Leave a Reply

Your email address will not be published. Required fields are marked *