Lanchester equations have been weighed….


There have been a number of tests of Lanchester equations to historical data over the years. Versions of Lanchester equations were implemented in various ground combat models in the late 1960s and early 1970s without any rigorous testing. As John Stockfish of RAND stated in 1975 in his report: Models, Data, and War: A Critique of the Study of Conventional Forces:

However Lanchester is presently esteemed for his ‘combat model,’ and specifically his ‘N-square law’ of combat, which is nothing more than a mathematical formulation of the age-old military principal of force concentration. That there is no clear empirical verification of this law, or that Lanchester’s model or present versions of it may in fact be incapable of verification, have not detracted from this source of his luster.”

Since John Stockfish’s report in 1975 the tests of Lanchester have included:

(1) Janice B. Fain, “The Lanchester Equations and Historical Warfare: An Analysis of Sixty World War II Land Engagements.” Combat Data Subscription Service (HERO, Arlington, VA, Spring 1977);

(2) D. S. Hartley and R. L. Helmbold, “Validating Lanchester’s Square Law and Other Attrition Models,” in Warfare Modeling, J. Bracken, M. Kress, and R. E. Rosenthal, ed., (New York: John Wiley & Sons, 1995) and originally published in 1993;

(3) Jerome Bracken, “Lanchester Models of the Ardennes Campaign in Warfare Modeling (John Wiley & sons, Danvers, MA, 1995);

(4) R. D. Fricker, “Attrition Models of the Ardennes Campaign,” Naval Research Logistics, vol. 45, no. 1, January 1997;

(5) S. C. Clemens, “The Application of Lanchester Models to the Battle of Kursk” (unpublished manuscript, May 1997);

(6) 1LT Turker Turkes, Turkish Army, “Fitting Lanchester and Other Equations to the Battle of Kursk Data,” Dissertation for MS in Operations Research, March 2000;

(7) Captain John Dinges, U.S. Army, “Exploring the Validation of Lanchester Equations for the Battle of Kursk,” MS in Operations Research, June 2001;

(8) Tom Lucas and Turker Turkes, “Fitting Lanchester Equations to the Battles of Kursk and Ardennes,” Naval Research Logistics, 51, February 2004, pp. 95-116;

(9) Thomas W. Lucas and John A. Dinges, “The Effect of Battle Circumstances on Fitting Lanchester Equations to the Battle of Kursk,” forthcoming in Military Operations Research.

In all cases, it was from different data sets developed by us, with eight of the tests conducted completely independently of us and without our knowledge.

In all cases, they could not establish a Lanchester square law and really could not establish the Lanchester linear law. That is nine separate and independent tests in a row with basically no result. Furthermore, there has never been a test to historical data (meaning real-world combat data) that establishes Lanchester does apply to ground combat. This is added to the fact that Lanchester himself did not think it should. It does not get any clearer than that.

As Morse & Kimball stated in 1951 in Methods of Operations Research

Occasionally, however, it is useful to insert these constants into differential equations, to see what would happen in the long run if conditions were to remain the same, as far as the constants go. These differential equations, in order to be soluble, will have to represent extremely simplified forms of warfare; and therefore their range of applicability will be small.

And later they state:

Indeed an important problem in operations research for any type of warfare is the investigation, both theoretical and statistical, as to how nearly Lanchester’s laws apply.

I think this has now been done for land warfare, at last. Therefore, I conclude: Lanchester equations have been weighed, they have been measured, and they have been found wanting.


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.



Series of Tubes


RAND has published a report on its analysis of “NATO’s Eastern Flank” (meaning the three Baltic states). The PDF can be obtained here:  Of particular interest to us is Appendix A: Methodology and Data (page 12).

RAND is using a hex board game with counters that appears to have strength and movement factors on them. This is Tactics II…Avalon Hill…..SPI. RAND does have their own combat model, JICM (Joint Integrated Contingency Model), so why are they using a hex board game? According to their article:

RAND developed this map-based tabletop exercise because existing models were ill-suited to represent the many unknowns and uncertainties surrounding a conventional military campaign in the Baltics, where low force-to-space ratios and relatively open terrain meant that maneuver between dispersed forces—rather than pushing and shoving between opposing units arrayed along a linear front—would likely be the dominant mode of combat.

The problem is that JICM does movement down to having a series of “places” that are connected by “links.“ These links are tubes of variable width, connecting between each “place”. So for example, there might be a tube between St. Petersburg and Talinin. All combat would occur up and down this tube, but there could be no real movement out of the tube. This is a limited and somewhat inflexible movement system that has been used in a few other models (SOTACA comes to mind).

Now, I gather RAND has the whole map of the world set up for JICM as a “series of tubes.” According a 1995 report, there were nearly 1000 “places” and 2000 “links” for the entire world. This does not give a lot of fidelity, as the map of Korea shows at the top of the post. I suspect the fidelity is such that there are few tubes in an area as small as Estonia.

Estonia is small. It is 17,505 square miles. This is smaller than West Virginia (24,038 sq. miles), and it is a lot flatter. But, somehow, they have managed to maintain an independent language of over a million speakers (1.2 million actually). This language has managed to survive for over a thousand years! I am always impressed by that. Their capital is only about 100 miles from several points along the Russian border. This is about the distance between Washington DC and Richmond. Now granted, it took several years to cover that distance during the American Civil War, but there was a significant Confederate Army in the path. Therefore, to examine scenarios, I suspect they needed a map of considerably more fidelity than JICM and its “series of tubes.”

Other Oil Producers


The graphic is pulled from an article on Russia and Saudi Arabia agreeing to hold production at current levels.

Holding production at current levels, of course, does not cause the price of oil to go up, but may limit the amount it will decline. Added to that, Iran is still increasing production and Iraq might if it could ever regain control of Mosul and surrounding areas. There is still considerable pressure to further reduce the price of oil.

I am no expert on the oil market, so I will leave making more precise incorrect predictions to those experts. But I gather the price of oil will not be climbing stratospherically upwards for the next year or two. This puts significant economic, budgetary, and of course, political pressure on a number of major oil producers. Russia is not alone in this regard.

Our focus has been on Russia, but there are a number of other countries clearly being impacted by the long-term decline in oil prices. The countries on that list that get my attention are:

  1. Saudi Arabia
  2. Iraq
  3. Iran
  4. Venezuela
  5. Nigeria
  6. Algeria
  7. Bahrain (which is not on that list)

Pay Cut

Latest estimates for ISIL strength: Pay cut

A few things that caught my attention:

“U.S. intelligence estimates of the number of Islamic State fighters, which for the first 17 months of coalition operations ranged from 19,000 to 31,000, had been revised to 20,000 to 25,000 – a level he said the group would struggle to maintain.”

“”They have been able to replenish their forces at roughly the same rate as we’ve been able to kill their forces. That’s hard to sustain,” he said.”

It does not state, but I wonder how much of the pay cut for Jihadists is due to declining oil prices. Also, do they have health care and a retirement plan?



What Russia’s Failing Economy Means

An article in the Huffington Post caught my attention: What Russia’s Failing Economy Means

A few lines from it:

“But the economic decline in Russia started in the very beginning of 2012. The growth rate was only 1.3 percent in 2013, for example, when oil was well above $100 per barrel”

“The key problem of the economy, and the key reason for the decline, was the decline in investment. The economy cannot grow without investment…In 2012, investment stopped growing. In 2014, investment started to decline. That’s the main reason why the Russian economy is contracting.”

“That means that the only one real chance the Russian economy has is if the government improves the investment climate and boosts investment. But in order to do this, Russia needs to implement the rule of law. Once again, that’s not in the interest of Putin, because implementing the rule of law is the best way for him to lose power” (I put this line in bold)

The increase in military budget by 0.8 percent when inflation in the country is 13 percent actually means shrinking of the military budget. I would not pay big attention to the nominal numbers because inflation in Russia is very high.

“It’s important to note that the Russian economy is not in free fall. It’s not like a landslide, like in Venezuela” (which nicely serves as a lead-in to my next post)

And finally:

“They [poverty and unemployment] may change the political climate, but it won’t happen in a year, or in two years. It may take a decade, maybe, but it’s not a very fast and rapid process.”


Five Percent Cut in Russian Defense Spending

Russia could cut defense procurement spending

To quote a couple of paragraphs towards the end of the article:

“When Putin announced his defense revamp in 2011, the government expected GDP growth of 6 percent throughout the decade. This year the economy is facing its second year in row of falling GDP, its longest recession in two decades.

Oil, which together with a small basket of other commodities makes up half of state revenues, is now selling at slightly above $30 per barrel, just over half the level the Russian government had expected for this year in late 2015.”


War by Numbers III

The table of contents for the book:

—             Preface                                                                                    6
One          Understanding War                                                                 8
Two          Force Ratios                                                                          15
Three       Attacker versus Defender                                                      22
Four         Human Factors                                                                      24
Five          Measuring Human Factors in Combat: Italy                          27
Six            Measuring Human Factors in Combat: Ardennes & Kursk   40
Seven       Measuring Human Factors in Combat: Modern Wars          55
Eight         Outcome of Battles                                                               67
Nine          Exchange Ratios                                                                  75
Ten           The Combat Value of Superior Situational Awareness        83
Eleven      The Combat Value of Surprise                                           113
Twelve      The Nature of Lower Level Combat                                   135
Thirteen    The Effects of Dispersion on Combat                                150
Fourteen   Advance Rates                                                                  164
Fifteen       Casualties                                                                         171
Sixteen      Urban Legends                                                                 197
Seventeen The Use of Case Studies                                                 248
Eighteen    Modeling Warfare                                                             270
Nineteen    Validation of the TNDM                                                    286
Twenty       Conclusions                                                                     313

Appendix I:   Dupuy’s Timeless Verities of Combat                           317
Appendix II:  Dupuy’s Combat Advance Rate Verities                       322
Appendix III: Dupuy’s Combat Attrition Verities                                 326

Bibliography                                                                                       331

Page numbers are based upon the manuscript and will certainly change. The book is 342 pages and 121,095 words. Definitely a lot shorter than the Kursk book.


War by Numbers II

What is it about (these two paragraphs are from my proposal):

War by Numbers looks at the basic nature of conventional warfare based upon extensive analysis of historical combat. Never passé, conventional combat capability has been a feature of the current growth of Islamic State in Iraq and the Levant (ISIL) and has returned as a threat in Eastern Europe. This book attempts to establish what we actually know about conventional combat and why we know it. It also provides an indication of how much impact various factors have on combat. It is the next step in analysis of combat that goes one step beyond what was addressed by theorists like Clausewitz.

It is the nature of the scientific process that hypothesis and theories do need to be tested and challenge. In a sense, we are attempting to add that rigor to a field that often does not operate with such rigor. In a profession where errors in judgment can result in the loss of lives, a rigorous understanding of warfare should be desired. War by Numbers attempts to provide such an understanding.