Tag Lanchester equations

Human Factors In Warfare: Interaction Of Variable Factors

The Second Battle of Ypres, 22 April to 25 May 1915 by Richard Jack [Canadian War Museum]

Trevor Dupuy thought that it was possible to identify and quantify the effects of some individual moral and behavioral (i.e. human) factors on combat. He also believed that many of these factors interacted with each other and with environmental and operational (i.e. physical) variables in combat as well, although parsing and quantifying these effects was a good deal more difficult. Among the combat phenomena he considered to be the result of interaction with human factors were:

Dupuy was critical of combat models and simulations that failed to address these relationships. The prevailing approach to the design of combat modeling used by the U.S. Department of Defense is known as the aggregated, hierarchical, or “bottom-up” construct. Bottom-up models generally use the Lanchester equations, or some variation on them, to calculate combat outcomes between individual soldiers, tanks, airplanes, and ships. These results are then used as inputs for models representing warfare at the brigade/division level, the outputs of which are then fed into theater-level simulations. Many in the American military operations research community believe bottom-up models to be the most realistic method of modeling combat.

Dupuy criticized this approach for many reasons (including the inability of the Lanchester equations to accurately replicate real-world combat outcomes), but mainly because it failed to represent human factors and their interactions with other combat variables.

It is almost undeniable that there must be some interaction among and within the effects of physical as well as behavioral variable factors. I know of no way of measuring this. One thing that is reasonably certain is that the use of the bottom-up approach to model design and development cannot capture such interactions. (Most models in use today are bottom-up models, built up from one-on-one weapons interactions to many-on-many.) Presumably these interactions are captured in a top-down model derived from historical experience, of which there is at least one in existence [by which, Dupuy meant his own].

Dupuy was convinced that any model of combat that failed to incorporate human factors would invariably be inaccurate, which put him at odds with much of the American operations research community.

War does not consist merely of a number of duels. Duels, in fact, are only a very small—though integral—part of combat. Combat is a complex process involving interaction over time of many men and numerous weapons combined in a great number of different, and differently organized, units. This process cannot be understood completely by considering the theoretical interactions of individual men and weapons. Complete understanding requires knowing how to structure such interactions and fit them together. Learning how to structure these interactions must be based on scientific analysis of real combat data.[1]

While this unresolved debate went dormant some time ago, bottom-up models became the simulations of choice in Defense Department campaign planning and analysis. It should be noted, however, that the Defense Department disbanded its campaign-level modeling capabilities in 2011 because the use of the simulations in strategic analysis was criticized as “slow, manpower-intensive, opaque, difficult to explain because of its dependence on complex models, inflexible, and weak in dealing with uncertainty.”

NOTES

[1] Trevor N. Dupuy, Understanding War: History and Theory of Combat (New York: Paragon House, 1987), p. 195.

Aussie OR

Over the years I have run across a number of Australian Operations Research and Historical Analysis efforts. Overall, I have been impressed with what I have seen. Below is one of their papers written by Nigel Perry. He is not otherwise known to me. It is dated December 2011: Applications of Historical Analyses in Combat Modeling

It does address the value of Lanchester equations in force-on-force combat models, which in my mind is already a settled argument (see: Lanchester Equations Have Been Weighed). His is the latest argument that I gather reinforces this point.

The author of this paper references the work of Robert Helmbold and Dean Hartley (see page 14). He does favorably reference the work of Trevor Dupuy but does not seem to be completely aware of the extent or full nature of it (pages 14, 16, 17, 24 and 53). He does not seem to aware that the work of Helmbold and Hartley was both built from a database that was created by Trevor Dupuy’s companies HERO & DMSI. Without Dupuy, Helmbold and Hartley would not have had data to work from.

Specifically, Helmbold was using the Chase database, which was programmed by the government from the original paper version provided by Dupuy. I think it consisted of 597-599 battles (working from memory here). It also included a number of coding errors when they programmed it and did not include the battle narratives. Hartley had Oakridge National Laboratories purchase a computerized copy from Dupuy of what was now called the Land Warfare Data Base (LWDB). It consisted of 603 or 605 engagements (and did not have the coding errors but still did not include the narratives). As such, they both worked from almost the same databases.

Dr. Perrty does take a copy of Hartley’s  database and expands it to create more engagements. He says he expanded it from 750 battles (except the database we sold to Harley had 603 or 605 cases) to around 1600. It was estimated in the 1980s by Curt Johnson (Director and VP of HERO) to take three man-days to create a battle. If this estimate is valid (actually I think it is low), then to get to 1600 engagements the Australian researchers either invested something like 10 man-years of research, or relied heavily on secondary sources without any systematic research, or only partly developed each engagement (for example, only who won and lost). I suspect the latter.

Dr. Perry shows on page 25:

Data-segment……..Start…….End……Number of……Attacker…….Defender

Epoch…………………Year…….Year……..Battles………Victories……Victories

Ancient………………- 490…….1598………….63………………36……………..27

17th Century……….1600…….1692………….93………………67……………..26

18th Century……….1700…….1798………..147…………….100……………..47

Revolution…………..1792……1800…………238…………….168…………….70

Empire……………….1805……1815…………327……………..203…………..124

ACW………………….1861……1865…………143……………….75…………….68

19th Century……….1803…….1905…………126……………….81…………….45

WWI………………….1914…….1918…………129……………….83…………….46

WWII…………………1920…….1945…………233……………..165…………….68

Korea………………..1950…….1950…………..20……………….20………………0

Post WWII………….1950……..2008…………118……………….86…………….32

 

We, of course, did something very similar. We took the Land Warfare Data Base (the 605 engagement version), expanded in considerably with WWII and post-WWII data, proofed and revised a number of engagements using more primarily source data, divided it into levels of combat (army-level, division-level, battalion-level, company-level) and conducted analysis with the 1280 or so engagements we had. This was a much more powerful and better organized tool. We also looked at winner and loser, but used the 605 engagement version (as we did the analysis in 1996). An example of this, from pages 16 and 17 of my manuscript for War by Numbers shows:

Attacker Won:

 

                        Force Ratio                Force Ratio    Percent Attack Wins:

                        Greater than or         less than          Force Ratio Greater Than

                        equal to 1-to-1            1-to1                or equal to 1-to-1

1600-1699        16                              18                         47%

1700-1799        25                              16                         61%

1800-1899        47                              17                         73%

1900-1920        69                              13                         84%

1937-1945      104                                8                         93%

1967-1973        17                              17                         50%

Total               278                              89                         76%

 

Defender Won:

 

                        Force Ratio                Force Ratio    Percent Defense Wins:

                        Greater than or         less than          Force Ratio Greater Than

                        equal to 1-to-1            1-to1                or equal to 1-to-1

1600-1699           7                                6                       54%

1700-1799         11                              13                       46%

1800-1899         38                              20                       66%

1900-1920         30                              13                       70%

1937-1945         33                              10                       77%

1967-1973         11                                5                       69%

Total                130                              67                       66%

 

Anyhow, from there (pages 26-59) the report heads into an extended discussion of the analysis done by Helmbold and Hartley (which I am not that enamored with). My book heads in a different direction: War by Numbers III (Table of Contents)

 

 

Osipov

Back in 1915, a Russian named M. Osipov published a paper in a Tsarist military journal that was Lanchester like: http://www.dtic.mil/dtic/tr/fulltext/u2/a241534.pdf

He actually tested his equations to historical data, which are presented in his paper. He ended up coming up with something similar to Lanchester equations but it did not have a square law, but got a similar effect by putting things to the 3/2nds power.

As far as we know, because of the time it was published (June-October 1915), it was not influenced or done with any awareness of work that the far more famous Frederick Lanchester had done (and Lanchester was famous for a lot more than just his modeling equations).  Lanchester first published his work in the fall of 1914 (after the Great War had already started). It is possible that Osipov was aware of it, but he does not mention Lanchester. He was probably not aware of Lanchester’s work. It appears to be the case of him independently coming up with the use of differential equations to describe combat attrition. This was also the case with Rear Admiral J. V. Chase, who wrote a classified staff paper for U.S. Navy in 1902 that was not revealed until 1972.

Osipov, after he had written his paper, may have served in World War I, which was already underway at the time it was published. Between the war, the Russian revolutions, the civil war afterwards, the subsequent repressions by Cheka and later Stalin, we do not know what happened to M. Osipov. At the time I was asked by CAA if our Russian research team knew about him. I passed the question to Col. Sverdlov and Col. Vainer and they were not aware of him. It is probably possible to chase him down, but would probably take some effort. Perhaps some industrious researcher will find out more about him.

It does not appear that Osipov had any influence on Soviet operations research or military analysis. It appears that he was ignored or forgotten. His article was re-published in the September 1988  of the Soviet Military-Historical Journal with the propaganda influenced statement that they also had their own “Lanchester.” Of course, this “Soviet Lanchester” was publishing in a Tsarist military journal, hardly a demonstration of the strength of the Soviet system.

 

Are They Channeling Trevor Dupuy?

TrevorCoverShot

Continuing the RAND description of their hex boardgame:

Ground unit combat strengths were based on a systematic scoring of individual weapons, from tanks and artillery down to light machine guns, which were then aggregated according to the tables of organization and equipment for the various classes of NATO and Russian units. Overall unit scores were adjusted to account for differences in training, sustainment, and other factors not otherwise captured. Air unit combat strengths were derived from the results of offline engagement, mission, and campaign-level modeling.

This looks like some kind of firepower or combat power score, or perhaps Trevor Dupuy’s OLIs (Operational Lethality Indexes). As they say “systematic scoring” one wonders what system they used. Know of only one scoring system that is systematic (meaning the OLIs, which are based upon formulae). The subject is probably best summarized in Dr. James Taylor’s article on “Consistent Scoring of Weapons and Aggregation of Forces:” http://www.dupuyinstitute.org/pdf/v2n2.pdf. This is the same James Taylor who wrote the definitive two-volume work on Lanchester equations.

I do note with interest the adjustment for “differences in training, sustainment, and other factors.” That is always good to see.

Also noted:

Full documentation of the gaming platform will be forthcoming in a subsequent report.

Look forward to reading it.

Lanchester equations have been weighed….

a-knights-tale_1

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.

Really…..Lanchester?

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.