“The Battle of Leipzig, 16-19 October 1813” by A.I. Zauerweid (1783-1844) [Wikimedia]The thirteenth and last of Trevor Dupuy’s Timeless Verities of Combat is:
Combat is too complex to be described in a single, simple aphorism.
This is amply demonstrated by the preceding [verities]. All writers on military affairs (including this one) need periodically to remind themselves of this. In military analysis it is often necessary to focus on some particular aspect of combat. However, the results of such closely focused analyses must the be evaluated in the context of the brutal, multifarious, overlapping realities of war.
Trevor Dupuy was sometimes accused of attempting to reduce war to a mathematical equation. A casual reading of his writings might give that impression, but anyone who honestly engages with his ideas quickly finds this to be an erroneous conclusion. Yet, Dupuy believed the temptation to simplify and abstract combat and warfare to be common enough that he he embedded a warning against doing so into his basic theory on the subject. He firmly believed that human behavior comprises the most important aspect of combat, yet it is all too easy to miss the human experience of war figuring who lost or won and why, and counts of weapons, people, and casualties. As a military historian, he was keenly aware that the human stories behind the numbers—however imperfectly recorded and told—tell us more about the reality of war than mere numbers on their own ever will.
Today’s edition of TDI Friday Read is a roundup of posts by TDI President Christopher Lawrence exploring the details of tank combat between German and Soviet forces at the Battle of Kursk in 1943. The prevailing historical interpretation of Kursk is of the Soviets using their material and manpower superiority to blunt and then overwhelm the German offensive. This view is often buttressed by looking at the ratio of the numbers of tanks destroyed in combat. Chris takes a deeper look at the data, the differences in the ways “destroyed” tanks were counted and reported, and the differing philosophies between the German and Soviet armies regarding damaged tank recovery and repair. This yields a much more nuanced perspective on the character of tank combat at Kursk that does not necessarily align with the prevailing historical interpretations. Historians often discount detailed observational data on combat as irrelevant or too difficult to collect and interpret. We at TDI believe that with history, the devil is always in the details.
The ground forces were the last branch of the Army to incorporate OR into their efforts during World War II, lagging behind the Army Air Forces, the technical services, and the Navy. Where the Army was a step ahead, however, was in creating a robust wartime historical field history documentation program. (After the war, this enabled the publication of the U.S. Army in World War II series, known as the “Green Books,” which set a new standard for government sponsored military histories.)
As Shrader related, the first OR personnel the Army deployed forward in 1944-45 often crossed paths with War Department General Staff Historical Branch field historian detachments. They both engaged in similar activities: collecting data on real-world combat operations, which was then analyzed and used for studies and reports written for the use of the commands to which they were assigned. The only significant difference was in their respective methodologies, with the historians using historical methods and the OR analysts using mathematical and scientific tools.
History and OR after World War II
The usefulness of historical approaches to collecting operational data did not go unnoticed by the OR practitioners, according to Shrader. When the Army established the Operations Research Office (ORO) in 1948, it hired a contingent of historians specifically for the purpose of facilitating research and analysis using WWII Army records, “the most likely source for data on operational matters.”
When the Korean War broke out in 1950, ORO sent eight multi-disciplinary teams, including the historians, to collect operational data and provide analytical support for U.S. By 1953, half of ORO’s personnel had spent time in combat zones. Throughout the 1950s, about 40-43% of ORO’s staff was comprised of specialists in the social sciences, history, business, literature, and law. Shrader quoted one leading ORO analyst as noting that, “there is reason to believe that the lawyer, social scientist or historian is better equipped professionally to evaluate evidence which is derived from the mind and experience of the human species.”
Among the notable historians who worked at or with ORO was Dr. Hugh M. Cole, an Army officer who had served as a staff historian for General George Patton during World War II. Cole rose to become a senior manager at ORO and later served as vice-president and president of ORO’s successor, the Research Analysis Corporation (RAC). Cole brought in WWII colleague Forrest C. Pogue (best known as the biographer of General George C. Marshall) and Charles B. MacDonald. ORO also employed another WWII field historian, the controversial S. L. A. Marshall, as a consultant during the Korean War. Dorothy Kneeland Clark did pioneering historical analysis on combat phenomena while at ORO.
The Demise of ORO…and Historical Combat Analysis?
By the late 1950s, considerable institutional friction had developed between ORO, the Johns Hopkins University (JHU)—ORO’s institutional owner—and the Army. According to Shrader,
Continued distrust of operations analysts by Army personnel, questions about the timeliness and focus of ORO studies, the ever-expanding scope of ORO interests, and, above all, [ORO director] Ellis Johnson’s irascible personality caused tensions that led in August 1961 to the cancellation of the Army’s contract with JHU and the replacement of ORO with a new, independent research organization, the Research Analysis Corporation [RAC].
RAC inherited ORO’s research agenda and most of its personnel, but changing events and circumstances led Army OR to shift its priorities away from field collection and empirical research on operational combat data in favor of the use of modeling and wargaming in its analyses. As Chris Lawrence described in his history of federally-funded Defense Department “think tanks,” the rise and fall of scientific management in DOD, the Vietnam War, social and congressional criticism, and an unhappiness by the military services with the analysis led to retrenchment in military OR by the end of the 60s. The Army sold RAC and created its own in-house Concepts Analysis Agency (CAA; now known as the Center for Army Analysis).
By the early 1970s, analysts, such as RAND’s Martin Shubik and Gary Brewer, and John Stockfisch, began to note that the relationships and processes being modeled in the Army’s combat simulations were not based on real-world data and that empirical research on combat phenomena by the Army OR community had languished. In 1991, Paul Davis and Donald Blumenthal gave this problem a name: the “Base of Sand.”
There are three versions of force ratio versus casualty exchange ratio rules, such as the three-to-one rule (3-to-1 rule), as it applies to casualties. The earliest version of the rule as it relates to casualties that we have been able to find comes from the 1958 version of the U.S. Army Maneuver Control manual, which states: “When opposing forces are in contact, casualties are assessed in inverse ratio to combat power. For friendly forces advancing with a combat power superiority of 5 to 1, losses to friendly forces will be about 1/5 of those suffered by the opposing force.”[1]
The RAND version of the rule (1992) states that: “the famous ‘3:1 rule ’, according to which the attacker and defender suffer equal fractional loss rates at a 3:1 force ratio the battle is in mixed terrain and the defender enjoys ‘prepared ’defenses…” [2]
Finally, there is a version of the rule that dates from the 1967 Maneuver Control manual that only applies to armor that shows:
As the RAND construct also applies to equipment losses, then this formulation is directly comparable to the RAND construct.
Therefore, we have three basic versions of the 3-to-1 rule as it applies to casualties and/or equipment losses. First, there is a rule that states that there is an even fractional loss ratio at 3-to-1 (the RAND version), Second, there is a rule that states that at 3-to-1, the attacker will suffer one-third the losses of the defender. And third, there is a rule that states that at 3-to-1, the attacker and defender will suffer the same losses as the defender. Furthermore, these examples are highly contradictory, with either the attacker suffering three times the losses of the defender, the attacker suffering the same losses as the defender, or the attacker suffering 1/3 the losses of the defender.
Therefore, what we will examine here is the relationship between force ratios and exchange ratios. In this case, we will first look at The Dupuy Institute’s Battles Database (BaDB), which covers 243 battles from 1600 to 1900. We will chart on the y-axis the force ratio as measured by a count of the number of people on each side of the forces deployed for battle. The force ratio is the number of attackers divided by the number of defenders. On the x-axis is the exchange ratio, which is a measured by a count of the number of people on each side who were killed, wounded, missing or captured during that battle. It does not include disease and non-battle injuries. Again, it is calculated by dividing the total attacker casualties by the total defender casualties. The results are provided below:
As can be seen, there are a few extreme outliers among these 243 data points. The most extreme, the Battle of Tippennuir (l Sep 1644), in which an English Royalist force under Montrose routed an attack by Scottish Covenanter militia, causing about 3,000 casualties to the Scots in exchange for a single (allegedly self-inflicted) casualty to the Royalists, was removed from the chart. This 3,000-to-1 loss ratio was deemed too great an outlier to be of value in the analysis.
As it is, the vast majority of cases are clumped down into the corner of the graph with only a few scattered data points outside of that clumping. If one did try to establish some form of curvilinear relationship, one would end up drawing a hyperbola. It is worthwhile to look inside that clump of data to see what it shows. Therefore, we will look at the graph truncated so as to show only force ratios at or below 20-to-1 and exchange rations at or below 20-to-1.
Again, the data remains clustered in one corner with the outlying data points again pointing to a hyperbola as the only real fitting curvilinear relationship. Let’s look at little deeper into the data by truncating the data on 6-to-1 for both force ratios and exchange ratios. As can be seen, if the RAND version of the 3-to-1 rule is correct, then the data should show at 3-to-1 force ratio a 3-to-1 casualty exchange ratio. There is only one data point that comes close to this out of the 243 points we examined.
If the FM 105-5 version of the rule as it applies to armor is correct, then the data should show that at 3-to-1 force ratio there is a 1-to-1 casualty exchange ratio, at a 4-to-1 force ratio a 1-to-2 casualty exchange ratio, and at a 5-to-1 force ratio a 1-to-3 casualty exchange ratio. Of course, there is no armor in these pre-WW I engagements, but again no such exchange pattern does appear.
If the 1958 version of the FM 105-5 rule as it applies to casualties is correct, then the data should show that at a 3-to-1 force ratio there is 0.33-to-1 casualty exchange ratio, at a 4-to-1 force ratio a .25-to-1 casualty exchange ratio, and at a 5-to-1 force ratio a 0.20-to-5 casualty exchange ratio. As can be seen, there is not much indication of this pattern, or for that matter any of the three patterns.
Still, such a construct may not be relevant to data before 1900. For example, Lanchester claimed in 1914 in Chapter V, “The Principal of Concentration,” of his book Aircraft in Warfare, that there is greater advantage to be gained in modern warfare from concentration of fire.[3] Therefore, we will tap our more modern Division-Level Engagement Database (DLEDB) of 675 engagements, of which 628 have force ratios and exchange ratios calculated for them. These 628 cases are then placed on a scattergram to see if we can detect any similar patterns.
Even though this data covers from 1904 to 1991, with the vast majority of the data coming from engagements after 1940, one again sees the same pattern as with the data from 1600-1900. If there is a curvilinear relationship, it is again a hyperbola. As before, it is useful to look into the mass of data clustered into the corner by truncating the force and exchange ratios at 20-to-1. This produces the following:
Again, one sees the data clustered in the corner, with any curvilinear relationship again being a hyperbola. A look at the data further truncated to a 10-to-1 force or exchange ratio does not yield anything more revealing.
And, if this data is truncated to show only 5-to-1 force ratio and exchange ratios, one again sees:
Again, this data appears to be mostly just noise, with no clear patterns here that support any of the three constructs. In the case of the RAND version of the 3-to-1 rule, there is again only one data point (out of 628) that is anywhere close to the crossover point (even fractional exchange rate) that RAND postulates. In fact, it almost looks like the data conspires to make sure it leaves a noticeable “hole” at that point. The other postulated versions of the 3-to-1 rules are also given no support in these charts.
While we can attempt to torture the data to find a better fit, or can try to argue that the patterns are obscured by various factors that have not been considered, we do not believe that such a clear pattern and relationship exists. More advanced mathematical methods may show such a pattern, but to date such attempts have not ferreted out these alleged patterns. For example, we refer the reader to Janice Fain’s article on Lanchester equations, The Dupuy Institute’s Capture Rate Study, Phase I & II, or any number of other studies that have looked at Lanchester.[4]
The fundamental problem is that there does not appear to be a direct cause and effect between force ratios and exchange ratios. It appears to be an indirect relationship in the sense that force ratios are one of several independent variables that determine the outcome of an engagement, and the nature of that outcome helps determines the casualties. As such, there is a more complex set of interrelationships that have not yet been fully explored in any study that we know of, although it is briefly addressed in our Capture Rate Study, Phase I & II.
[3] F. W. Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm (Lanchester Press Incorporated, Sunnyvale, Calif., 1995), 46-60. One notes that Lanchester provided no data to support these claims, but relied upon an intellectual argument based upon a gross misunderstanding of ancient warfare.
A crane barge allegedly pulling up scrap metal from a World War II wreck in the Java Sea. [The Daily Mail]
An investigation by the British newspaper The Daily Mail has alleged that 10 British shipwrecks from World War II lying of the coasts of Malaysia and Indonesia have been illegally salvaged for scrap by “pirates,” including Chinese, Mongolian, and Cambodian-flagged vessels. The shipwrecks have been designated war graves and are protected from looting by the U.N. International Salvaging Convention and British, Indonesian and Malaysian law.
British Defense Minister Gavin Williamson has demanded an immediate investigation into allegations that dozens of barges with cranes have been plundering the wrecks for many years.
One Chinese shipping giant, Fujian Jiada, which owns five of eight barges alleged to be recently actively salvaging, has denied any involvement. The Malaysian Navy impounded the Fujian Jiada-owned Hai Wei Gong 889 in 2014 on charges of illegally salvaging Japanese and Dutch shipwrecks, and detained another Vietnamese-crewed barge in 2015 for doing the same.
Both vessels were also accused of looting the wrecks of the battleship H.M.S. Prince of Wales and battlecruiser H.M.S. Repulse, sunk by Japanese aircraft off the coast of Malaysia in 1941. Marine experts estimate half of the remains of the two ships have disappeared and stolen artifacts have been discovered being offered for auction.
In 2016, the British and Dutch Defense Ministries revealed the discovery that the wrecks of three Dutch Navy, three British Navy, and one U.S. Navy ships sunk off the coast of Indonesia during World War II had disappeared from the seabed.
Sonar image of the Java Sea bed location where the wreck of the HMS Exeter used to be. [BBC]
Metals salvaged from the wrecks can be quite lucrative, each vessel yielding up to ₤1 million, and brass propellers and fixtures selling for ₤2,000 per metric ton. Metals fabricated before post-World War II atmospheric nuclear testing are particularly useful for medical devices. The Daily Mail found that the barges drop the cranes on to the wrecks to break off large pieces. These are then taken to scrapyards in Indonesia to be cut into smaller pieces, which are then shipped to China and sold into the global steel markets.
And earlier TDI post on the this subject can be found here:
Allied force dispositions at the Battle of Anzio, on 1 February 1944. [U.S. Army/Wikipedia]
[The article below is reprinted from History, Numbers And War: A HERO Journal, Vol. 1, No. 1, Spring 1977, pp. 34-52]
The Lanchester Equations and Historical Warfare: An Analysis of Sixty World War II Land Engagements
By Janice B. Fain
Background and Objectives
The method by which combat losses are computed is one of the most critical parts of any combat model. The Lanchester equations, which state that a unit’s combat losses depend on the size of its opponent, are widely used for this purpose.
In addition to their use in complex dynamic simulations of warfare, the Lanchester equations have also sewed as simple mathematical models. In fact, during the last decade or so there has been an explosion of theoretical developments based on them. By now their variations and modifications are numerous, and “Lanchester theory” has become almost a separate branch of applied mathematics. However, compared with the effort devoted to theoretical developments, there has been relatively little empirical testing of the basic thesis that combat losses are related to force sizes.
One of the first empirical studies of the Lanchester equations was Engel’s classic work on the Iwo Jima campaign in which he found a reasonable fit between computed and actual U.S. casualties (Note 1). Later studies were somewhat less supportive (Notes 2 and 3), but an investigation of Korean war battles showed that, when the simulated combat units were constrained to follow the tactics of their historical counterparts, casualties during combat could be predicted to within 1 to 13 percent (Note 4).
Taken together, these various studies suggest that, while the Lanchester equations may be poor descriptors of large battles extending over periods during which the forces were not constantly in combat, they may be adequate for predicting losses while the forces are actually engaged in fighting. The purpose of the work reported here is to investigate 60 carefully selected World War II engagements. Since the durations of these battles were short (typically two to three days), it was expected that the Lanchester equations would show a closer fit than was found in studies of larger battles. In particular, one of the objectives was to repeat, in part, Willard’s work on battles of the historical past (Note 3).
The Data Base
Probably the most nearly complete and accurate collection of combat data is the data on World War II compiled by the Historical Evaluation and Research Organization (HERO). From their data HERO analysts selected, for quantitative analysis, the following 60 engagements from four major Italian campaigns:
Salerno, 9-18 Sep 1943, 9 engagements
Volturno, 12 Oct-8 Dec 1943, 20 engagements
Anzio, 22 Jan-29 Feb 1944, 11 engagements
Rome, 14 May-4 June 1944, 20 engagements
The complete data base is described in a HERO report (Note 5). The work described here is not the first analysis of these data. Statistical analyses of weapon effectiveness and the testing of a combat model (the Quantified Judgment Method, QJM) have been carried out (Note 6). The work discussed here examines these engagements from the viewpoint of the Lanchester equations to consider the question: “Are casualties during combat related to the numbers of men in the opposing forces?”
The variables chosen for this analysis are shown in Table 1. The “winners” of the engagements were specified by HERO on the basis of casualties suffered, distance advanced, and subjective estimates of the percentage of the commander’s objective achieved. Variable 12, the Combat Power Ratio, is based on the Operational Lethality Indices (OLI) of the units (Note 7).
The general characteristics of the engagements are briefly described. Of the 60, there were 19 attacks by British forces, 28 by U.S. forces, and 13 by German forces. The attacker was successful in 34 cases; the defender, in 23; and the outcomes of 3 were ambiguous. With respect to terrain, 19 engagements occurred in flat terrain; 24 in rolling, or intermediate, terrain; and 17 in rugged, or difficult, terrain. Clear weather prevailed in 40 cases; 13 engagements were fought in light or intermittent rain; and 7 in medium or heavy rain. There were 28 spring and summer engagements and 32 fall and winter engagements.
Comparison of World War II Engagements With Historical Battles
Since one purpose of this work is to repeat, in part, Willard’s analysis, comparison of these World War II engagements with the historical battles (1618-1905) studied by him will be useful. Table 2 shows a comparison of the distribution of battles by type. Willard’s cases were divided into two categories: I. meeting engagements, and II. sieges, attacks on forts, and similar operations. HERO’s World War II engagements were divided into four types based on the posture of the defender: 1. delay, 2. hasty defense, 3. prepared position, and 4. fortified position. If postures 1 and 2 are considered very roughly equivalent to Willard’s category I, then in both data sets the division into the two gross categories is approximately even.
The distribution of engagements across force ratios, given in Table 3, indicated some differences. Willard’s engagements tend to cluster at the lower end of the scale (1-2) and at the higher end (4 and above), while the majority of the World War II engagements were found in mid-range (1.5 – 4) (Note 8). The frequency with which the numerically inferior force achieved victory is shown in Table 4. It is seen that in neither data set are force ratios good predictors of success in battle (Note 9).
Table 3.
Results of the Analysis Willard’s Correlation Analysis
There are two forms of the Lanchester equations. One represents the case in which firing units on both sides know the locations of their opponents and can shift their fire to a new target when a “kill” is achieved. This leads to the “square” law where the loss rate is proportional to the opponent’s size. The second form represents that situation in which only the general location of the opponent is known. This leads to the “linear” law in which the loss rate is proportional to the product of both force sizes.
As Willard points out, large battles are made up of many smaller fights. Some of these obey one law while others obey the other, so that the overall result should be a combination of the two. Starting with a general formulation of Lanchester’s equations, where g is the exponent of the target unit’s size (that is, g is 0 for the square law and 1 for the linear law), he derives the following linear equation:
log (nc/mc) = log E + g log (mo/no) (1)
where nc and mc are the casualties, E is related to the exchange ratio, and mo and no are the initial force sizes. Linear regression produces a value for g. However, instead of lying between 0 and 1, as expected, the) g‘s range from -.27 to -.87, with the majority lying around -.5. (Willard obtains several values for g by dividing his data base in various ways—by force ratio, by casualty ratio, by historical period, and so forth.) A negative g value is unpleasant. As Willard notes:
Military theorists should be disconcerted to find g < 0, for in this range the results seem to imply that if the Lanchester formulation is valid, the casualty-producing power of troops increases as they suffer casualties (Note 3).
From his results, Willard concludes that his analysis does not justify the use of Lanchester equations in large-scale situations (Note 10).
Analysis of the World War II Engagements
Willard’s computations were repeated for the HERO data set. For these engagements, regression produced a value of -.594 for g (Note 11), in striking agreement with Willard’s results. Following his reasoning would lead to the conclusion that either the Lanchester equations do not represent these engagements, or that the casualty producing power of forces increases as their size decreases.
However, since the Lanchester equations are so convenient analytically and their use is so widespread, it appeared worthwhile to reconsider this conclusion. In deriving equation (1), Willard used binomial expansions in which he retained only the leading terms. It seemed possible that the poor results might he due, in part, to this approximation. If the first two terms of these expansions are retained, the following equation results:
log (nc/mc) = log E + log (Mo-mc)/(no-nc) (2)
Repeating this regression on the basis of this equation leads to g = -.413 (Note 12), hardly an improvement over the initial results.
A second attempt was made to salvage this approach. Starting with raw OLI scores (Note 7), HERO analysts have computed “combat potentials” for both sides in these engagements, taking into account the operational factors of posture, vulnerability, and mobility; environmental factors like weather, season, and terrain; and (when the record warrants) psychological factors like troop training, morale, and the quality of leadership. Replacing the factor (mo/no) in Equation (1) by the combat power ratio produces the result) g = .466 (Note 13).
While this is an apparent improvement in the value of g, it is achieved at the expense of somewhat distorting the Lanchester concept. It does preserve the functional form of the equations, but it requires a somewhat strange definition of “killing rates.”
Analysis Based on the Differential Lanchester Equations
Analysis of the type carried out by Willard appears to produce very poor results for these World War II engagements. Part of the reason for this is apparent from Figure 1, which shows the scatterplot of the dependent variable, log (nc/mc), against the independent variable, log (mo/no). It is clear that no straight line will fit these data very well, and one with a positive slope would not be much worse than the “best” line found by regression. To expect the exponent to account for the wide variation in these data seems unreasonable.
Here, a simpler approach will be taken. Rather than use the data to attempt to discriminate directly between the square and the linear laws, they will be used to estimate linear coefficients under each assumption in turn, starting with the differential formulation rather than the integrated equations used by Willard.
In their simplest differential form, the Lanchester equations may be written;
Square Law; dA/dt = -kdD and dD/dt = kaA (3)
Linear law: dA/dt = -k’dAD and dD/dt = k’aAD (4)
where
A(D) is the size of the attacker (defender)
dA/dt (dD/dt) is the attacker’s (defender’s) loss rate,
ka, k’a (kd, k’d) are the attacker’s (defender’s) killing rates
For this analysis, the day is taken as the basic time unit, and the loss rate per day is approximated by the casualties per day. Results of the linear regressions are given in Table 5. No conclusions should be drawn from the fact that the correlation coefficients are higher in the linear law case since this is expected for purely technical reasons (Note 14). A better picture of the relationships is again provided by the scatterplots in Figure 2. It is clear from these plots that, as in the case of the logarithmic forms, a single straight line will not fit the entire set of 60 engagements for either of the dependent variables.
To investigate ways in which the data set might profitably be subdivided for analysis, T-tests of the means of the dependent variable were made for several partitionings of the data set. The results, shown in Table 6, suggest that dividing the engagements by defense posture might prove worthwhile.
Results of the linear regressions by defense posture are shown in Table 7. For each posture, the equation that seemed to give a better fit to the data is underlined (Note 15). From this table, the following very tentative conclusions might be drawn:
In an attack on a fortified position, the attacker suffers casualties by the square law; the defender suffers casualties by the linear law. That is, the defender is aware of the attacker’s position, while the attacker knows only the general location of the defender. (This is similar to Deitchman’s guerrilla model. Note 16).
This situation is apparently reversed in the cases of attacks on prepared positions and hasty defenses.
Delaying situations seem to be treated better by the square law for both attacker and defender.
Table 8 summarizes the killing rates by defense posture. The defender has a much higher killing rate than the attacker (almost 3 to 1) in a fortified position. In a prepared position and hasty defense, the attacker appears to have the advantage. However, in a delaying action, the defender’s killing rate is again greater than the attacker’s (Note 17).
Figure 3 shows the scatterplots for these cases. Examination of these plots suggests that a tentative answer to the study question posed above might be: “Yes, casualties do appear to be related to the force sizes, but the relationship may not be a simple linear one.”
In several of these plots it appears that two or more functional forms may be involved. Consider, for example, the defender‘s casualties as a function of the attacker’s initial strength in the case of a hasty defense. This plot is repeated in Figure 4, where the points appear to fit the curves sketched there. It would appear that there are at least two, possibly three, separate relationships. Also on that plot, the individual engagements have been identified, and it is interesting to note that on the curve marked (1), five of the seven attacks were made by Germans—four of them from the Salerno campaign. It would appear from this that German attacks are associated with higher than average defender casualties for the attacking force size. Since there are so few data points, this cannot be more than a hint or interesting suggestion.
Future Research
This work suggests two conclusions that might have an impact on future lines of research on combat dynamics:
Tactics appear to be an important determinant of combat results. This conclusion, in itself, does not appear startling, at least not to the military. However, it does not always seem to have been the case that tactical questions have been considered seriously by analysts in their studies of the effects of varying force levels and force mixes.
Historical data of this type offer rich opportunities for studying the effects of tactics. For example, consideration of the narrative accounts of these battles might permit re-coding the engagements into a larger, more sensitive set of engagement categories. (It would, of course, then be highly desirable to add more engagements to the data set.)
While predictions of the future are always dangerous, I would nevertheless like to suggest what appears to be a possible trend. While military analysis of the past two decades has focused almost exclusively on the hardware of weapons systems, at least part of our future analysis will be devoted to the more behavioral aspects of combat.
Janice Bloom Fain, a Senior Associate of CACI, lnc., is a physicist whose special interests are in the applications of computer simulation techniques to industrial and military operations; she is the author of numerous reports and articles in this field. This paper was presented by Dr. Fain at the Military Operations Research Symposium at Fort Eustis, Virginia.
[5.] HERO, “A Study of the Relationship of Tactical Air Support Operations to Land Combat, Appendix B, Historical Data Base.” Historical Evaluation and Research Organization, report prepared for the Defense Operational Analysis Establishment, U.K.T.S.D., Contract D-4052 (1971).
[6.] T. N. Dupuy, The Quantified Judgment Method of Analysis of Historical Combat Data, HERO Monograph, (January 1973); HERO, “Statistical Inference in Analysis in Combat,” Annex F, Historical Data Research on Tactical Air Operations, prepared for Headquarters USAF, Assistant Chief of Staff for Studies and Analysis, Contract No. F-44620-70-C-0058 (1972).
[7.] The Operational Lethality Index (OLI) is a measure of weapon effectiveness developed by HERO.
[8.] Since Willard’s data did not indicate which side was the attacker, his force ratio is defined to be (larger force/smaller force). The HERO force ratio is (attacker/defender).
[9.] Since the criteria for success may have been rather different for the two sets of battles, this comparison may not be very meaningful.
[10.] This work includes more complex analysis in which the possibility that the two forces may be engaging in different types of combat is considered, leading to the use of two exponents rather than the single one, Stochastic combat processes are also treated.
[11.] Correlation coefficient = -.262;
Intercept = .00115; slope = -.594.
[12.] Correlation coefficient = -.184;
Intercept = .0539; slope = -,413.
[13.] Correlation coefficient = .303;
Intercept = -.638; slope = .466.
[14.] Correlation coefficients for the linear law are inflated with respect to the square law since the independent variable is a product of force sizes and, thus, has a higher variance than the single force size unit in the square law case.
[15.] This is a subjective judgment based on the following considerations Since the correlation coefficient is inflated for the linear law, when it is lower the square law case is chosen. When the linear law correlation coefficient is higher, the case with the intercept closer to 0 is chosen.
[17.] As pointed out by Mr. Alan Washburn, who prepared a critique on this paper, when comparing numerical values of the square law and linear law killing rates, the differences in units must be considered. (See footnotes to Table 7).
Today’s edition of TDI Friday Read compiles some previous posts featuring maps we have found to be interesting, useful, or just plain cool. The history of military affairs would be incomprehensible without maps. Without them, it would be impossible to convey the temporal and geographical character of warfare or the situational awareness of the combatants. Of course, maps are susceptible to the same methodological distortions, fallacies, inaccuracies, and errors in interpretation to be found in any historical work. As with any historical resource, they need to be regarded with respectful skepticism.
As an added bonus, here are two more links of interest. The first describes the famous map based on 1860 U.S. Census data that Abraham Lincoln used to understand the geographical distribution of slavery in the Southern states.
The second shows the potential of maps to provide new insights into history. It is an animated, interactive depiction of the trans-Atlantic slave trade derived from a database covering 315 years and 20,528 slave ship transits. It is simultaneously fascinating and sobering.
Informal portrait of Charles E. W. Bean working on official files in his Victoria Barracks office during the writing of the Official History of Australia in the War of 1914-1918. The files on his desk are probably the Operations Files, 1914-18 War, that were prepared by the army between 1925 and 1930 and are now held by the Australian War Memorial as AWM 26. Courtesy of the Australian War Memorial. [Defence in Depth]
Although the posts are a couple of years old now, Dr. Robert T. Foley of the Defence Studies Department at King’s College London has provided a wonderful compilation of links to digital holdings and resources documenting the experiences of many of the many belligerents in the First World War. The links include digitized archival holdings and electronic copies of often hard-to-find official histories of ground, sea, and air operations.
For TDI, the availability of such materials greatly broadens potential sources for research on historical combat. For example, TDI made use of German regional archival holdings for to compile data on the use of chemical weapons in urban environments from the separate state armies that formed part of the Imperial German Army in the First World War. Although much of the German Army’s historical archives were destroyed by Allied bombing at the end of the Second World War, a great deal of material survived in regional state archives and in other places, as Dr. Foley shows. Access to the highly detailed official histories is another boon for such research.
The Digital Era hints at unprecedented access to historical resources and more materials are being added all the time. Current historians should benefit greatly. Future historians, alas, are not as likely to be so fortunate when it comes time to craft histories of the the current era.
Strachan’s lecture, “The Changing Character of War,” proceeds from Carl von Clausewitz’s discussions in On Waron change and continuity in the history of war to look at the trajectories of recent conflicts. Among the topics Strachan’s lecture covers are technological determinism, the irregular conflicts of the early 21st century, political and social mobilization, the spectrum of conflict, the impact of the Second World War on contemporary theorizing about war and warfare, and deterrence.
This is well worth the time to listen to and think about.
Due to their elegant simplicity, U.S. military operations researchers nevertheless began incorporating the Lanchester equations into their land warfare computer combat models and simulations in the 1950s and 60s. The equations are the basis for many models and simulations used throughout the U.S. defense community today.
The problem with using Lanchester’s equations is that, despite numerous efforts, no one has been able to demonstrate that they accurately represent real-world combat.
Trevor Dupuy was critical of combat models based on the Lanchester equations because they cannot account for the role behavioral and moral (i.e. human) factors play in combat.
He was also critical of models and simulations that had not been tested to see whether they could reliably represent real-world combat experience. In the modeling and simulation community, this sort of testing is known as validation.
The use of unvalidated concepts, like the Lanchester equations, and unvalidated combat models and simulations persists. Critics have dubbed this the “base of sand” problem, and it continues to affect not only models and simulations, but all abstract theories of combat, including those represented in military doctrine.
Today’s edition of TDI Friday Read is a roundup of posts by TDI President Christopher Lawrence exploring the details of tank combat between German and Soviet forces 
While perusing Charles Shrader’s fascinating 
Today’s edition of TDI Friday Read compiles some previous posts featuring maps we have found to be interesting, useful, or just plain cool. The history of military affairs would be incomprehensible without maps. Without them, it would be impossible to convey the temporal and geographical character of warfare or the situational awareness of the combatants. Of course, maps are susceptible to the same methodological distortions, fallacies, inaccuracies, and errors in interpretation to be found in any historical work. As with any historical resource, they need to be regarded with respectful skepticism.
