Jeffrey H Michaels, a Senior Lecturer in Defence Studies at the British the Joint Services Command and Staff College, has published a detailed look at how Hackett and several senior NATO and diplomatic colleagues constructed the scenario portrayed in the book. Scenario construction is an important aspect of institutional war gaming. A war game will only be as useful if the assumptions that underpin it are valid. As Michaels points out,
Regrettably, far too many scenarios and models, whether developed by military organizations, political scientists, or fiction writers, tend to focus their attention on the battlefield and the clash of armies, navies, air forces, and especially their weapons systems. By contrast, the broader context of the war – the reasons why hostilities erupted, the political and military objectives, the limits placed on military action, and so on – are given much less serious attention, often because they are viewed by the script-writers as a distraction from the main activity that occurs on the battlefield.
Modelers and war gamers always need to keep in mind the fundamental importance of context in designing their simulations.
It is quite easy to project how one weapon system might fare against another, but taken out of a broader strategic context, such a projection is practically meaningless (apart from its marketing value), or worse, misleading. In this sense, even if less entertaining or exciting, the degree of realism of the political aspects of the scenario, particularly policymakers’ rationality and cost-benefit calculus, and the key decisions that are taken about going to war, the objectives being sought, the limits placed on military action, and the willingness to incur the risks of escalation, should receive more critical attention than the purely battlefield dimensions of the future conflict.
These are crucially important points to consider when deciding how to asses the outcomes of hypothetical scenarios.
It is my understanding that he was the person who was responsible for making sure that DACM (Dupuy Air Combat Model) was funded by AFSC. He then retired from the Air Force in 1994. We completed the demonstration phase of the DACM and quite simply, there was no one left in the Air Force who was interested in funding it. So, work stopped. I never met General McInerney and was not involved in the marketing of the initial effort.
But, this is typical of the problems with doing business with the Pentagon, where an officer will take an interest in your work, generate funding for it, but by the time the first steps are completed, that officer has moved on to another assignment. This has happened to us with other projects. One of these efforts was a joint research project that was done by TDI and former Army surgeon on casualty rates. It was for J-4 of the Joint Staff. The project officer there was extremely interested and involved in the work, but then moved to another assignment. By the time we got original effort completed, the division was headed by an Air Force Colonel who appeared to be only interested in things that flew. Therefore, the project died (except that parts of it were used for Chapter 15: Casualties, pages 193-198, in War by Numbers).
Our experience in dealing with the U.S. defense establishment is that sometimes research efforts that takes longer than a few months will die……because the people interested in it have moved on. This sometimes leads to simple, short-term analysis and fewer properly funded long-term projects.
Consistent Scoring of Weapons and Aggregation of Forces: The Cornerstone of Dupuy’s Quantitative Analysis of Historical Land Battles by
James G. Taylor, PhD,
Dept. of Operations Research, Naval Postgraduate School
Introduction
Col. Trevor N. Dupuy was an American original, especially as regards the quantitative study of warfare. As with many prophets, he was not entirely appreciated in his own land, particularly its Military Operations Research (OR) community. However, after becoming rather familiar with the details of his mathematical modeling of ground combat based on historical data, I became aware of the basic scientific soundness of his approach. Unfortunately, his documentation of methodology was not always accepted by others, many of whom appeared to confuse lack of mathematical sophistication in his documentation with lack of scientific validity of his basic methodology.
The purpose of this brief paper is to review the salient points of Dupuy’s methodology from a system’s perspective, i.e., to view his methodology as a system, functioning as an organic whole to capture the essence of past combat experience (with an eye towards extrapolation into the future). The advantage of this perspective is that it immediately leads one to the conclusion that if one wants to use some functional relationship derived from Dupuy’s work, then one should use his methodologies for scoring weapons, aggregating forces, and adjusting for operational circumstances; since this consistency is the only guarantee of being able to reproduce historical results and to project them into the future.
Implications (of this system’s perspective on Dupuy’s work) for current DOD models will be discussed. In particular, the Military OR community has developed quantitative methods for imputing values to weapon systems based on their attrition capability against opposing forces and force interactions.[1] One such approach is the so-called antipotential-potential method[2] used in TACWAR[3] to score weapons. However, one should not expect such scores to provide valid casualty estimates when combined with historically derived functional relationships such as the so-called ATLAS casualty-rate curves[4] used in TACWAR, because a different “yard-stick” (i.e. measuring system for estimating the relative combat potential of opposing forces) was used to develop such a curve.
Overview of Dupuy’s Approach
This section briefly outlines the salient features of Dupuy’s approach to the quantitative analysis and modeling of ground combat as embodied in his Tactical Numerical Deterministic Model (TNDM) and its predecessor the Quantified Judgment Model (QJM). The interested reader can find details in Dupuy [1979] (see also Dupuy [1985][5], [1987], [1990]). Here we will view Dupuy’s methodology from a system approach, which seeks to discern its various components and their interactions and to view these components as an organic whole. Essentially Dupuy’s approach involves the development of functional relationships from historical combat data (see Fig. 1) and then using these functional relationships to model future combat (see Fig, 2).
At the heart of Dupuy’s method is the investigation of historical battles and comparing the relationship of inputs (as quantified by relative combat power, denoted as Pa/Pd for that of the attacker relative to that of the defender in Fig. l)(e.g. see Dupuy [1979, pp. 59-64]) to outputs (as quantified by extent of mission accomplishment, casualty effectiveness, and territorial effectiveness; see Fig. 2) (e.g. see Dupuy [1979, pp. 47-50]), The salient point is that within this scheme, the main input[6] (i.e. relative combat power) to a historical battle is a derived quantity. It is computed from formulas that involve three essential aspects: (1) the scoring of weapons (e.g, see Dupuy [1979, Chapter 2 and also Appendix A]), (2) aggregation methodology for a force (e.g. see Dupuy [1979, pp. 43-46 and 202-203]), and (3) situational-adjustment methodology for determining the relative combat power of opposing forces (e.g. see Dupuy [1979, pp. 46-47 and 203-204]). In the force-aggregation step the effects on weapons of Dupuy’s environmental variables and one operational variable (air superiority) are considered[7], while in the situation-adjustment step the effects on forces of his behavioral variables[8] (aggregated into a single factor called the relative combat effectiveness value (CEV)) and also the other operational variables are considered (Dupuy [1987, pp. 86-89])
Figure 1.
Moreover, any functional relationships developed by Dupuy depend (unless shown otherwise) on his computational system for derived quantities, namely OLls, force strengths, and relative combat power. Thus, Dupuy’s results depend in an essential manner on his overall computational system described immediately above. Consequently, any such functional relationship (e.g. casualty-rate curve) directly or indirectly derivative from Dupuy‘s work should still use his computational methodology for determination of independent-variable values.
Fig l also reveals another important aspect of Dupuy’s work, the development of reliable data on historical battles, Military judgment plays an essential role in this development of such historical data for a variety of reasons. Dupuy was essentially the only source of new secondary historical data developed from primary sources (see McQuie [1970] for further details). These primary sources are well known to be both incomplete and inconsistent, so that military judgment must be used to fill in the many gaps and reconcile observed inconsistencies. Moreover, military judgment also generates the working hypotheses for model development (e.g. identification of significant variables).
At the heart of Dupuy’s quantitative investigation of historical battles and subsequent model development is his own weapons-scoring methodology, which slowly evolved out of study efforts by the Historical Evaluation Research Organization (HERO) and its successor organizations (cf. HERO [1967] and compare with Dupuy [1979]). Early HERO [1967, pp. 7-8] work revealed that what one would today call weapons scores developed by other organizations were so poorly documented that HERO had to create its own methodology for developing the relative lethality of weapons, which eventually evolved into Dupuy’s Operational Lethality Indices (OLIs). Dupuy realized that his method was arbitrary (as indeed is its counterpart, called the operational definition, in formal scientific work), but felt that this would be ameliorated if the weapons-scoring methodology be consistently applied to historical battles. Unfortunately, this point is not clearly stated in Dupuy’s formal writings, although it was clearly (and compellingly) made by him in numerous briefings that this author heard over the years.
Figure 2.
In other words, from a system’s perspective, the functional relationships developed by Colonel Dupuy are part of his analysis system that includes this weapons-scoring methodology consistently applied (see Fig. l again). The derived functional relationships do not stand alone (unless further empirical analysis shows them to hold for any weapons-scoring methodology), but function in concert with computational procedures. Another essential part of this system is Dupuy‘s aggregation methodology, which combines numbers, environmental circumstances, and weapons scores to compute the strength (S) of a military force. A key innovation by Colonel Dupuy [1979, pp. 202- 203] was to use a nonlinear (more precisely, a piecewise-linear) model for certain elements of force strength. This innovation precluded the occurrence of military absurdities such as air firepower being fully substitutable for ground firepower, antitank weapons being fully effective when armor targets are lacking, etc‘ The final part of this computational system is Dupuy’s situational-adjustment methodology, which combines the effects of operational circumstances with force strengths to determine relative combat power, e.g. Pa/Pd.
To recapitulate, the determination of an Operational Lethality Index (OLI) for a weapon involves the combination of weapon lethality, quantified in terms of a Theoretical Lethality Index (TLI) (e.g. see Dupuy [1987, p. 84]), and troop dispersion[9] (e.g. see Dupuy [1987, pp. 84- 85]). Weapons scores (i.e. the OLIs) are then combined with numbers (own side and enemy) and combat- environment factors to yield force strength. Six[10] different categories of weapons are aggregated, with nonlinear (i.e. piecewise-linear) models being used for the following three categories of weapons: antitank, air defense, and air firepower (i.e. c1ose—air support). Operational, e.g. mobility, posture, surprise, etc. (Dupuy [1987, p. 87]), and behavioral variables (quantified as a relative combat effectiveness value (CEV)) are then applied to force strength to determine a side’s combat-power potential.
Requirement for Consistent Scoring of Weapons, Force Aggregation, and Situational Adjustment for Operational Circumstances
The salient point to be gleaned from Fig.1 and 2 is that the same (or at least consistent) weapons—scoring, aggregation, and situational—adjustment methodologies be used for both developing functional relationships and then playing them to model future combat. The corresponding computational methods function as a system (organic whole) for determining relative combat power, e.g. Pa/Pd. For the development of functional relationships from historical data, a force ratio (relative combat power of the two opposing sides, e.g. attacker’s combat power divided by that of the defender, Pa/Pd is computed (i.e. it is a derived quantity) as the independent variable, with observed combat outcome being the dependent variable. Thus, as discussed above, this force ratio depends on the methodologies for scoring weapons, aggregating force strengths, and adjusting a force’s combat power for the operational circumstances of the engagement. It is a priori not clear that different scoring, aggregation, and situational-adjustment methodologies will lead to similar derived values. If such different computational procedures were to be used, these derived values should be recomputed and the corresponding functional relationships rederived and replotted.
However, users of the Tactical Numerical Deterministic Model (TNDM) (or for that matter, its predecessor, the Quantified Judgment Model (QJM)) need not worry about this point because it was apparently meticulously observed by Colonel Dupuy in all his work. However, portions of his work have found their way into a surprisingly large number of DOD models (usually not explicitly acknowledged), but the context and range of validity of historical results have been largely ignored by others. The need for recalibration of the historical data and corresponding functional relationships has not been considered in applying Dupuy’s results for some important current DOD models.
Implications for Current DOD Models
A number of important current DOD models (namely, TACWAR and JICM discussed below) make use of some of Dupuy’s historical results without recalibrating functional relationships such as loss rates and rates of advance as a function of some force ratio (e.g. Pa/Pd). As discussed above, it is not clear that such a procedure will capture the essence of past combat experience. Moreover, in calculating losses, Dupuy first determines personnel losses (expressed as a percent loss of personnel strength, i.e., number of combatants on a side) and then calculates equipment losses as a function of this casualty rate (e.g., see Dupuy [1971, pp. 219-223], also [1990, Chapters 5 through 7][11]). These latter functional relationships are apparently not observed in the models discussed below. In fact, only Dupuy (going back to Dupuy [1979][12] takes personnel losses to depend on a force ratio and other pertinent variables, with materiel losses being taken as derivative from this casualty rate.
For example, TACWAR determines personnel losses[13] by computing a force ratio and then consulting an appropriate casualty-rate curve (referred to as empirical data), much in the same fashion as ATLAS did[14]. However, such a force ratio is computed using a linear model with weapon values determined by the so-called antipotential-potential method[15]. Unfortunately, this procedure may not be consistent with how the empirical data (i.e. the casualty-rate curves) was developed. Further research is required to demonstrate that valid casualty estimates are obtained when different weapon scoring, aggregation, and situational-adjustment methodologies are used to develop casualty-rate curves from historical data and to use them to assess losses in aggregated combat models. Furthermore, TACWAR does not use Dupuy’s model for equipment losses (see above), although it does purport, as just noted above, to use “historical data” (e.g., see Kerlin et al. [1975, p. 22]) to compute personnel losses as a function (among other things) of a force ratio (given by a linear relationship), involving close air support values in a way never used by Dupuy. Although their force-ratio determination methodology does have logical and mathematical merit, it is not the way that the historical data was developed.
Moreover, RAND (Allen [1992]) has more recently developed what is called the situational force scoring (SFS) methodology for calculating force ratios in large-scale, aggregated-force combat situations to determine loss and movement rates. Here, SFS refers essentially to a force- aggregation and situation-adjustment methodology, which has many conceptual elements in common with Dupuy‘s methodology (except, most notably, extensive testing against historical data, especially documentation of such efforts). This SFS was originally developed for RSAS[16] and is today used in JICM[17]. It also apparently uses a weapon-scoring system developed at RAND[18]. It purports (no documentation given [citation of unpublished work]) to be consistent with historical data (including the ATLAS casualty-rate curves) (Allen [1992, p.41]), but again no consideration is given to recalibration of historical results for different weapon scoring, force-aggregation, and situational-adjustment methodologies. SFS emphasizes adjusting force strengths according to operational circumstances (the “situation”) of the engagement (including surprise), with many innovative ideas (but in some major ways has little connection with previous work of others[19]). The resulting model contains many more details than historical combat data would support. It also is methodology that differs in many essential ways from that used previously by any investigator. In particular, it is doubtful that it develops force ratios in a manner consistent with Dupuy’s work.
Final Comments
Use of (sophisticated) mathematics for modeling past historical combat (and extrapolating it into the future for planning purposes) is no reason for ignoring Dupuy’s work. One would think that the current Military OR community would try to understand Dupuy’s work before trying to improve and extend it. In particular, Colonel Dupuy’s various computational procedures (including constants) must be considered as an organic whole (i.e. a system) supporting the development of functional relationships. If one ignores this computational system and simply tries to use some isolated aspect, the result may be interesting and even logically sound, but it probably lacks any scientific validity.
REFERENCES
P. Allen, “Situational Force Scoring: Accounting for Combined Arms Effects in Aggregate Combat Models,” N-3423-NA, The RAND Corporation, Santa Monica, CA, 1992.
L. B. Anderson, “A Briefing on Anti-Potential Potential (The Eigen-value Method for Computing Weapon Values), WP-2, Project 23-31, Institute for Defense Analyses, Arlington, VA, March 1974.
B. W. Bennett, et al, “RSAS 4.6 Summary,” N-3534-NA, The RAND Corporation, Santa Monica, CA, 1992.
B. W. Bennett, A. M. Bullock, D. B. Fox, C. M. Jones, J. Schrader, R. Weissler, and B. A. Wilson, “JICM 1.0 Summary,” MR-383-NA, The RAND Corporation, Santa Monica, CA, 1994.
P. K. Davis and J. A. Winnefeld, “The RAND Strategic Assessment Center: An Overview and Interim Conclusions About Utility and Development Options,” R-2945-DNA, The RAND Corporation, Santa Monica, CA, March 1983.
T.N, Dupuy, Numbers. Predictions and War: Using History to Evaluate Combat Factors and Predict the Outcome of Battles, The Bobbs-Merrill Company, Indianapolis/New York, 1979,
T.N. Dupuy, Numbers Predictions and War, Revised Edition, HERO Books, Fairfax, VA 1985.
T.N. Dupuy, Understanding War: History and Theory of Combat, Paragon House Publishers, New York, 1987.
T.N. Dupuy, Attrition: Forecasting Battle Casualties and Equipment Losses in Modem War, HERO Books, Fairfax, VA, 1990.
General Research Corporation (GRC), “A Hierarchy of Combat Analysis Models,” McLean, VA, January 1973.
Historical Evaluation and Research Organization (HERO), “Average Casualty Rates for War Games, Based on Historical Data,” 3 Volumes in 1, Dunn Loring, VA, February 1967.
E. P. Kerlin and R. H. Cole, “ATLAS: A Tactical, Logistical, and Air Simulation: Documentation and User’s Guide,” RAC-TP-338, Research Analysis Corporation, McLean, VA, April 1969 (AD 850 355).
E.P. Kerlin, L.A. Schmidt, A.J. Rolfe, M.J. Hutzler, and D,L. Moody, “The IDA Tactical Warfare Model: A Theater-Level Model of Conventional, Nuclear, and Chemical Warfare, Volume II- Detailed Description” R-21 1, Institute for Defense Analyses, Arlington, VA, October 1975 (AD B009 692L).
R. McQuie, “Military History and Mathematical Analysis,” Military Review 50, No, 5, 8-17 (1970).
S.M. Robinson, “Shadow Prices for Measures of Effectiveness, I: Linear Model,” Operations Research 41, 518-535 (1993).
J.G. Taylor, Lanchester Models of Warfare. Vols, I & II. Operations Research Society of America, Alexandria, VA, 1983. (a)
J.G. Taylor, “A Lanchester-Type Aggregated-Force Model of Conventional Ground Combat,” Naval Research Logistics Quarterly 30, 237-260 (1983). (b)
NOTES
[1] For example, see Taylor [1983a, Section 7.18], which contains a number of examples. The basic references given there may be more accessible through Robinson [I993].
[2] This term was apparently coined by L.B. Anderson [I974] (see also Kerlin et al. [1975, Chapter I, Section D.3]).
[3] The Tactical Warfare (TACWAR) model is a theater-level, joint-warfare, computer-based combat model that is currently used for decision support by the Joint Staff and essentially all CINC staffs. It was originally developed by the Institute for Defense Analyses in the mid-1970s (see Kerlin et al. [1975]), originally referred to as TACNUC, which has been continually upgraded until (and including) the present day.
[4] For example, see Kerlin and Cole [1969], GRC [1973, Fig. 6-6], or Taylor [1983b, Fig. 5] (also Taylor [1983a, Section 7.13]).
[5] The only apparent difference between Dupuy [1979] and Dupuy [1985] is the addition of an appendix (Appendix C “Modified Quantified Judgment Analysis of the Bekaa Valley Battle”) to the end of the latter (pp. 241-251). Hence, the page content is apparently the same for these two books for pp. 1-239.
[6] Technically speaking, one also has the engagement type and possibly several other descriptors (denoted in Fig. 1 as reduced list of operational circumstances) as other inputs to a historical battle.
[7] In Dupuy [1979, e.g. pp. 43-46] only environmental variables are mentioned, although basically the same formulas underlie both Dupuy [1979] and Dupuy [1987]. For simplicity, Fig. 1 and 2 follow this usage and employ the term “environmental circumstances.”
[8] In Dupuy [1979, e.g. pp. 46-47] only operational variables are mentioned, although basically the same formulas underlie both Dupuy [1979] and Dupuy [1987]. For simplicity, Fig. 1 and 2 follow this usage and employ the term “operational circumstances.”
[9] Chris Lawrence has kindly brought to my attention that since the same value for troop dispersion from an historical period (e.g. see Dupuy [1987, p. 84]) is used for both the attacker and also the defender, troop dispersion does not actually affect the determination of relative combat power PM/Pd.
[10] Eight different weapon types are considered, with three being classified as infantry weapons (e.g. see Dupuy [1979, pp, 43-44], [1981 pp. 85-86]).
[11] Chris Lawrence has kindly informed me that Dupuy‘s work on relating equipment losses to personnel losses goes back to the early 1970s and even earlier (e.g. see HERO [1966]). Moreover, Dupuy‘s [1992] book Future Wars gives some additional empirical evidence concerning the dependence of equipment losses on casualty rates.
[12] But actually going back much earlier as pointed out in the previous footnote.
[13] See Kerlin et al. [1975, Chapter I, Section D.l].
[14] See Footnote 4 above.
[15] See Kerlin et al. [1975, Chapter I, Section D.3]; see also Footnotes 1 and 2 above.
[16] The RAND Strategy Assessment System (RSAS) is a multi-theater aggregated combat model developed at RAND in the early l980s (for further details see Davis and Winnefeld [1983] and Bennett et al. [1992]). It evolved into the Joint Integrated Contingency Model (JICM), which is a post-Cold War redesign of the RSAS (starting in FY92).
[17] The Joint Integrated Contingency Model (JICM) is a game-structured computer-based combat model of major regional contingencies and higher-level conflicts, covering strategic mobility, regional conventional and nuclear warfare in multiple theaters, naval warfare, and strategic nuclear warfare (for further details, see Bennett et al. [1994]).
[18] RAND apparently replaced one weapon-scoring system by another (e.g. see Allen [1992, pp. 9, l5, and 87-89]) without making any other changes in their SFS System.
[19] For example, both Dupuy’s early HERO work (e.g. see Dupuy [1967]), reworks of these results by the Research Analysis Corporation (RAC) (e.g. see RAC [1973, Fig. 6-6]), and Dupuy’s later work (e.g. see Dupuy [1979]) considered daily fractional casualties for the attacker and also for the defender as basic casualty-outcome descriptors (see also Taylor [1983b]). However, RAND does not do this, but considers the defender’s loss rate and a casualty exchange ratio as being the basic casualty-production descriptors (Allen [1992, pp. 41-42]). The great value of using the former set of descriptors (i.e. attacker and defender fractional loss rates) is that not only is casualty assessment more straight forward (especially development of functional relationships from historical data) but also qualitative model behavior is readily deduced (see Taylor [1983b] for further details).
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).
French retreat from Russia in 1812 by Illarion Mikhailovich Pryanishnikov (1812) [Wikipedia]
After discussing with Chris the series of recent posts on the subject of breakpoints, it seemed appropriate to provide a better definition of exactly what a breakpoint is.
Dorothy Kneeland Clark was the first to define the notion of a breakpoint in her study, Casualties as a Measure of the Loss of Combat Effectiveness of an Infantry Battalion (Operations Research Office, The Johns Hopkins University: Baltimore, 1954). She found it was not quite as clear-cut as it seemed and the working definition she arrived at was based on discussions and the specific combat outcomes she found in her data set [pp 9-12].
DETERMINATION OF BREAKPOINT
The following definitions were developed out of many discussions. A unit is considered to have lost its combat effectiveness when it is unable to carry out its mission. The onset of this inability constitutes a breakpoint. A unit’s mission is the objective assigned in the current operations order or any other instructional directive, written or verbal. The objective may be, for example, to attack in order to take certain positions, or to defend certain positions.
How does one determine when a unit is unable to carry out its mission? The obvious indication is a change in operational directive: the unit is ordered to stop short of its original goal, to hold instead of attack, to withdraw instead of hold. But one or more extraneous elements may cause the issue of such orders:
(1) Some other unit taking part in the operation may have lost its combat effectiveness, and its predicament may force changes, in the tactical plan. For example the inability of one infantry battalion to take a hill may require that the two adjoining battalions be stopped to prevent exposing their flanks by advancing beyond it.
(2) A unit may have been assigned an objective on the basis of a G-2 estimate of enemy weakness which, as the action proceeds, proves to have been over-optimistic. The operations plan may, therefore, be revised before the unit has carried out its orders to the point of losing combat effectiveness.
(3) The commanding officer, for reasons quite apart from the tactical attrition, may change his operations plan. For instance, General Ridgway in May 1951 was obliged to cancel his plans for a major offensive north of the 38th parallel in Korea in obedience to top level orders dictated by political considerations.
(4) Even if the supposed combat effectiveness of the unit is the determining factor in the issuance of a revised operations order, a serious difficulty in evaluating the situation remains. The commanding officer’s decision is necessarily made on the basis of information available to him plus his estimate of his unit’s capacities. Either or both of these bases may be faulty. The order may belatedly recognize a collapse which has in factor occurred hours earlier, or a commanding officer may withdraw a unit which could hold for a much longer time.
It was usually not hard to discover when changes in orders resulted from conditions such as the first three listed above, but it proved extremely difficult to distinguish between revised orders based on a correct appraisal of the unit’s combat effectiveness and those issued in error. It was concluded that the formal order for a change in mission cannot be taken as a definitive indication of the breakpoint of a unit. It seemed necessary to go one step farther and search the records to learn what a given battalion did regardless of provisions in formal orders…
CATEGORIES OF BREAKPOINTS SELECTED
In the engagements studied the following categories of breakpoint were finally selected:
Category of Breakpoint
No. Analyzed
I. Attack [Symbol] rapid reorganization [Symbol] attack
9
II. Attack [Symbol] defense (no longer able to attack without a few days of recuperation and reinforcement
21
III. Defense [Symbol] withdrawal by order to a secondary line
13
IV. Defense [Symbol] collapse
5
Disorganization and panic were taken as unquestionable evidence of loss of combat effectiveness. It appeared, however, that there were distinct degrees of magnitude in these experiences. In addition to the expected breakpoints at attack [Symbol] defense and defense [Symbol] collapse, a further category, I, seemed to be indicated to include situations in which an attacking battalion was ‘pinned down” or forced to withdraw in partial disorder but was able to reorganize in 4 to 24 hours and continue attacking successfully.
Category II includes (a) situations in which an attacking battalion was ordered into the defensive after severe fighting or temporary panic; (b) situations in which a battalion, after attacking successfully, failed to gain ground although still attempting to advance and was finally ordered into defense, the breakpoint being taken as occurring at the end of successful advance. In other words, the evident inability of the unit to fulfill its mission was used as the criterion for the breakpoint whether orders did or did not recognize its inability. Battalions after experiencing such a breakpoint might be able to recuperate in a few days to the point of renewing successful attack or might be able to continue for some time in defense.
The sample of breakpoints coming under category IV, defense [Symbol] collapse, proved to be very small (5) and unduly weighted in that four of the examples came from the same engagement. It was, therefore, discarded as probably not representative of the universe of category IV breakpoints,* and another category (III) was added: situations in which battalions on the defense were ordered withdrawn to a quieter sector. Because only those instances were included in which the withdrawal orders appeared to have been dictated by the condition of the unit itself, it is believed that casualty levels for this category can be regarded as but slightly lower than those associated with defense [Symbol] collapse.
In both categories II and III, “‘defense” represents an active situation in which the enemy is attacking aggressively.
* It had been expected that breakpoints in this category would be associated with very high losses. Such did not prove to be the case. In whatever way the data were approached, most of the casualty averages were only slightly higher than those associated with category II (attack [Symbol] defense), although the spread in data was wider. It is believed that factors other than casualties, such as bad weather, difficult terrain, and heavy enemy artillery fire undoubtedly played major roles in bringing about the collapse in the four units taking part in the same engagement. Furthermore, the casualty figures for the four units themselves is in question because, as the situation deteriorated, many of the men developed severe cases of trench foot and combat exhaustion, but were not evacuated, as they would have been in a less desperate situation, and did not appear in the casualty records until they had made their way to the rear after their units had collapsed.
In 1987-1988, Trevor Dupuy and colleagues at Data Memory Systems, Inc. (DMSi), Janice Fain, Rich Anderson, Gay Hammerman, and Chuck Hawkins sought to create a broader, more generally applicable definition for breakpoints for the study, Forced Changes of Combat Posture (DMSi, Fairfax, VA, 1988) [pp. I-2-3]
The combat posture of a military force is the immediate intention of its commander and troops toward the opposing enemy force, together with the preparations and deployment to carry out that intention. The chief combat postures are attack, defend, delay, and withdraw.
A change in combat posture (or posture change) is a shift from one posture to another, as, for example, from defend to attack or defend to withdraw. A posture change can be either voluntary or forced.
A forced posture change (FPC) is a change in combat posture by a military unit that is brought about, directly or indirectly, by enemy action. Forced posture changes are characteristically and almost always changes to a less aggressive posture. The most usual FPCs are from attack to defend and from defend to withdraw (or retrograde movement). A change from withdraw to combat ineffectiveness is also possible.
Breakpoint is a term sometimes used as synonymous with forced posture change, and sometimes used to mean the collapse of a unit into ineffectiveness or rout. The latter meaning is probably more common in general usage, while forced posture change is the more precise term for the subject of this study. However, for brevity and convenience, and because this study has been known informally since its inception as the “Breakpoints” study, the term breakpoint is sometimes used in this report. When it is used, it is synonymous with forced posture change.
Hopefully this will help clarify the previous discussions of breakpoints on the blog.
Reilly starts with a very nice statement of the issue:
Clearly breakpoints are crucial when modelling battlefield combat. I have read extensively about it using mostly first hand accounts of battles rather than high level summaries. Some of the major factors causing it appear to be loss of leadership (e.g. Harald’s death at Hastings), loss of belief in the units capacity to achieve its objectives (e.g. the retreat of the Old Guard at Waterloo, surprise often figured in Mongol successes, over confidence resulting in impetuous attacks which fail dramatically (e.g. French attacks at Agincourt and Crecy), loss of control over the troops (again Crecy and Agincourt) are some of the main ones I can think of off hand.
The break-point crisis seems to occur against a background of confusion, disorder, mounting casualties, increasing fatigue and loss of morale. Casualties are part of the background but not usually the actual break point itself.
He then states:
Perhaps a way forward in the short term is to review a number of first hand battle accounts (I am sure you can think of many) and calculate the percentage of times these factors and others appear as breakpoints in the literature.
This has been done. In effect this is what Robert McQuie did in his article and what was the basis for the DMSI breakpoints study.
Why wait for the military to do something? You will die of old age before that happens!
That is distinctly possible. If this really was a simple issue that one person working for a year could produce a nice definitive answer for…..it would have already been done !!!
Let us look at the 1988 Breakpoints study. There was some effort leading up to that point. Trevor Dupuy and DMSI had already looked into the issue. This included developing a database of engagements (the Land Warfare Data Base or LWDB) and using that to examine the nature of breakpoints. The McQuie article was developed from this database, and his article was closely coordinated with Trevor Dupuy. This was part of the effort that led to the U.S. Army’s Concepts Analysis Agency (CAA) to issue out a RFP (Request for Proposal). It was competitive. I wrote the proposal that won the contract award, but the contract was given to Dr. Janice Fain to lead. My proposal was more quantitative in approach than what she actually did. Her effort was more of an intellectual exploration of the issue. I gather this was done with the assumption that there would be a follow-on contract (there never was). Now, up until that point at least a man-year of effort had been expended, and if you count the time to develop the databases used, it was several man-years.
Now the Breakpoints study was headed up by Dr. Janice B. Fain, who worked on it for the better part of a year. Trevor N. Dupuy worked on it part-time. Gay M. Hammerman conducted the interview with the veterans. Richard C. Anderson researched and created an additional 24 engagements that had clear breakpoints in them for the study (that is DMSI report 117B). Charles F. Hawkins was involved in analyzing the engagements from the LWDB. There were several other people also involved to some extent. Also, 39 veterans were interviewed for this effort. Many were brought into the office to talk about their experiences (that was truly entertaining). There were also a half-dozen other staff members and consultants involved in the effort, including Lt. Col. James T. Price (USA, ret), Dr. David Segal (sociologist), Dr. Abraham Wolf (a research psychologist), Dr. Peter Shapiro (social psychology) and Col. John R. Brinkerhoff (USA, ret). There were consultant fees, travel costs and other expenses related to that. So, the entire effort took at least three “man-years” of effort. This was what was needed just get to the point where we are able to take the next step.
This is not something that a single scholar can do. That is why funding is needed.
As to dying of old age before that happens…..that may very well be the case. Right now, I am working on two books, one of them under contract. I sort of need to finish those up before I look at breakpoints again. After that, I will decide whether to work on a follow-on to America’s Modern Wars (called Future American Wars) or work on a follow-on to War by Numbers (called War by Numbers II…being the creative guy that I am). Of course, neither of these books are selling well….so perhaps my time would be better spent writing another Kursk book, or any number of other interesting projects on my plate. Anyhow, if I do War by Numbers II, then I do plan on investing several chapters into addressing breakpoints. This would include using the 1,000+ cases that now populate our combat databases to do some analysis. This is going to take some time. So…….I may get to it next year or the year after that, but I may not. If someone really needs the issue addressed, they really need to contract for it.
U.S. Army prisoners of war captured by German forces during the Battle of the Bulge in 1944. [Wikipedia]
One of the least studied aspects of combat is battle termination. Why do units in combat stop attacking or defending? Shifts in combat posture (attack, defend, delay, withdrawal) are usually voluntary, directed by a commander, but they can also be involuntary, as a result of direct or indirect enemy action. Why do involuntary changes in combat posture, known as breakpoints, occur?
As Chris pointed out in a previous post, the topic of breakpoints has only been addressed by two known studies since 1954. Most existing military combat models and wargames address breakpoints in at least a cursory way, usually through some calculation based on personnel casualties. Both of the breakpoints studies suggest that involuntary changes in posture are seldom related to casualties alone, however.
Current U.S. Army doctrine addresses changes in combat posture through discussions of culmination points in the attack, and transitions from attack to defense, defense to counterattack, and defense to retrograde. But these all pertain to voluntary changes, not breakpoints.
Army doctrinal literature has little to say about breakpoints, either in the context of friendly forces or potential enemy combatants. The little it does say relates to the effects of fire on enemy forces and is based on personnel and material attrition.
According to ADRP 1-02 Terms and Military Symbols, an enemy combat unit is considered suppressed after suffering 3% personnel casualties or material losses, neutralized by 10% losses, and destroyed upon sustaining 30% losses. The sources and methodology for deriving these figures is unknown, although these specific terms and numbers have been a part of Army doctrine for decades.
The joint U.S. Army and U.S. Marine Corps vision of future land combat foresees battlefields that are highly lethal and demanding on human endurance. How will such a future operational environment affect combat performance? Past experience undoubtedly offers useful insights but there seems to be little interest in seeking out such knowledge.
A breakpoint or involuntary change in posture is an essential part of modeling. There is a breakpoint methodology in C-WAM. According to slide 18 and rule book section 5.7.2 is that ground unit below 50% strength can only defend. It is removed at below 30% strength. I gather this is a breakpoint for a brigade.
Let me just quote from Chapter 18 (Modeling Warfare) of my book War by Numbers: Understanding Conventional Combat (pages 288-289):
The original breakpoints study was done in 1954 by Dorothy Clark of ORO [which can be found here].[1] It examined forty-three battalion-level engagements where the units “broke,” including measuring the percentage of losses at the time of the break. Clark correctly determined that casualties were probably not the primary cause of the breakpoint and also declared the need to look at more data. Obviously, forty-three cases of highly variable social science-type data with a large number of variables influencing them are not enough for any form of definitive study. Furthermore, she divided the breakpoints into three categories, resulting in one category based upon only nine observations. Also, as should have been obvious, this data would apply only to battalion-level combat. Clark concluded “The statement that a unit can be considered no longer combat effective when it has suffered a specific casualty percentage is a gross oversimplification not supported by combat data.” She also stated “Because of wide variations in data, average loss percentages alone have limited meaning.”[2]
Yet, even with her clear rejection of a percent loss formulation for breakpoints, the 20 to 40 percent casualty breakpoint figures remained in use by the training and combat modeling community. Charts in the 1964 Maneuver Control field manual showed a curve with the probability of unit break based on percentage of combat casualties.[3] Once a defending unit reached around 40 percent casualties, the chance of breaking approached 100 percent. Once an attacking unit reached around 20 percent casualties, the chance of it halting (type I break) approached 100% and the chance of it breaking (type II break) reached 40 percent. These data were for battalion-level combat. Because they were also applied to combat models, many models established a breakpoint of around 30 or 40 percent casualties for units of any size (and often applied to division-sized units).
To date, we have absolutely no idea where these rule-of-thumb formulations came from and despair of ever discovering their source. These formulations persist despite the fact that in fifteen (35%) of the cases in Clark’s study, the battalions had suffered more than 40 percent casualties before they broke. Furthermore, at the division-level in World War II, only two U.S. Army divisions (and there were ninety-one committed to combat) ever suffered more than 30% casualties in a week![4] Yet, there were many forced changes in combat posture by these divisions well below that casualty threshold.
The next breakpoints study occurred in 1988.[5] There was absolutely nothing of any significance (meaning providing any form of quantitative measurement) in the intervening thirty-five years, yet there were dozens of models in use that offered a breakpoint methodology. The 1988 study was inconclusive, and since then nothing further has been done.[6]
This seemingly extreme case is a fairly typical example. A specific combat phenomenon was studied only twice in the last fifty years, both times with inconclusive results, yet this phenomenon is incorporated in most combat models. Sadly, similar examples can be pulled for virtually each and every phenomena of combat being modeled. This failure to adequately examine basic combat phenomena is a problem independent of actual combat modeling methodology.
[3] Headquarters, Department of the Army, FM 105-5 Maneuver Control (Washington, D.C., December, 1967), pages 128-133.
[4] The two exceptions included the U.S. 106th Infantry Division in December 1944, which incidentally continued fighting in the days after suffering more than 40 percent losses, and the Philippine Division upon its surrender in Bataan on 9 April 1942 suffered 100% losses in one day in addition to very heavy losses in the days leading up to its surrender.
[5] This was HERO Report number 117, Forced Changes of Combat Posture (Breakpoints) (Historical Evaluation and Research Organization, Fairfax, VA., 1988). The intervening years between 1954 and 1988 were not entirely quiet. See HERO Report number 112, Defeat Criteria Seminar, Seminar Papers on the Evaluation of the Criteria for Defeat in Battle (Historical Evaluation and Research Organization, Fairfax, VA., 12 June 1987) and the significant article by Robert McQuie, “Battle Outcomes: Casualty Rates as a Measure of Defeat” in Army, issue 37 (November 1987). Some of the results of the 1988 study was summarized in the book by Trevor N. Dupuy, Understanding Defeat: How to Recover from Loss in Battle to Gain Victory in War (Paragon House Publishers, New York, 1990).
[6] The 1988 study was the basis for Trevor Dupuy’s book: Col. T. N. Dupuy, Understanding Defeat: How to Recover From Loss in Battle to Gain Victory in War (Paragon House Publishers, New York, 1990).
“All models are wrong, some models are useful.” – George Box
Models, no matter what their subjects, must always be an imperfect copy of the original. The term “model” inherently has this connotation. If the subject is exact and precise, then it is a duplicate, a replica, a clone, or a copy, but not a “model.” The most common dimension to be compromised is generally size, or more literally the three spatial dimensions of length, width and height. A good example of this would be a scale model airplane, generally available in several ratios from the original, such as 1/144, 1/72 or 1/48 (which are interestingly all factors of 12 … there are also 1/100 for the more decimal-minded). These mean that the model airplane at 1/72 scale would be 72 times smaller … take the length, width and height measurements of the real item, and divide by 72 to get the model’s value.
If we take the real item’s weight and divide by 72, we would not expect our model to weight 72 times less! Not unless the same or similar materials would be used, certainly. Generally, the model has a different purpose than replicating the subject’s functionality. It is helping to model the subject’s qualities, or to mimic them in some useful way. In the case of the 1/72 plastic model airplane of the F-15J fighter, this might be replicating the sight of a real F-15J, to satisfy the desire of the youth to look at the F-15J and to imagine themselves taking flight. Or it might be for pilots at a flight school to mimic air combat with models instead of ha
The model aircraft is a simple physical object; once built, it does not change over time (unless you want to count dropping it and breaking it…). A real F-15J, however, is a dynamic physical object, which changes considerably over the course of its normal operation. It is loaded with fuel, ordnance, both of which have a huge effect on its weight, and thus its performance characteristics. Also, it may be occupied by different crew members, whose experience and skills may vary considerably. These qualities of the unit need to be taken into account, if the purpose of the model is to represent the aircraft. The classic example of this is a flight envelope model of an F-15A/C:
[Quora]
This flight envelope itself is a model, it represents the flight characteristics of the F-15 using two primary quantitative axes – altitude and speed (in numbers of mach), and also throttle setting. Perhaps the most interesting thing about this is the realization than an F-15 slows down as it descends. Are these particular qualities of an F-15 required to model air combat involving such and aircraft?
How to Apply This Modeling Process to a Wargame?
The purpose of the war game is to model or represent the possible outcome of a real combat situation, played forward in the model at whatever pace and scale the designer has intended.
As mentioned previously, my colleague and I are playing Asian Fleet, a war game that covers several types of naval combat, including those involving air units, surface units and submarine units. This was published in 2007, and updated in 2010. We’ve selected a scenario that has only air units on either side. The premise of this scenario is quite simple:
The Chinese air force, in trying to prevent the United States from intervening in a Taiwan invasion, will carry out an attack on the SDF as well as the US military base on Okinawa. Forces around Shanghai consisting of state-of-the-art fighter bombers and long-range attack aircraft have been placed for the invasion of Taiwan, and an attack on Okinawa would be carried out with a portion of these forces. [Asian Fleet Scenario Book]
Of course, this game is a model of reality. The infinite geospatial and temporal possibilities of space-time which is so familiar to us has been replaced by highly aggregated discreet buckets, such as turns that may last for a day, or eight hours. Latitude, longitude and altitude are replaced with a two-dimensional hexagonal “honey comb” surface. Hence, distance is no longer computed in miles or meters, but rather in “hexes”, each of which is about 50 nautical miles. Aircraft are effectively aloft, or on the ground, although a “high mission profile” will provide endurance benefits. Submarines are considered underwater, or may use “deep mode” attempting to hide from sonar searches.
Maneuver units are represented by “counters” or virtual chits to be moved about the map as play progresses. Their level of aggregation varies from large and powerful ships and subs represented individually, to smaller surface units and weaker subs grouped and represented by a single counter (a “flotilla”), to squadrons or regiments of aircraft represented by a single counter. Depending upon the nation and the military branch, this may be a few as 3-5 aircraft in a maritime patrol aircraft (MPA) detachment (“recon” in this game), to roughly 10-12 aircraft in a bomber unit, to 24 or even 72 aircraft in a fighter unit (“interceptor” in this game).
Enough Theory, What Happened?!
The Chinese Air Force mobilized their H6H bomber, escorted by large numbers of Flankers (J11 and Su-30MK2 fighters from the Shanghai area, and headed East towards Okinawa. The US Air Force F-15Cs supported by airborne warning and control system (AWACS) detected this inbound force and delayed engagement until their Japanese F-15J unit on combat air patrol (CAP) could support them, and then engaged the Chinese force about 50 miles from the AWACS orbits. In this game, air combat is broken down into two phases, long-range air to air (LRAA) combat (aka beyond visual range, BVR), and “regular” air combat, or within visual range (WVR) combat.
In BVR combat, only units marked as equipped with BVR capability may attack:
2 x F-15C units have a factor of 32; scoring a hit in 5 out of 10 cases, or roughly 50%.
Su-30MK2 unit has a factor of 16; scoring a hit in 4 out of 10 cases, ~40%.
To these numbers a modifier of +2 exists when the attacker is supported by AWACS, so the odds to score a hit increase to roughly 70% for the F-15Cs … but in our example they miss, and the Chinese shot misses as well. Thus, the combat proceeds to WVR.
In WVR combat, each opposing side sums their aerial combat factors:
2 x F-15C (32) + F-15J (13) = 45
Su-30MK2 (15) + J11 (13) + H6H (1) = 29
These two numbers are then expressed as a ratio, attacker-to-defender (45:29), and rounded down in favor of the defender (1:1), and then a ten-sided-die (d10) is rolled to consult the Air-to-Air Combat Results Table, on the “CAP/AWACS Interception” line. The die was rolled, and a result of “0/0r” was achieved, which basically says that neither side takes losses, but the defender is turned back from the mission (“r” being code for “return to base”). Given the +2 modifier for the AWACS, the worst outcome for the Allies would be a mutual return to base result (“0r/0r”). The best outcome would be inflicting two “steps” of damage, and sending the rest home (“0/2r”). A step of loss is about one half of an air unit, represented by flipping over the counter or chit, and operating with the combat factors at about half strength.
To sum this up, as the Allied commander, my conclusion was that the Americans were hung-over or asleep for this engagement.
I am encouraged by some similarities between this game and the fantastic detail that TDI has just posted about the DACM model, here and here. Thus, I plan to not only dissect this Asian Fleet game (VGAF), but also go a gap analysis between VGAF and DACM.
The Dupuy Air Campaign Model
by Col. Joseph A. Bulger, Jr., USAF, Ret.
The Dupuy Institute, as part of the DACM [Dupuy Air Campaign Model], created a draft model in a spreadsheet format to show how such a model would calculate attrition. Below are the actual printouts of the “interim methodology demonstration,” which shows the types of inputs, outputs, and equations used for the DACM. The spreadsheet was created by Col. Bulger, while many of the formulae were the work of Robert Shaw.
