Tag Attrition

The Lanchester Equations and Historical Warfare

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.

NOTES

[1.] J. H. Engel, “A Verification of Lanchester’s Law,” Operations Research 2, 163-171 (1954).

[2.] For example, see R. L. Helmbold, “Some Observations on the Use of Lanchester’s Theory for Prediction,” Operations Research 12, 778-781 (1964); H. K. Weiss, “Lanchester-Type Models of Warfare,” Proceedings of the First International Conference on Operational Research, 82-98, ORSA (1957); H. K. Weiss, “Combat Models and Historical Data; The U.S. Civil War,” Operations Research 14, 750-790 (1966).

[3.] D. Willard, “Lanchester as a Force in History: An Analysis of Land Battles of the Years 1618-1905,” RAC-TD-74, Research Analysis Corporation (1962). 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.

[4.] The method of computing the killing rates forced a fit at the beginning and end of the battles. See W. Fain, J. B. Fain, L. Feldman, and S. Simon, “Validation of Combat Models Against Historical Data,” Professional Paper No. 27, Center for Naval Analyses, Arlington, Virginia (1970).

[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.

[16.] S. J. Deitchman, “A Lanchester Model of Guerrilla Warfare,” Operations Research 10, 818-812 (1962).

[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).

Attrition In Future Land Combat

Soldiers with Battery C, 1st Battalion, 82nd Field Artillery Regiment, 1st Brigade Combat Team, 1st Cavalry Division maneuver their Paladins through Hohenfels Training Area, Oct. 26. Photo Credit: Capt. John Farmer, 1st Brigade Combat Team, 1st Cav

[This post was originally published on June 9, 2017]

Last autumn, U.S. Army Chief of Staff General Mark Milley asserted that “we are on the cusp of a fundamental change in the character of warfare, and specifically ground warfare. It will be highly lethal, very highly lethal, unlike anything our Army has experienced, at least since World War II.” He made these comments while describing the Army’s evolving Multi-Domain Battle concept for waging future combat against peer or near-peer adversaries.

How lethal will combat on future battlefields be? Forecasting the future is, of course, an undertaking fraught with uncertainties. Milley’s comments undoubtedly reflect the Army’s best guesses about the likely impact of new weapons systems of greater lethality and accuracy, as well as improved capabilities for acquiring targets. Many observers have been closely watching the use of such weapons on the battlefield in the Ukraine. The spectacular success of the Zelenopillya rocket strike in 2014 was a convincing display of the lethality of long-range precision strike capabilities.

It is possible that ground combat attrition in the future between peer or near-peer combatants may be comparable to the U.S. experience in World War II (although there were considerable differences between the experiences of the various belligerents). Combat losses could be heavier. It certainly seems likely that they would be higher than those experienced by U.S. forces in recent counterinsurgency operations.

Unfortunately, the U.S. Defense Department has demonstrated a tenuous understanding of the phenomenon of combat attrition. Despite wildly inaccurate estimates for combat losses in the 1991 Gulf War, only modest effort has been made since then to improve understanding of the relationship between combat and casualties. The U.S. Army currently does not have either an approved tool or a formal methodology for casualty estimation.

Historical Trends in Combat Attrition

Trevor Dupuy did a great deal of historical research on attrition in combat. He found several trends that had strong enough empirical backing that he deemed them to be verities. He detailed his conclusions in Understanding War: History and Theory of Combat (1987) and Attrition: Forecasting Battle Casualties and Equipment Losses in Modern War (1995).

Dupuy documented a clear relationship over time between increasing weapon lethality, greater battlefield dispersion, and declining casualty rates in conventional combat. Even as weapons became more lethal, greater dispersal in frontage and depth among ground forces led daily personnel loss rates in battle to decrease.

The average daily battle casualty rate in combat has been declining since 1600 as a consequence. Since battlefield weapons continue to increase in lethality and troops continue to disperse in response, it seems logical to presume the trend in loss rates continues to decline, although this may not necessarily be the case. There were two instances in the 19th century where daily battle casualty rates increased—during the Napoleonic Wars and the American Civil War—before declining again. Dupuy noted that combat casualty rates in the 1973 Arab-Israeli War remained roughly the same as those in World War II (1939-45), almost thirty years earlier. Further research is needed to determine if average daily personnel loss rates have indeed continued to decrease into the 21st century.

Dupuy also discovered that, as with battle outcomes, casualty rates are influenced by the circumstantial variables of combat. Posture, weather, terrain, season, time of day, surprise, fatigue, level of fortification, and “all out” efforts affect loss rates. (The combat loss rates of armored vehicles, artillery, and other other weapons systems are directly related to personnel loss rates, and are affected by many of the same factors.) Consequently, yet counterintuitively, he could find no direct relationship between numerical force ratios and combat casualty rates. Combat power ratios which take into account the circumstances of combat do affect casualty rates; forces with greater combat power inflict higher rates of casualties than less powerful forces do.

Winning forces suffer lower rates of combat losses than losing forces do, whether attacking or defending. (It should be noted that there is a difference between combat loss rates and numbers of losses. Depending on the circumstances, Dupuy found that the numerical losses of the winning and losing forces may often be similar, even if the winner’s casualty rate is lower.)

Dupuy’s research confirmed the fact that the combat loss rates of smaller forces is higher than that of larger forces. This is in part due to the fact that smaller forces have a larger proportion of their troops exposed to enemy weapons; combat casualties tend to concentrated in the forward-deployed combat and combat support elements. Dupuy also surmised that Prussian military theorist Carl von Clausewitz’s concept of friction plays a role in this. The complexity of interactions between increasing numbers of troops and weapons simply diminishes the lethal effects of weapons systems on real world battlefields.

Somewhat unsurprisingly, higher quality forces (that better manage the ambient effects of friction in combat) inflict casualties at higher rates than those with less effectiveness. This can be seen clearly in the disparities in casualties between German and Soviet forces during World War II, Israeli and Arab combatants in 1973, and U.S. and coalition forces and the Iraqis in 1991 and 2003.

Combat Loss Rates on Future Battlefields

What do Dupuy’s combat attrition verities imply about casualties in future battles? As a baseline, he found that the average daily combat casualty rate in Western Europe during World War II for divisional-level engagements was 1-2% for winning forces and 2-3% for losing ones. For a divisional slice of 15,000 personnel, this meant daily combat losses of 150-450 troops, concentrated in the maneuver battalions (The ratio of wounded to killed in modern combat has been found to be consistently about 4:1. 20% are killed in action; the other 80% include mortally wounded/wounded in action, missing, and captured).

It seems reasonable to conclude that future battlefields will be less densely occupied. Brigades, battalions, and companies will be fighting in spaces formerly filled with armies, corps, and divisions. Fewer troops mean fewer overall casualties, but the daily casualty rates of individual smaller units may well exceed those of WWII divisions. Smaller forces experience significant variation in daily casualties, but Dupuy established average daily rates for them as shown below.

For example, based on Dupuy’s methodology, the average daily loss rate unmodified by combat variables for brigade combat teams would be 1.8% per day, battalions would be 8% per day, and companies 21% per day. For a brigade of 4,500, that would result in 81 battle casualties per day, a battalion of 800 would suffer 64 casualties, and a company of 120 would lose 27 troops. These rates would then be modified by the circumstances of each particular engagement.

Several factors could push daily casualty rates down. Milley envisions that U.S. units engaged in an anti-access/area denial environment will be constantly moving. A low density, highly mobile battlefield with fluid lines would be expected to reduce casualty rates for all sides. High mobility might also limit opportunities for infantry assaults and close quarters combat. The high operational tempo will be exhausting, according to Milley. This could also lower loss rates, as the casualty inflicting capabilities of combat units decline with each successive day in battle.

It is not immediately clear how cyberwarfare and information operations might influence casualty rates. One combat variable they might directly impact would be surprise. Dupuy identified surprise as one of the most potent combat power multipliers. A surprised force suffers a higher casualty rate and surprisers enjoy lower loss rates. Russian combat doctrine emphasizes using cyber and information operations to achieve it and forces with degraded situational awareness are highly susceptible to it. As Zelenopillya demonstrated, surprise attacks with modern weapons can be devastating.

Some factors could push combat loss rates up. Long-range precision weapons could expose greater numbers of troops to enemy fires, which would drive casualties up among combat support and combat service support elements. Casualty rates historically drop during night time hours, although modern night-vision technology and persistent drone reconnaissance might will likely enable continuous night and day battle, which could result in higher losses.

Drawing solid conclusions is difficult but the question of future battlefield attrition is far too important not to be studied with greater urgency. Current policy debates over whether or not the draft should be reinstated and the proper size and distribution of manpower in active and reserve components of the Army hinge on getting this right. The trend away from mass on the battlefield means that there may not be a large margin of error should future combat forces suffer higher combat casualties than expected.

TDI Friday Read: The Lanchester Equations

Frederick W. Lanchester (1868-1946), British engineer and author of the Lanchester combat attrition equations. [Lanchester.com]

Today’s edition of TDI Friday Read addresses the Lanchester equations and their use in U.S. combat models and simulations. In 1916, British engineer Frederick W. Lanchester published a set of calculations he had derived for determining the results of attrition in combat. Lanchester intended them to be applied as an abstract conceptualization of aerial combat, stating that he did not believe they were applicable to ground combat.

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.

Lanchester equations have been weighed….

Really…..Lanchester?

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.

Human Factors In Warfare: Interaction Of Variable Factors

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.

Military History and Validation of Combat Models

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.

https://dupuyinstitute.org/2017/04/10/wargaming-multi-domain-battle-the-base-of-sand-problem/

TDI Friday Read: Tank Warfare In World War II

American troops advance under the cover of M4 Sherman tank ‘Lucky Legs II’ during mop up operations on Bougainville, Solomon Islands, March 1944. [National Archives/ww2dbase]

In honor of Tony Buzbee, who has parked a fully-functional vintage World War II era M-4 Sherman tank in front of his house in Houston, Texas (much to the annoyance of his home owner’s association), here is a selection of posts addressing various aspects of tank warfare in World War II for you weekend leisure reading.

https://dupuyinstitute.org/2016/08/23/counting-holes-in-tanks-in-tunisia/

U.S. Tank Losses and Crew Casualties in World War II

Tank Loss Rates in Combat: Then and Now

https://dupuyinstitute.org/2017/04/03/was-kursk-the-largest-tank-battle-in-history/

A2/D2 Study

Against the Panzers

And, of course, Chris Lawrence has written the largest existing book on the largest tank battle in history, Kursk.

Attrition In Future Land Combat

Soldiers with Battery C, 1st Battalion, 82nd Field Artillery Regiment, 1st Brigade Combat Team, 1st Cavalry Division maneuver their Paladins through Hohenfels Training Area, Oct. 26. Photo Credit: Capt. John Farmer, 1st Brigade Combat Team, 1st Cav

Last autumn, U.S. Army Chief of Staff General Mark Milley asserted that “we are on the cusp of a fundamental change in the character of warfare, and specifically ground warfare. It will be highly lethal, very highly lethal, unlike anything our Army has experienced, at least since World War II.” He made these comments while describing the Army’s evolving Multi-Domain Battle concept for waging future combat against peer or near-peer adversaries.

How lethal will combat on future battlefields be? Forecasting the future is, of course, an undertaking fraught with uncertainties. Milley’s comments undoubtedly reflect the Army’s best guesses about the likely impact of new weapons systems of greater lethality and accuracy, as well as improved capabilities for acquiring targets. Many observers have been closely watching the use of such weapons on the battlefield in the Ukraine. The spectacular success of the Zelenopillya rocket strike in 2014 was a convincing display of the lethality of long-range precision strike capabilities.

It is possible that ground combat attrition in the future between peer or near-peer combatants may be comparable to the U.S. experience in World War II (although there were considerable differences between the experiences of the various belligerents). Combat losses could be heavier. It certainly seems likely that they would be higher than those experienced by U.S. forces in recent counterinsurgency operations.

Unfortunately, the U.S. Defense Department has demonstrated a tenuous understanding of the phenomenon of combat attrition. Despite wildly inaccurate estimates for combat losses in the 1991 Gulf War, only modest effort has been made since then to improve understanding of the relationship between combat and casualties. The U.S. Army currently does not have either an approved tool or a formal methodology for casualty estimation.

Historical Trends in Combat Attrition

Trevor Dupuy did a great deal of historical research on attrition in combat. He found several trends that had strong enough empirical backing that he deemed them to be verities. He detailed his conclusions in Understanding War: History and Theory of Combat (1987) and Attrition: Forecasting Battle Casualties and Equipment Losses in Modern War (1995).

Dupuy documented a clear relationship over time between increasing weapon lethality, greater battlefield dispersion, and declining casualty rates in conventional combat. Even as weapons became more lethal, greater dispersal in frontage and depth among ground forces led daily personnel loss rates in battle to decrease.

The average daily battle casualty rate in combat has been declining since 1600 as a consequence. Since battlefield weapons continue to increase in lethality and troops continue to disperse in response, it seems logical to presume the trend in loss rates continues to decline, although this may not necessarily be the case. There were two instances in the 19th century where daily battle casualty rates increased—during the Napoleonic Wars and the American Civil War—before declining again. Dupuy noted that combat casualty rates in the 1973 Arab-Israeli War remained roughly the same as those in World War II (1939-45), almost thirty years earlier. Further research is needed to determine if average daily personnel loss rates have indeed continued to decrease into the 21st century.

Dupuy also discovered that, as with battle outcomes, casualty rates are influenced by the circumstantial variables of combat. Posture, weather, terrain, season, time of day, surprise, fatigue, level of fortification, and “all out” efforts affect loss rates. (The combat loss rates of armored vehicles, artillery, and other other weapons systems are directly related to personnel loss rates, and are affected by many of the same factors.) Consequently, yet counterintuitively, he could find no direct relationship between numerical force ratios and combat casualty rates. Combat power ratios which take into account the circumstances of combat do affect casualty rates; forces with greater combat power inflict higher rates of casualties than less powerful forces do.

Winning forces suffer lower rates of combat losses than losing forces do, whether attacking or defending. (It should be noted that there is a difference between combat loss rates and numbers of losses. Depending on the circumstances, Dupuy found that the numerical losses of the winning and losing forces may often be similar, even if the winner’s casualty rate is lower.)

Dupuy’s research confirmed the fact that the combat loss rates of smaller forces is higher than that of larger forces. This is in part due to the fact that smaller forces have a larger proportion of their troops exposed to enemy weapons; combat casualties tend to concentrated in the forward-deployed combat and combat support elements. Dupuy also surmised that Prussian military theorist Carl von Clausewitz’s concept of friction plays a role in this. The complexity of interactions between increasing numbers of troops and weapons simply diminishes the lethal effects of weapons systems on real world battlefields.

Somewhat unsurprisingly, higher quality forces (that better manage the ambient effects of friction in combat) inflict casualties at higher rates than those with less effectiveness. This can be seen clearly in the disparities in casualties between German and Soviet forces during World War II, Israeli and Arab combatants in 1973, and U.S. and coalition forces and the Iraqis in 1991 and 2003.

Combat Loss Rates on Future Battlefields

What do Dupuy’s combat attrition verities imply about casualties in future battles? As a baseline, he found that the average daily combat casualty rate in Western Europe during World War II for divisional-level engagements was 1-2% for winning forces and 2-3% for losing ones. For a divisional slice of 15,000 personnel, this meant daily combat losses of 150-450 troops, concentrated in the maneuver battalions (The ratio of wounded to killed in modern combat has been found to be consistently about 4:1. 20% are killed in action; the other 80% include mortally wounded/wounded in action, missing, and captured).

It seems reasonable to conclude that future battlefields will be less densely occupied. Brigades, battalions, and companies will be fighting in spaces formerly filled with armies, corps, and divisions. Fewer troops mean fewer overall casualties, but the daily casualty rates of individual smaller units may well exceed those of WWII divisions. Smaller forces experience significant variation in daily casualties, but Dupuy established average daily rates for them as shown below.

For example, based on Dupuy’s methodology, the average daily loss rate unmodified by combat variables for brigade combat teams would be 1.8% per day, battalions would be 8% per day, and companies 21% per day. For a brigade of 4,500, that would result in 81 battle casualties per day, a battalion of 800 would suffer 64 casualties, and a company of 120 would lose 27 troops. These rates would then be modified by the circumstances of each particular engagement.

Several factors could push daily casualty rates down. Milley envisions that U.S. units engaged in an anti-access/area denial environment will be constantly moving. A low density, highly mobile battlefield with fluid lines would be expected to reduce casualty rates for all sides. High mobility might also limit opportunities for infantry assaults and close quarters combat. The high operational tempo will be exhausting, according to Milley. This could also lower loss rates, as the casualty inflicting capabilities of combat units decline with each successive day in battle.

It is not immediately clear how cyberwarfare and information operations might influence casualty rates. One combat variable they might directly impact would be surprise. Dupuy identified surprise as one of the most potent combat power multipliers. A surprised force suffers a higher casualty rate and surprisers enjoy lower loss rates. Russian combat doctrine emphasizes using cyber and information operations to achieve it and forces with degraded situational awareness are highly susceptible to it. As Zelenopillya demonstrated, surprise attacks with modern weapons can be devastating.

Some factors could push combat loss rates up. Long-range precision weapons could expose greater numbers of troops to enemy fires, which would drive casualties up among combat support and combat service support elements. Casualty rates historically drop during night time hours, although modern night-vision technology and persistent drone reconnaissance might will likely enable continuous night and day battle, which could result in higher losses.

Drawing solid conclusions is difficult but the question of future battlefield attrition is far too important not to be studied with greater urgency. Current policy debates over whether or not the draft should be reinstated and the proper size and distribution of manpower in active and reserve components of the Army hinge on getting this right. The trend away from mass on the battlefield means that there may not be a large margin of error should future combat forces suffer higher combat casualties than expected.

U.S. Tank Losses and Crew Casualties in World War II

Attrition-CoverIn his 1990 book Attrition: Forecasting Battle Casualties and Equipment Losses in Modern War, Trevor Dupuy took a look at the relationship between tank losses and crew casualties in the U.S. 1st  Army between June 1944 and May 1945 (pp. 80-81). The data sampled included 797 medium (averaging 5 crewmen) and 101 light (averaging 4 crewmen) tanks. For each tank loss, an average of one crewman was killed or wounded. Interestingly, although gunfire accounted for the most tank and crew casualties, infantry anti-tank rockets (such as the Panzerfaust) inflicted 13% of the tank losses, but caused 21% of the crew losses.

Attrition, Fig. 50Casualties were evenly distributed among the crew positions.

Attrition, Fig. 51Whether or not a destroyed tank caught fire made a big difference for the crew. Only 40% of the tanks in the sample burned, but casualties were distributed evenly between the tanks that burned and those that did not. This was due to the higher casualty rate in the tanks that caught fire (1.28 crew casualties per tank) and those that did not (0.78 casualties per tank).

Attrition, Fig. 52Dupuy found the relationship between tank losses and casualties to be straightforward and obvious. This relationship would not be so simple when viewed at the battalion level. More on that in a future post [Tank Loss Rates in Combat: Then and Now].