Category Dupuy’s Verities

People keep referencing us on the 3-to-1 Rule

Several people in their articles have referenced a 3-to-1 rule and then reference us as the source. The latest example is in a German article on Taiwan: Storming Taiwan by force of arms? | Telepolis

Of course, we are the people who are saying the 3-to-1 rule is really not correct. They obviously do not read that far.

This is the reference they use: The Source of the U.S. Army Three-to-One Rule – The Dupuy Institute. My final sentence in that article is “Are we training the next generation of George B. McCellans?”


Various links related to the 3-to-1 rule:

Trevor Dupuy and the 3-1 Rule – The Dupuy Institute

The U.S. Army Three-to-One Rule – The Dupuy Institute

The 3-to-1 Rule in Histories – The Dupuy Institute

The 3-to-1 Rule in Recent History Books – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900 – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles – The Dupuy Institute

The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991 – The Dupuy Institute

Summation of Force Ratio Posts – The Dupuy Institute

JSTOR, Trevor Dupuy, Combat Data and the 3:1 Rule – The Dupuy Institute

The 3:1 Ratio – The Dupuy Institute

Army- and Division-level force ratio posts – The Dupuy Institute

The 3-to-1 rule and the War in Ukraine – The Dupuy Institute

We have been talking about this for a while. It appears that some people are not listening.




Average Losses per Day in Division-level Engagements on the Eastern Front in 1943

Trevor N. Dupuy, among his 56 verities of combat, states that “Average World War II division engagement casualty rates were 1-3% a day.”[1]

This was based primarily on his research on the Western Front during World War II. For example, just to draw from data from real world experience, the average losses per U.S. division in 82 selected engagements was 1.2% per day in 1943-44. The average strength of these divisions was 14,000. The average loss per German division in 82 selected engagements was 1.8% per day. The average strength of these divisions was 12,000. These engagements were all from the Italian Campaign and the European Theater of Operations (primarily France).[2]

Now for Germany versus the Soviet Union, the loss rates in 1943 were higher for both sides. We do have daily unit records and have assembled them into a series of 192 division-level engagements for the southern part of Battle of Kursk in July 1943 and 64 division-level engagements for the battles around Kharkov in February, March and August of 1943. They show the following statistics:[3]

Battle of Kursk:

                                                            Average Losses:            Average           Average

                                             Cases     Mean     Median             Strength          Force Ratio

Germans attacking               124         0.99        0.78                21,487               1.44

Germans defending                68         0.68        0.52               16,945                0.91

Soviets attacking                    68         3.25        1.67               18,631                1.10

Soviets defending                 124         4.31        3.82               14,930                0.69


Battles for Kharkov:

Germans attacking                 35         0.58        0.48                17,326                2.77

Germans defending                29         0.64        0.50                14,834                0.87

Soviets attacking                    29         2.18        1.56                 17,001               1.15

Soviets defending                   35         5.21        3.05                  6,837                0.36


Slightly different figures will be created using differing selection criteria, but out of the 124 cases of the Germans attacking at Kursk, in only two cases were German losses greater than 3% [4]. They were both cross-river attacks done on 5 July 1943 by the 106th and 320th Infantry Divisions. German losses at Kursk while defending never exceeded 3%. German losses in the Kharkov engagements never exceeded 2% a day.

Soviet losses exceeded 3% per day in 24 cases while attacking at Kursk and exceeded 6% in ten of those cases. Soviet losses exceeded 3% per day in 67 cases while defending at Kursk (in over half the cases) and exceeded 6% in 39 of those cases. Soviet losses exceeded 3% a day in only two cases while attacking at Kharkov and in 16 cases while defending, of which in seven of those cases Soviet losses exceeded 6% per day.



[1] See Colonel Trevor N. Dupuy, Understanding War: History and Theory of Combat (Paragon House Publishers, New York, 1987), page 179.

[2] See Dupuy, Understanding War, page 169. Note that all these WWII engagements were tagged with the note that the data was approximate, more research required. The Dupuy Institute has 282 division-level engagements from the Italian Campaign and ETO that are created from the unit records of both sides. We have not done this comparison using our further developed and more extensive data collection, but suspect the results would be similar.

[3] The data used for this calculation is presented for the Battle of Kursk in a series of 192 engagement sheets in the book by Lawrence, Kursk: The Battle of Prokhorova. This work can be cross-checked by others. The data used for the battles around Kharkov have not been published yet. It might be at some point in the future. The data is currently company proprietary of The Dupuy Institute.

[4] More precise would be to remove all the engagements coded as limited action and limited attack, leaving only those coded as failed attack, attack advances, defender penetrated, defender enveloped and other. In the 124 Kursk cases of the German attacking this would remove 15 cases of limited action, 14 cases of limited attack, and 26 cases where the outcome has not been coded yet. The force ratio is now up to 1.56-to-1 and the average German percent losses are 1.25% while the average Soviet percent losses are 5.83%. Conversely, in the 68 cases where the Soviet are attacking, there are 7 cases are limited action, 9 cases are limited attack and 33 cases where the outcome has not been coded yet. The force ratio for these remaining 19 cases is 1.27 and average Soviet percent losses are 4.05 while the average German percent losses are 0.86.

 In all cases, the mean is calculated as a weighted mean, meaning that it is based upon total strengths compared to total losses. The median is calculated, naturally, by finding the midpoint of all 124 or 68 engagements.


The actual paper this was drawn from is here: Average Losses per Day

Response to Question on Dupuy’s Combat Attrition Verities

Someone just sent an email asking about a particular single line on slide 44 of my Data for Wargames briefing I gave at HAAC: “Self-propelled artillery loss rates are about three times greater than for towed guns”. The briefing is here: Data for Wargames (Summary) – 2

I noted that this from Trevor Dupuy combat attrition verities. He specifically states on page 179 of Understanding War that:

“Self-propelled artillery loss rates are about three times greater than for towed guns. This is due to a combination of factors. larger exposed target; presence of fuel and ammunition in the self-propelled guns carriages; and vulnerability of engines to damage even when the weapon is still able to fire effectively. They are also more likely to be committed under more immediately lethal combat circumstances than are towed artillery pieces. It should be noted, however, that crew loss rates are slightly lower for self-propelled guns than for towed guns.”

This is clearly taken from one of his earlier studies in the 1970s or 19780s. See: TDI – The Dupuy Institute Publications or TDI – The Dupuy Institute Publications or TDI – The Dupuy Institute Publications. Off the top of my head, I do not recall which study it was from.

Trevor Dupuy also made the comment in private conversation that one other advantage to towed artillery is that after you deployed the piece, you then had a truck available to go get more ammunition.

Dupuy’s Verities: The Complexities of Combat

“The Battle of Leipzig, 16-19 October 1813” by A.I. Zauerweid (1783-1844) [Wikimedia]
The thirteenth and last of Trevor Dupuy’s Timeless Verities of Combat is:

Combat is too complex to be described in a single, simple aphorism.

From Understanding War (1987):

This is amply demonstrated by the preceding [verities]. All writers on military affairs (including this one) need periodically to remind themselves of this. In military analysis it is often necessary to focus on some particular aspect of combat. However, the results of such closely focused analyses must the be evaluated in the context of the brutal, multifarious, overlapping realities of war.

Trevor Dupuy was sometimes accused of attempting to reduce war to a mathematical equation. A casual reading of his writings might give that impression, but anyone who honestly engages with his ideas quickly finds this to be an erroneous conclusion. Yet, Dupuy believed the temptation to simplify and abstract combat and warfare to be common enough that he he embedded a warning against doing so into his basic theory on the subject. He firmly believed that human behavior comprises the most important aspect of combat, yet it is all too easy to miss the human experience of war figuring who lost or won and why, and counts of weapons, people, and casualties. As a military historian, he was keenly aware that the human stories behind the numbers—however imperfectly recorded and told—tell us more about the reality of war than mere numbers on their own ever will.

Dupuy’s Verities: Combat Power =/= Firepower

A U.S. 11th Marines 75mm pack howitzer and crew on Guadalcanal, September or October, 1942. The lean condition of the crewmembers indicate that they haven’t been getting enough nutrition during this period. [Wikipedia]

The ninth of Trevor Dupuy’s Timeless Verities of Combat is:

Superior Combat Power Always Wins.

From Understanding War (1987):

Military history demonstrates that whenever an outnumbered force was successful, its combat power was greater than that of the loser. All other things being equal, God has always been on the side of the heaviest battalions and always will be.

In recent years two or three surveys of modern historical experience have led to the finding that relative strength is not a conclusive factor in battle outcome. As we have seen, a superficial analysis of historical combat could support this conclusion. There are a number of examples of battles won by the side with inferior numbers. In many battles, outnumbered attackers were successful.

These examples are not meaningful, however, until the comparison includes the circumstances of the battles and opposing forces. If one take into consideration surprise (when present), relative combat effectiveness of the opponents, terrain features, and the advantage of defensive posture, the result may be different. When all of the circumstances are quantified and applied to the numbers of troops and weapons, the side with the greater combat power on the battlefield is always seen to prevail.

The concept of combat power is foundational to Dupuy’s theory of combat. He did not originate it; the notion that battle encompasses something more than just “physics-based” aspects likely originated with British theorist J.F.C. Fuller during World War I and migrated into U.S. Army thinking via post-war doctrinal revision. Dupuy refined and sharpened the Army’s vague conceptualization of it in the first iterations of his Quantified Judgement Model (QJM) developed in the 1970s.

Dupuy initially defined his idea of combat power in formal terms, as an equation in the QJM:

P = (S x V x CEV)


P = Combat Power
S = Force Strength
V = Environmental and Operational Variable Factors
CEV = Combat Effectiveness Value

Essentially, combat power is the product of:

  • force strength as measured in his models through the Theoretical/Operational Lethality Index (TLI/OLI), a firepower scoring method for comparing the lethality of weapons relative to each other;
  • the intangible environmental and operational variables that affect each circumstance of combat; and
  • the intangible human behavioral (or moral) factors that determine the fighting quality of a combat force.

Dupuy’s theory of combat power and its functional realization in his models have two virtues. First, unlike most existing combat models, it incorporates the effects of those intangible factors unique to each engagement or battle that influence combat outcomes, but are not readily measured in physical terms. As Dupuy argued, combat consists of more than duels between weapons systems. A list of those factors can be found below.

Second, the analytical research in real-world combat data done by him and his colleagues allowed him to begin establishing the specific nature combat processes and their interaction that are only abstracted in other combat theories and models. Those factors and processes for which he had developed a quantification hypothesis are denoted by an asterisk below.

Dupuy’s Verities: The Inefficiency of Combat

The “Mud March” of the Union Army of the Potomac, January 1863.

The twelfth of Trevor Dupuy’s Timeless Verities of Combat is:

Combat activities are always slower, less productive, and less efficient than anticipated.

From Understanding War (1987):

This is the phenomenon that Clausewitz called “friction in war.” Friction is largely due to the disruptive, suppressive, and dispersal effects of firepower upon an aggregation of people. This pace of actual combat operations will be much slower than the progress of field tests and training exercises, even highly realistic ones. Tests and exercises are not truly realistic portrayals of combat, because they lack the element of fear in a lethal environment, present only in real combat. Allowances must be made in planning and execution for the effects of friction, including mistakes, breakdowns, and confusion.

While Clausewitz asserted that the effects of friction on the battlefield could not be measured because they were largely due to chance, Dupuy believed that its influence could, in fact, be gauged and quantified. He identified at least two distinct combat phenomena he thought reflected measurable effects of friction: the differences in casualty rates between large and small sized forces, and diminishing returns from adding extra combat power beyond a certain point in battle. He also believed much more research would be necessary to fully understand and account for this.

Dupuy was skeptical of the accuracy of combat models that failed to account for this interaction between operational and human factors on the battlefield. He was particularly doubtful about approaches that started by calculating the outcomes of combat between individual small-sized units or weapons platforms based on the Lanchester equations or “physics-based” estimates, then used these as inputs for brigade and division-level-battles, the results of which in turn were used as the basis for determining the consequences of theater-level campaigns. He thought that such models, known as “bottom up,” hierarchical, or aggregated concepts (and the prevailing approach to campaign combat modeling in the U.S.), would be incapable of accurately capturing and simulating the effects of friction.

Dupuy’s Verities: The Effects of Firepower in Combat

A German artillery barrage falling on Allied trenches, probably during the Second Battle of Ypres in 1915, during the First World War. [Wikimedia]

The eleventh of Trevor Dupuy’s Timeless Verities of Combat is:

Firepower kills, disrupts, suppresses, and causes dispersion.

From Understanding War (1987):

It is doubtful if any of the people who are today writing on the effect of technology on warfare would consciously disagree with this statement. Yet, many of them tend to ignore the impact of firepower on dispersion, and as a consequence they have come to believe that the more lethal the firepower, the more deaths, disruption, and suppression it will cause. In fact, as weapons have become more lethal intrinsically, their casualty-causing capability has either declined or remained about the same because of greater dispersion of targets. Personnel and tank loss rates of the 1973 Arab-Israeli War, for example, were quite similar to those of intensive battles of World War II and the casualty rates in both of these wars were less than in World War I. (p. 7)

Research and analysis of real-world historical combat data by Dupuy and TDI has identified at least four distinct combat effects of firepower: infliction of casualties (lethality), disruption, suppression, and dispersion. All of them were found to be heavily influenced—if not determined—by moral (human) factors.

Again, I have written extensively on this blog about Dupuy’s theory about the historical relationship between weapon lethality, dispersion on the battlefield, and historical decline in average daily combat casualty rates. TDI President Chris Lawrence has done further work on the subject as well.

TDI Friday Read: Lethality, Dispersion, And Mass On Future Battlefields

Human Factors In Warfare: Dispersion

Human Factors In Warfare: Suppression

There appears to be a fundamental difference in interpretation of the combat effects of firepower between Dupuy’s emphasis on the primacy of human factors and Defense Department models that account only for the “physics-based” casualty-inflicting capabilities of weapons systems. While U.S. Army combat doctrine accounts for the interaction of firepower and human behavior on the battlefield, it has no clear method for assessing or even fully identifying the effects of such factors on combat outcomes.

Dupuy’s Verities: Surprise

The Death of Paulus Aemilius at the Battle of Cannae by John Trumbell (1773). [Wikimedia]

The tenth of Trevor Dupuy’s Timeless Verities of Combat is:

Surprise substantially enhances combat power.

From Understanding War (1987):

Achieving surprise in combat has always been important. It is perhaps more important today than ever. Quantitative analysis of historical combat shows that surprise has increased the combat power of military forces in those engagements in which it was achieved. Surprise has proven to be the greatest of all combat multipliers. It may be the most important of the Principles of War; it is at least as important as Mass and Maneuver.

I have already written quite a bit on Dupuy’s conceptualization of surprise so I won’t go into it in detail here. These previous posts provide a summary:

The Combat Value of Surprise

Human Factors In Warfare: Surprise

Dupuy’s analysis focused on how surprise influenced combat power by enhancing the mobility and reducing the vulnerability of the side with surprise, and by increasing the vulnerability of the side that was surprised. In 2004, TDI undertook a study for the late Andy Marshall’s Office of the Secretary of Defense/Net Assessment to measure the historical combat value of situational awareness (more knowledge by one side than the other) and informational advantage (better knowledge by one side than the other) and how each of these factors related to surprise in combat. Chris Lawrence detailed this research and its conclusions in chapters 10 and 11 in his 2017 book, War by Numbers: Understanding Conventional Combat.

In general, the study found that both superior situational awareness and better information enhanced combat power, though perhaps not quite as much as inferred from the relevant literature. It also confirmed that surprise conferred an even greater combat power benefit, above and beyond that provided by battlefield awareness or informational advantages. It also suggested that the primary benefit of a situational or knowledge advantage in combat was not in achieving surprise over an enemy, but in preventing an opponent from achieving surprise itself.

These results, though quite suggestive, were tentative and more research is necessary. However, no follow on studies on this subject have been funded to date.

A Comment On The Importance Of Reserves In Combat

An German Army A7V near the Somme on March 26, 1918 [] Operation Michael was the first of a series of German Army offensives on the Western Front in the spring of 1918. In late March, 74 German divisions employing infiltration tactics created a breach in a sector of the line held by the British Army. The Germans advanced up to 40 miles and captured over 75,000 British soldiers, but the ability of the British and French to redeploy reserves via rail halted the offensive in early April short of strategic success.

In response to my previous post on Trevor Dupuy’s verity regarding the importance of depth and reserves for successful defense, a commenter posed the following question: “Is the importance of reserves mainly in its own right, or to mitigate the advantages of attacker surprise?”

The importance of reserves to both attacker and defender is as a hedge against the circumstantial uncertainties of combat. Reserves allow attacking and defending commanders the chance to maintain or regain initiative in response to the outcomes of battle. The side that commits its last reserves before its opponent does concedes the initiative to the enemy, probably irrevocably.

In Trevor Dupuy’s theory of combat, the intrinsic superiority of the defensive posture (as per Clausewitz) is the corollary to the attacker’s inherent advantage in initiative. When combined with the combat multipliers of favorable terrain and prepared positions or fortifications, the combat power of a defending force is greatly enhanced. This permits a defending commander to reap the benefit of economy of force to create reserves. When arrayed in sufficient depth to prevent an attacker from engaging them, reserves grant flexibility of response to the defender. A linear defense or improperly placed reserves concede this benefit to the attacker at the outset, permitting the attacking commander to exploit initiative to mass superior combat power at a decisive point without reserves to interfere.

A defender’s reserves are certainly useful in mitigating attacker surprise, but in Dupuy’s theories and models, surprise is a combat multiplier available to both attacker and defender. As perhaps the most powerful combat multiplier available on the battlefield, surprise in the form of a well-timed counterattack by a defender can devastate an attacking force. Even an unexpected tactical wrinkle by a defender can yield effective surprise.

Dupuy’s Verities: The Requirements For Successful Defense

A Sherman tank of the U.S. Army 9th Armored Division heads into action against the advancing Germans during the Battle of the Bulge. {Warfare History Network]

The eighth of Trevor Dupuy’s Timeless Verities of Combat is:

Successful defense requires depth and reserves.

From Understanding War (1987):

Successful defense requires depth and reserves. It has been asserted that outnumbered military forces cannot afford to withhold valuable firepower from ongoing defensive operations and keep it idle in reserve posture. History demonstrates that this is specious logic, and that linear defense is disastrously vulnerable. Napoleon’s crossing of the Po in his first campaign in 1796 is perhaps the classic demonstration of the fallacy of linear (or cordon) defense.

The defender may have all of his firepower committed to the anticipated operational area, but the attacker’s advantage in having the initiative can always render much of that defensive firepower useless. Anyone who suggests that modern technology will facilitate the shifting of engaged firepower in battle overlooks three considerations: (a) the attacker can inhibit or prevent such movement by both direct and indirect means, (b) a defender engaged in a fruitless firefight against limited attacks by numerically inferior attackers is neither physically nor psychologically attuned to making lateral movements even if the enemy does not prevent or inhibit it, and (c) withdrawal of forces from the line (even if possible) provides an alert attacker with an opportunity for shifting the thrust of his offensive to the newly created gap in the defenses.

Napoleon recognized that hard-fought combat is usually won by the side committing the last reserves. Marengo, Borodino, and Ligny are typical examples of Napoleonic victories that demonstrated the importance of having resources available to tip the scales. His two greatest defeats, Leipzig and Waterloo, were suffered because his enemies still had reserves after his were all committed. The importance of committing the last reserves was demonstrated with particular poignancy at Antietam in the American Civil War. In World War II there is no better example than that of Kursk. [pp. 5-6]

Dupuy’s observations about the need for depth and reserves for a successful defense take on even greater current salience in light of the probably character of the near-future battlefield. Terrain lost by an unsuccessful defense may be extremely difficult to regain under prevailing circumstances.

The interaction of increasing weapon lethality and the operational and human circumstantial variables of combat continue to drive the long-term trend in dispersion of combat forces in frontage and depth.

Long-range precision firepower, ubiquitous battlefield reconnaissance and surveillance, and the effectiveness of cyber and information operations will make massing of forces and operational maneuver risky affairs.

As during the Cold War, the stability of alliances may depend on a willingness to defend forward in the teeth of effective anti-access/area denial (A2/AD) regimes that will make the strategic and operational deployment of reserves risky as well. The successful suppression of A2/AD networks might court a nuclear response, however.

Finding an effective solution for enabling a successful defense-in-depth in the future will be a task of great difficulty.