War By Numbers Published

Christopher A. Lawrence, War by Numbers Understanding Conventional Combat (Lincoln, NE: Potomac Books, 2017) 390 pages, $39.95

War by Numbers assesses the nature of conventional warfare through the analysis of historical combat. Christopher A. Lawrence (President and Executive Director of The Dupuy Institute) establishes what we know about conventional combat and why we know it. By demonstrating the impact a variety of factors have on combat he moves such analysis beyond the work of Carl von Clausewitz and into modern data and interpretation.

Using vast data sets, Lawrence examines force ratios, the human factor in case studies from World War II and beyond, the combat value of superior situational awareness, and the effects of dispersion, among other elements. Lawrence challenges existing interpretations of conventional warfare and shows how such combat should be conducted in the future, simultaneously broadening our understanding of what it means to fight wars by the numbers.

The book is available in paperback directly from Potomac Books and in paperback and Kindle from Amazon.

Table of Contents: War by Numbers

Preface                                                                                                   ix

Acknowledgments                                                                                  xi

Abbreviations                                                                                         xiii

  1. Understanding War                                                                        1

  2. Force Ratios                                                                                   8
  3. Attacker versus Defender                                                             14
  4. Human Factors                                                                             16
  5. Measuring Human Factors in Combat: Italy 1943-1944               19
  6. Measuring Human Factors in Combat: Ardennes and Kursk       32
  7. Measuring Human Factors in Combat: Modern Wars                  49
  8. Outcome of Battles                                                                       60
  9. Exchange Ratios                                                                          72
  10. The Combat Value of Superior Situational Awareness                79
  11. The Combat Value of Surprise                                                   121
  12. The Nature of Lower Levels of Combat                                      146
  13. The Effects of Dispersion on Combat                                         163
  14. Advance Rates                                                                            174
  15. Casualties                                                                                    181
  16. Urban Legends                                                                            206
  17. The Use of Case Studies                                                             265
  18. Modeling Warfare                                                                        285
  19. Validation of the TNDM                                                               299
  20. Conclusions                                                                                 325

Appendix I: Dupuy’s Timeless Verities of Combat                                329

Appendix II: Dupuy’s Combat Advance Rate Verities                           335

Appendix III: Dupuy’s Combat Attrition Verities                                    339

Notes                                                                                                     345

Bibliography                                                                                           369


The book is 374 pages plus 14 pages of front matter.


15 Books Received !!!

I just received my 15 author copies of War by Numbers. So it is now available for $39.95 from Potomac Books (University of Nebraska Press): War by Numbers

This means it should be available from Amazon.com next week: War by Numbers

I don’t how quickly the foreign book sellers will receive them, but expect them to have  copies available in the next couple of weeks.

I did not order 200 copies for The Dupuy Institute to sell, unlike I did with America’s Modern Wars, so it will not be directly available from us: http://www.dupuyinstitute.org/booksfs.htm

This figure is on page 175 of the book, Chapter 14: Advance Rates:



Economics of Warfare 19 – 3

Continuing with the next posting on the nineteenth lecture from Professor Michael Spagat’s Economics of Warfare course that he gives at Royal Holloway University. It is posted on his blog Wars, Numbers and Human Losses at: https://mikespagat.wordpress.com/

This lecture continues the discussion of terrorism, this time he is looking at a paper by Gassebner and Luechinger on terrorism (starts on page 13 of the lecture). This is similar to what was done for causes of war in a paper by Hegre and Sambanis that was presented in lecture 11:

Economics of Warfare 19 – 2 and 11 – 2

So, the two authors ended up running a large number of regressions trying out many different combinations of variables and looking for those that are consistently significant. They used three different terrorism databases, resulting in them testing 18 different variables to each of the three different databases and looking at locations, victims and perpetrators (see slides 14 and 15). This gets a little involved and you are probably not going to sort it all out unless you read their paper (which costs $40 to order a copy…I did not).

What is particularly interesting to me is that the same variable has different values depending on what database is used. The values are of Coef. (median coefficient estimate), CDF (cumulative distribution function) and % sig. (the percent the estimate was statistically signicant). For example “Ethnic tensions” has values of -0.0007, 0.544 and 18.4 in the Iterate database, has values of 0.040, 0.911 and 63.1 in the GTD databases, and has values of 0.011, 0.627 and 15.2 in the MIPT database. Not sure what this really means (see slide 14). I have never done any analysis using someone else’s data base. I have always collected by own data and analyzed it.

Anyhow, the results are (see slides 18 & 19).

  1. Strong police states with religious tensions seem to be favored targets of terrorists.
  2. Bigger, economically repressive and richer countries seem to attract terrorist attacks.
  3. “Law and order” seems to discourage terrorism (this does conflict with point 1 above).
  4. A more foreign portfolio investment seen positively associated with terrorism.
  5. Higher natural resource exports as associated with fewer attacks on a county’s citizens.
  6. Citizens from countries with a “youth bulge” are attacked relatively less and do not attack more often.
  7. Fewer telephones are associated with more attacks.
  8. Countries with centrist governments seem to export terrorists

Anyhow, not finished with this lecture yet. Will have one more posting to do. The link to his lecture is here: http://personal.rhul.ac.uk/uhte/014/Economics%20of%20Warfare/Lecture%2019.pdf

Human Factors In Warfare: Fatigue

Tom Lea, “The 2,000 Yard Stare” 1944 [Oil on canvas, 36 x 28 Life Collection of Art WWII, U.S. Army Center of Military History, Fort Belvoir, Virginia]

That idea that fatigue is a human factor in combat seems relatively uncontroversial. Military history is replete with examples of how the limits of human physical and mental endurance have affected the character of fighting and the outcome of battles. Perhaps the most salient aspect of military training is preparing soldiers to deal with the rigors of warfare.

Trevor Dupuy was aware that fatigue has a degrading effect on the effectiveness of troops in combat, but he never was able to study the topic specifically himself. He was aware of other examinations of historical experience that were relevant to the issue.

The effectiveness of a military force declines steadily every day that it is engaged in sustained combat. This is an indication that fear has a physical effect on human beings equitable with severe exertion. S.L.A. Marshall documented this extremely well in a report that he wrote a few years before he died. I shall shortly have more to say about S.L.A. Marshall…

An approximate value for the daily effect of fatigue upon the effectiveness of weapons employment emerged from a HERO study several years ago. There is no question that fatigue has a comparable degrading effect upon the ability of a force to advance. I know of no research to ascertain that effect. Until such research is performed, I have arbitrarily assumed that the degrading effect of fatigue upon advance rates is the same as its degrading effect upon weapons effectiveness. To those who might be shocked at such an assumption, my response is: We know there is an effect; it is better to use a crude approximation of that effect than to ignore it…

During World War II when Colonel S.L.A. Marshall was the Chief Historian of the US European Theater of Operations, he undertook a number of interviews of units just after they had been in combat. After the war, in his book Men Against Fire, Marshall asserted that his interviews revealed that only 15% of US infantry soldiers fired their small arms weapons in combat. This revelation created something of a sensation at the time.

It has since been demonstrated that Marshall did not really have solid, scientific data for his assertion. But those who criticize Marshall for unscholarly, unscientific work should realize that in private life he was an exceptionally good newspaper reporter. His conclusions, based upon his observations, may have been largely intuitive, but I am convinced that they were generally, if not specifically, sound…

One of the few examples of the use of military history in the West in recent years was an important study done at the British Defence Operational Analysis Establishment (DOAE) by David Rowland. An unclassified condensation of that study was published in the June 1986 issue of the Journal of the Royal United Services Institution (RUSI). The article, “Assessments of Combat Degradation,” demonstrates conclusively that, in historical combat, small arms weapons have had only one-seventh to one-tenth of their theoretical effectiveness. Rowland does not attempt to say why this is so, but it is interesting that his value of one-seventh is very close to the S. L. A. Marshall 15% figure. Both values translate into casualty effects very similar to those that have emerged from my own research.

The intent of this post is not to rehash the debate on Marshall. As Dupuy noted above, even if Marshall’s conclusions were not based on empirical evidence, his observations on combat were nevertheless on to something important. (Details on the Marshall debate can be easily found with a Google search. A brief discussion took place on the old TDI Forum in 2007.)

David Rowland also presented a paper on the same topic Dupuy referenced above at the Military Operations Research Society (MORS) MORIMOC II conference in 1989, “Assessment of Combat Performance With Small Arms” He later published a book detailing his research on the subject in 2006, The Stress of Battle: Quantifying Human Performance in Combat, which is very much worth tracking down and reading.

Dupuy provided a basic version of his theoretical combat exhaustion methodology on pages 223-224 in Numbers, Predictions and War: Using History to Evaluate Combat Factors and Predict the Outcome of Battles (Indianapolis; New York: The Bobbs-Merrill Co., 1979).

Rules For Exhaustion Rates, 20th Century*

  1. The exhaustion factor (ex) of a fresh unit is 1.0; this is the maximum ex value.
  2. At the conclusion of an engagement, a new ex factor will be calculated for each side.
  3. A unit in normal offensive or defensive combat has its ex factor reduced by .05 for each consecutive day of combat; the ex factor cannot be less than 0.5.
  4. An attacking unit opposed by delaying tactics has its ex factor reduced by 0.05 per day.
  5. A defending unit in delay posture neither loses nor gains in its ex factor.
  6. A withdrawing unit, not seriously engaged, has its ex factor augmented at the rate of 0.05 per day.
  7. An advancing unit in pursuit, and not seriously delayed, neither loses nor gains in its ex factor.
  8. For a unit in reserve, or in non-active posture, an exhaustion factor of less than 1.0 is augmented at the rate of .1 per day.
  9. When a unit in combat, or recently in combat, is reinforced by a unit at least half of its size (in numbers of men), it adopts the ex factor of the reinforcing unit or—if the ex factor of the reinforcing unit is the same or lower than that of the reinforced—both adopt an ex factor 0.1 higher than that of the reinforced unit at the time of reinforcement, save that an ex factor cannot be greater than 1.0.
  10. When a unit in combat, or recently in combat, is reinforced by a unit less than half its size, but not less than one quarter its size, augmentations or modifications of ex factors will be 0.5 times those provided for in paragraph 9, above. When the reinforcing unit is less than one-quarter the size of the reinforced unit, but not less than one-tenth its size, augmentations or modifications of ex factors will be 0.25 times those provided for in paragraph 9, above.

* Approximate reflection of preliminary QJM assessment of effects of casualty and fatigue, WWII engagements. These rates are for division or smaller size; for corps and larger units exhaustion rates are calculated for component divisions and smaller separate units.


  1. A division in continuous offensive combat for five days stays in the line in inactive posture for two days, then resumes the offensive:
    1. Combat exhaustion effect: 1 – (5 x .05) = 0.75;
    2. Recuperation effect: 75 + (2 x .l) = 0.95.
  2. A division in defensive posture for fifteen days is ordered to undertake a counterattack:
    1. Combat exhaustion effect: 1 – (15 x .05) =0.25; this is below the minimum ex factor, which therefore applies: 0.5;
    2. Recuperation effect: None; ex factor is 0.5.
  3. A division in offensive posture for three days is reinforced by two fresh brigades:
    1. Combat exhaustion effect: 1 – (3 x .05) = 0.85;
    2. Reinforcement effect: Augmentation from 0.85 to 1.0.
  4. A division in offensive posture for three days is reinforced by one fresh brigade:
    1. Combat exhaustion effect: 1 – (3 x .05) = 0.85;
    2. Reinforcement effect: 0.5 x augmentation from 0.85 to 1 = 0.93.

Economics of Warfare 19 – 2 and 11 – 2

Continuing with a second posting on the nineteenth and second to last lecture from Professor Michael Spagat’s Economics of Warfare course that he gives at Royal Holloway University. It is posted on his blog Wars, Numbers and Human Losses at: https://mikespagat.wordpress.com/

This lecture continues the discussion of terrorism, this time he is looking at a paper by Gassebner and Luechinger on terrorism. This is similar to what was done for causes of war in a paper by Hegre and Sambanis that was presented in lecture 11:

Economics of Warfare 11

This discussion of Hegre and Sambanis covered only the last two pages of the lecture (slides 23 and 24 of lecture 11) and I did not mention it when I first blogged about it.. I guess I probably need to now, turning this posting into the follow-up post on lecture 11. Hegre and Sambanis looked at 88 variables related to causes of war and by running regressions tried to determine which ones are consistently correlated with the onset of war.

  1. GDP per capita is negatively associate with civil war onset (meaning: rich countries are less likely to have civil wars).
  2. Having had a previous war is positively associated with civil war onset…the more recent the war the stronger the association (meaning: war beget wars?).
  3. Country size (population and territory) is positively associated with civil war onset (meaning: big countries tend to have more wars.).

This last point is interesting as country size and population also showed up in our insurgency studies related to the success of the insurgents. Big populated counties tended to have more successful insurgencies than small countries. In Chapter 3, page 47 of America’s Modern Wars I provided the following chart:

Insurgencies with Foreign Intervention

Circumstances                                                   Number of cases        Percent Blue Victory

Indigenous Population > 9 million                              10                                20

Intervening Force Commitment > 100,000                  8                                  0

Peak Insurgent Force Size > 30,000                         13                                23

“Blue Victory” = counterinsurgent victory

Anyhow, I have not gotten past the first sentence of slide 13 for this post, and we are already around 300 words in this post, so probably best to pick up the rest of lecture 19 in a subsequent post.

The link to lecture 19 is here: http://personal.rhul.ac.uk/uhte/014/Economics%20of%20Warfare/Lecture%2019.pdf

The link to lecture 11 is here: http://www.dupuyinstitute.org/blog/2017/01/31/economics-of-warfare-11/

Human Factors In Warfare: Combat Intensity [UPDATED]

I updated this post with tables! Click through to the original post and scroll to the bottom.

Human Factors In Warfare: Combat Intensity

Defeating an Insurgency by Air II

One of my earliest blog posts, done in December 2015 was on “Defeating an Insurgency by Air.” It was in part inspired by the Republican debate at the time and people talking about “carpet bombing” ISIL.

The post is here: http://www.dupuyinstitute.org/blog/2015/12/29/defeating-an-insurgency-by-air/

The same article is was posted on the History News Network: http://historynewsnetwork.org/article/161601

An expanded article was posted on the Small War Journal: http://smallwarsjournal.com/jrnl/art/airpower-just-part-of-the-counterinsurgency-equation

I gather the part of the article that gives people heartburn is: “So, we are left to state that we cannot think of a single insurgency that was defeated by airpower, primarily defeated by airpower, or even seriously undermined by airpower. Perhaps there is a case we are missing. It is probably safe to say that if it has never successfully been done in over a hundred insurgencies over the last hundred years, then it is something not likely to occur now.”

Now, we do go on a hunt for other cases. This led to the follow-up blog posts:

Is Your Washroom Breeding Bolsheviks?

Air Power Defeating an Insurgency

Chasing the Mad Mullah

Iraq Revolt of 1920

Bleeding an Insurgency to Death


Bombing Kosovo in 1999 versus the Islamic State in 2015

Of course, we are not the only people talking about this

Bleeding an Insurgency to Death

This last post was actually not tagged as an “air power” subject, but I felt it was particularly relevant….and yes, we do have two blog posts with the same title. But this second one has this cool graph:


$5,000 Book

Just browsing Amazon.com and notice that one of the re-sellers has my Kursk book up for sale for $5,008.00: https://www.amazon.com/gp/offer-listing/0971385254/ref=dp_olp_all_mbc?ie=UTF8&condition=all

Really? Has he sold any at that price? I would be willing to part with a couple of my author’s copies at that price.

Anyhow, the book is still available from Aberdeen Books at a much more modest $195: http://www.aberdeenbookstore.com/



See A Russian Su-35 Defy The Laws Of Physics

If you want to watch a breath-taking aerial maneuver by a Russian Sukhoi Su-35 Flanker-E fighter at the 2017 International Aviation and Space Show outside Moscow, click on the link below.