Category War by Numbers

The World War II Cases from the Division-level Database

There are 576 cases from World War II in our division-level database. There are no engagements from 1939, only two from 1940, seven from 1941, one from 1942 and the rest are from 1943-45.

World War II (576 cases) – complete data set

Force Ratio…………………….Percent Attacker Wins……………….Number of Cases

0.25 to 0.49………………………22%………………………………………………..9

0.50 to 0.98………………………30…………………………………………………50

1.00 to 1.49………………………55……………………………………………….128

1.50 to 1.96………………………61……………………………………………….117

2.01 to 2.49………………………73…………………………………………………48

2.52 to 2.99………………………82…………………………………………………44

3.00 to 3.49………………………76…………………………………………………41

3.50 to 3.98………………………85…………………………………………………26

4.06 to 5.86………………………68…………………………………………………59

6.17 to 7.90………………………87…………………………………………………15

8.20 to 17.87……………………100…………………………………………………20

 

This clearly makes our point in spades about the U.S. Army three-to-one rule. Above one-to-one odds the attacker wins over half the time and above two-to-one odds the attacker wins over 70% of the time. This is the un-culled data set. The culled data set with 102 cases removed that are “limited action,” limited attack” or “other” consists of only 474 cases. It shows the following:

World War II (474 cases) – culled data set

Force Ratio…………………Percent Attacker Wins…………………Number of Cases

0.25 to 0.49……………………..25%………………………………………………..8

0.50 to 0.98……………………..43………………………………………………….35

1.00 to 1.49……………………..63………………………………………………..111

1.50 to 1.96……………………..68………………………………………………..102

2.01 to 2.49……………………..83………………………………………………….41

2.52 to 2.99……………………..82………………………………………………….39

3.00 to 3.49……………………..79………………………………………………….33

3.50 to 3.98……………………..84………………………………………………….25

4.06 to 5.86……………………..77………………………………………………….48

6.17 to 7.90……………………..87………………………………………………….15

8.20 to 17.87…………………..100………………………………………………….15

22.84-198.69…………………..100…………………………………………………..2

 

Again, no surprises in this data, and of course, it parallels the patterns seen in the previous data sets.

The World War I Cases from the Division-level Database

There are several major periods of covered by this 752 cases division-level database, so let us separate them out. The periods covered are:

Era ………………………………………………Number of Cases

Russo-Japanese War (1904-1905)……………….3

The Balkan Wars (1912)……………………………1

World War I (1914-1918)…………………………25

Between the wars (1938)………………………….1

World War II (1939-1945)………………………576

Arab-Israeli Wars (1956 – 1973)………………..51

Gulf War (1991)………………,………………….15

 

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

Now, both World War I and World War II are so massive that with a diligent research effort, thousands of engagements could be assembled. This does take time. Our post-World War II includes almost every significant division-level engagement from the Arab-Israeli fighting of 1956, 1967, 1968 and 1973. The Gulf War category includes every significant division-level engagement from 1991. Let us look at each of them in turn:

World War I and others (30 cases)

 

Force Ratio……………………Percent Attacker Wins……………..Number of Cases

0.67 to 0.99-to-1………………..29%…………………………………………..7

1.01 to 1.47-to-1………………..11……………………………………………..9

1.58 to 1.80-to-1………………….0……………………………………………..2

2.00 to 2.13-to-1………………..67……………………………………………..3

2.50 to 2.80-to-1………………..67……………………………………………..3

3.00 to 3.20-to-1………………..33……………………………………………..3

4.04 to 4.38-to-1………………..50……………………………………………..2

6.32-to-1………………………..100……………………………………………..1

 

Note that the attacker is winning to majority of the time at two-to-one odds and higher. The 33% wins in the three-to-one category consists of one victory and two drawn engagements (Bazentin Ridge from the Somme and First Dardanelles Landing from Gallipoli). In both of these cases the attacker advanced, although the engagement is coded as a draw. These three cases do not make a strong argument. This data collection is too small to draw any real conclusions from. The database could certainly be expanded to thousands of cases given time and effort. We also have a collection of engagements from World War I at brigade- and battalion-level and a number of engagements above division-level. These will be explored later.

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

Our most developed database through is our division-level database of 752 cases covering combat from 1904 to 1991. As this addresses modern combat, it is a useful database for such a test. Of those 752 cases, we have the forces ratios and outcome for 672 of them. All the engagements previously discussed from ETO in 1944 and Kharkov and Kursk in 1943 are drawn from this database. As such, there is some overlap between these 672 cases and the 116 cases from ETO and 73 cases from the Eastern Front previously used. The data shows a very clear pattern related to force ratios.

Division-level Engagements 1904-1991 (672 cases)

Force Ratio…………………..Percent Attacker Wins………………Number of Cases

0.20 to 0.20-to-1………………..0%………………………………………………….2

0.25 to 04.9-to-1………………22…………………………………………………….9

0.50 to 0.99-to-1………………42…………………………………………………..77

1.00 to 1.49-to-1………………55…………………………………………………150

1.50 to 1.99-to-1………………59…………………………………………………123

2.00 to 2.49-to-1………………71…………………………………………………..56

2.50 to 2.99-to-1………………83…………………………………………………..53

3.00 to 3.49-to-1………………69…………………………………………………..48

3.50 to 3.98-to-1………………77…………………………………………………..30

4.06 to 5.87-to-1………………65…………………………………………………..66

6.06 to 7.90-to-1………………88…………………………………………………..17

8.20 to 17.87-to-1……………100…………………………………………………..22

 

This table drives home in spades the problem with the U.S. Army current interpretation of the three-to-one rule (50% chance of defender success). To start with, the attacker starts winning over half the time at 1.00 to 1.49-to-1 odds. By the time they get to 2.50 to 2.99-to-1 odds they are winning 83% of the time. It is quite clear from this data that the U.S. Army rule is wrong.

Now, this data is skewed a little bit by the inclusion of engagements with “limited action” or only “limited attack.” They include engagements where the attacker has a significant force ratio but conducted only an initial probing attack of battalion size. Sometimes those attacks did not succeed. So the success rate of some the higher odds engagements would actually be higher if these were eliminated. So, we ended up culling 102 of these engagements from the above table to produce the following table.  There is not a big difference in the results between this tighter table of 570 cases and the previous table of 672 cases. The primary difference is that the attacker tends to be more successful in all categories. All the culled engagements were from World War II.

Division-level Engagements, 1904-1991 (570 cases) – culled data set

 

Force Ratio………………….Percent Attacker Wins……………….Number of Cases

0.20 to 0.20-to-1………………..0%…………………………………………………2

0.25 to 04.9-to-1………………25……………………………………………………8

0.50 to 0.99-to-1………………52…………………………………………………..62

1.00 to 1.49-to-1………………62…………………………………………………133

1.50 to 1.99-to-1………………66…………………………………………………108

2.00 to 2.49-to-1………………80………………………………………………….49

2.50 to 2.99-to-1………………83………………………………………………….48

3.00 to 3.49-to-1………………70………………………………………………….40

3.50 to 3.98-to-1………………76………………………………………………….29

4.06 to 5.87-to-1………………73………………………………………………….55

6.06 to 7.90-to-1………………88………………………………………………….17

8.20 to 17.87-to-1……………100………………………………………………….17

56.20-109.98-to-1……………100…………………………………………………..2

 

Needless to say, this tighter data set is even further biased against the published U.S. Army three-to-one rule.

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

From 1st Alabama Cavalry, USV website (www.1stalabamacavalryusv.com). Alexander Lawrence was from Fayette County, Alabama and fought for the Union with the 1st Alabama Cavalry

As the three-to-one rule of thumb appears to have evolved out of the American Civil War (although not as published in FM 6-0), then we should probably look at just our Civil War battles in our database.

Among those 243 cases are 49 cases from the American Civil War. As the three-to-one rule may have evolved from that experience, let us looking at just those cases:

 Force Ratio……………………Percent Attacker Wins……………….Number of Cases

0.44 to 0.48-to-1…………………0%………………………………………………3

0.53 to 0.97-to-1………………..18……………………………………………….11

1.00 to 1.47-to-1………………..36……………………………………………….14

1.53 to 1.96-to-1………………..25……………………………………………….12

2.10 to 2.31-to-1………………..50…………………………………………………6

3.00-to-1……………………….100…………………………………………………1

5.00-to-1……………………….100…………………………………………………1

15.05-to-1……………………..100…………………………………………………1

 

The American Civil War is a very good test case for such an examination. Both officer corps were primarily trained at West Point (the U.S. military academy); both armies fought in the same style and doctrine; they used most of the same weapons, including the same muskets and same artillery; they were similar in culture; and they were similar in training, doctrine, background and capability. While some historical mythology has tried to make the southern Americans better fighters, it is hard to accept the argument that a farmer from North Carolina is a different, more motivated or a more capable fighter than a farmer from Pennsylvania. Most of the United States was rural. There wre also units raised to fight for the north from all of the southern states. This is about an equal comparison between two opponents that one is going to find.

The end results from these two tests are that the three-to-one rule as recorded in FM 6-0 clearly does not apply. In the case of the Civil War data at 2.10 to 2.31-to-1 odds the attacker is winning half the time. Where does one get the notion that at 3.00-to-1 odds the defender will win half the time? What historical data established that?

So the U.S. Army version of the three-to-one (meaning defender wins half the time) does not show up in the almost 400 years of history that we are examining here and does not show up in the American Civil War.

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

Now, at the time I wrote War by Numbers, I was not aware of this sentence planted in FM 6-0 and so therefore did not feel a need to respond to the “3-to-1 rule.” It is a rule of thumb, not completely without value, that had been discussed before. I thought this issue was properly understood in the U.S. analytical and defense community, therefore I did not feel a need to address it further. It turns out that I do. So, let me take a moment to tap into our databases and properly address this using all the resources at my disposal.

First of all, The Dupuy Institute has a database of 243 engagements from 1600-1900 called the Battles Data Base (BaDB). These are almost all field battles, where the two sides deployed their forces of tens of thousands of people and resolve their dispute that day. Of the 243 battles, only 40 of them last longer than a day. The largest engagement has the attacker fielding 365,000 men (Leipzig, 1813) and the smallest engagement had the defender fielding but 350 men (Majuba Hill, 1881).

As this rule of thumb evolved out of the U.S. Civil War, then an examination of historical field battles from 1600-1900 is particularly relevant. Looking at the force ratio for these battles shows:

Force Ratio…………………..Percent Attacker Wins………………..Number of Cases

0.26 to 04.9-to-1………………54%……………………………………………13

0.50 to 0.98-to-1………………54………………………………………………81

1.00 to 1.47-to-1………………56………………………………………………71

1.50 to 1.96-to-1………………63………………………………………………38

2.00 to 2.44-to-1………………50………………………………………………16

2.58 to 2.94-to-1………………57………………………………………………..7

3.00 to 3.43-to-1…………….100………………………………………………..5

3.75 to 3.76-to-1………………..0………………………………………………..2

4.00 to 4.93-to-1………………75………………………………………………..4

7.78 to 16.82-to-1……………..67………………………………………………..6

 

The pattern here is not particularly clear, as low odds attack, where the attacker is outnumbered, succeed over half the time, as do attacks at higher odds. Some of this is due to the selection of battles, some of this is due to the lack of regular trained armies, and some of this is due to the attacker choosing to attack because they have advantages in morale, training, experience, position, etc. that outweigh the numbers. But, the argument that is made in FM 6-0 that based upon historical data at three-to-one odds the defender wins 50% of the time is clearly not shown. For example, in this data set there are 12 cases between the odds of 2.50 to 3.50-to-1. Of those 12 cases, the attacker wins in 9 of them (75%). The three cases where the defender wins are: 1) Battle of Buena Vista in 1847 where Santa Anna’s Mexican Army attacked Zachary Taylor’s American Army at 2.94-to-1, 2) Battle of Inkeman in 1854 where the Russian Army attacked the French and British armies in Crimea at 2.63-to-1, and 3) Battle of Belfort in 1871 where the French Army attack the German Army at 2.75-to-1. One could certainly argue that in these three cases, the defenders held advantages in training, experience and overall combat effectiveness.

Next post will address the 49 American Civil War battles in our database.

The U.S. Army Three-to-One Rule

Various Three-to-one rules of thumbs have existed in the U.S. Army and in writings possibly as early as the American Civil War (1861-1865). These are fine as “rules of thumb” as long as one does not take them seriously and understands what they really mean. But, unfortunately, we have now seen something that is a loose rule of thumb turned into a codified and quantified rule. This is annoyingly overstating its importance and as given in U.S. Army manuals, is patently false.

The U.S. Army has apparently codified the “three-to-one rule” in its documentation and has given it a value. In the 2014 edition of FM 6-0, paragraph 9-103, it states that “For example, historically, defenders have over a 50 percent probability of defeating an attacking force approximately three times their equivalent strength.” This statement, on the surface, simply is incorrect. For example, the following table from my book War by Numbers is drawn from a series of 116 division-level engagements in France in 1944 against the Germans (see War by Numbers, page 10) They show the following relationship between force ratio and outcome:

European Theater of Operations (ETO) Data, 1944

 

Force Ratio………………..Result…………………Percent Failure…Number of cases

0.55 to 1.01-to-1.00………Attack Fails…………………..100%……………….5

1.15 to 1.88-to-1.00………Attack usually succeeds……21%………………..48

1.95 to 2.56-to-1.00………Attack usually succeeds……10%………………..21

2.71-to-1.00 and higher…Attacker Advances…………….0%……………….. 42

 

Now these engagements are from fighting between the U.S., UK and Germany in France and Germany in 1944. These are engagements between forces of roughly equal competence. As can be seen, based upon 42 division-level engagements, in all cases of attacks at three-to-one (more specifically 2.71-to-1 and greater), the attacker advanced. Meaning in all cases of attacks at three-to-one, the attacker won. This directly contradicts the statement in FM 6-0, and contradicts it based upon historical data.

This is supplemented by the following two tables on the next page of War by Numbers. The first table shows the German performance when attacking Soviet units in 1943.

Germans attacking Soviets (Battles of Kharkov and Kursk), 1943

 

Force Ratio………………..Result………………….Percent Failure…Number of cases

0.63 to 1.06-to-1.00………Attack usually succeeds……..20%……………………..5

1.18 to 1.87-to-1.00………Attack usually succeeds……….6%……………………17

1.91-to-1.00 and higher…Attacker Advances……………….0%……………………21

 

The next table shows the Soviet performance when attacking German units in 1943:

Soviets attacking Germans (Battles of Kharkov and Kursk), 1943

 

Force Ratio………………Result…………………..Percent Failure…Number of cases

0.40 to 1.05-to-1…………Attack usually fails…………70%……………………10

1.20 to 1.65-to-1.00…….Attack often fails…………….50%……………………11

1.91 to 2.89-to-1.00…….Attack sometimes fails…….44%……………………..9

 

These charts are from the fighting around Kharkov in February, March and August of 1943 and the fighting during the Battle of Kursk in July 1943. It is 73 engagements between the German and Soviet armies.

Now, there is a clear performance difference between the German and the Soviet armies at this time. This is discussed in considerable depth in War by Numbers and will not be addressed here. But, what it amounts to is that the German Army has an advantage in the casualty exchange and that advantage also shows up in the outcomes of the battles, as show above. If they attacked at two-to-one odds are greater, they would win. The Soviets attacking at the same odds would win only 56 percent of the time. Clearly, at the division-level, in a unit to unit comparison, the Germans were two or three times better than their Soviet opponents.

Still, even in the worse case, which is the Soviets attacking the Germans, we do not get to the claim made in FM 6-0, which is the defender won 50% of the time when attacked at three-to-one. In fact, the Soviets managed to win 50% of the time when attacking at 1.20 to 1.65-to-1. Something is clearly wrong with the statement in FM 6-0.

Now, at the time I wrote War by Numbers, I was not aware of this sentence planted in FM 6-0 and so therefore did not feel a need to respond to the “three-to-one rule.” It is a rule of thumb, not completely without value, that had been discussed before (see Dupuy, Understanding War, pages 31-37). I thought this issue was properly understood in the U.S. analytical and defense community, therefore I did not feel a need to address it further. It turns out that I do. So, I will take a moment to tap into our databases and properly address this using all the resources at my disposal. This will be in subsequent blog posts.

Dispersion versus Lethality

This is a follow-up post to the post discussing Trevor Dupuy’s work compared to the Army Research Laboratories (ARL) current work:

The Evolution of Weapons and Warfare?

The work by ARL produced a graph similar to this one by Trevor Dupuy, except it was used to forecast the “figure of regularity” (which I gather means firepower or lethality). But if you note there is another significant line on Trevor Dupuy’s graph, besides the weapons’ “theoretical killing capacity.” It is labeled Dispersion. Note the left side of the graph where it is labeled “Disperion: Square Meters per Man in Combat.” It also goes up as the “theoretical killing capacity” of the weapons goes up.

This is the other side of equation. For every action, there is an equal and opposite reaction to paraphrase a famous theorist. This results in this chart from Col. Dupuy:

Now….this is pretty damn significant….for as firepower, or lethality, or “theoretical killing capacity” has gone up, even geometrically…..daily casualty rates have declined. What is happening? Well, not only “for every action, there is an equal and opposite reaction,” but in fact, the reaction has outweighed the increase in firepower/lethality/killing capacity over time. This is worth thinking about. For as firepower has gone up, daily casualty rates have declined.

In fact, I did discuss this in my book War By Numbers (Chapter 13: The Effects of Dispersion on Combat). Clearly there was more to “dispersion” than just dispersion, and I tried to illustrate that with this chart:

To express it in simple English, people are dispersing, increasing engagement ranges and making more individual use of cover and concealment (page 166). Improvements in weapons, which occur on both sides, have also been counteracted by changes in deployment and defense. These changes have been more significant than the increases in lethality. See pages 166-169 of War by Numbers for a more complete explanation of this chart.

The issues related to lethality and forecasting the future of lethality gets a little complex and multifaceted.

Today – Speaking at Historicon in Lancaster, PA., Friday 12 July

I will be speaking at Historicon in Lancaster, PA., Friday 12 July, at 6 PM. Historicon is one of the three major annual wargaming conventions run by the Historical Miniatures Gaming Society (HMGS). It will be run from 10 July-14 July, 2019. Their website is here: https://www.hmgs.org/general/custom.asp?page=HconHome

As part of this large convention, they have organized a “War College.” This is an impressive effort that includes 18 lectures on Thursday, Friday and Saturday. I have the last lecture on Friday, from 6 – 7 PM. The speakers for this series include published authors Paul Westermeyer, Pete Panzeri, Steve R. Waddell and John Prados, among others. Lecture descriptions are here:                                                                               . https://cdn.ymaws.com/www.hmgs.org/resource/resmgr/historicon/hcon_19/pels/19_war_college_pel_6-19-2019.pdf

I will be doing a presentation similar to the one I did at the New York Military Affairs Symposium (NYMAS). It is based upon part of my book War by Numbers: Understanding Conventional Combat.

Reminder – Speaking at Historicon in Lancaster, PA., Friday 12 July

I will be speaking at Historicon in Lancaster, PA., Friday 12 July. Historicon is one of the three major annual wargaming conventions run by the Historical Miniatures Gaming Society (HMGS). It will be run from 10 July-14 July, 2019. Their website is here: https://www.hmgs.org/general/custom.asp?page=HconHome

As part of this large convention, they have organized a “War College.” This is an impressive effort that includes 18 lectures on Thursday, Friday and Saturday. I have the last lecture on Friday, from 6 – 7 PM. The speakers for this series include published authors Paul Westermeyer, Pete Panzeri, Steve R. Waddell and John Prados, among others. Lecture descriptions are here:                                                                               . https://cdn.ymaws.com/www.hmgs.org/resource/resmgr/historicon/hcon_19/pels/19_war_college_pel_6-19-2019.pdf

I will be doing a presentation similar to the one I did at the New York Military Affairs Symposium (NYMAS). It is based upon part of my book War by Numbers: Understanding Conventional Combat.

Reminder – Speaking at Historicon in Lancaster, PA., Friday 12 July

I will be speaking at Historicon in Lancaster, PA., Friday 12 July. Historicon is one of the three major annual wargaming conventions run by the Historical Miniatures Gaming Society (HMGS). It will be run from 10 July-14 July, 2019. Their website is here: https://www.hmgs.org/general/custom.asp?page=HconHome

As part of this large convention, they have organized a “War College.” This is an impressive effort that includes 18 lectures on Thursday, Friday and Saturday. I have the last lecture on Friday, from 6 – 7 PM. The speakers for this series include published authors Paul Westermeyer, Pete Panzeri, Steve R. Waddell and John Prados, among others. Lecture descriptions are here:                                                                               . https://cdn.ymaws.com/www.hmgs.org/resource/resmgr/historicon/hcon_19/pels/19_war_college_pel_6-19-2019.pdf

I will be doing a presentation similar to the one I did at the New York Military Affairs Symposium (NYMAS). It is based upon part of my book War by Numbers: Understanding Conventional Combat.