Measuring Unit Effectiveness in Italy

We are in discussion over revisiting the measurement of combat effectiveness of select units in Italy 1943-1945. This was done by Trevor Dupuy in Numbers, Predictions and Wars (1977) by division using the QJM (Quantified Judgment Model) and was done in aggregate by me in War by Numbers (2017) using simply comparative statistics.

For a little background on page 115 of Understanding War is a chart of German, UK and U.S. units in the Italian Campaign and their CEVs (Combat Effectiveness Values). Their values range from 0.60 to 1.49. The German Hermann Goering Division is the highest rated division at 1.49. This is based upon five engagements. The German 3rd PzGrD was rated 1.17 based upon 17 engagements and 15th PzGrD was rated 1.12 based upon 11 engagements. This was done using the QJM.
    For reference, I would recommend reading the following four books:
1. Understanding War
2. War by Numbers
3. Attrition (optional)
4. Numbers, Predictions and War (optional)
There are two ways to measure combat effectiveness. 1) Do a model run and compared the results of the model run to historical data. This requires 1) a historically validated combat model (there are very few), and 2) confidence in the model. 2) The other option is to do a statistical comparison of a large number of engagements. This is what I did in Chapters 5, 6 and 7 of War by Numbers.
One can measure combat effectiveness by three means: 1) Casualty effectiveness, 2) special effectiveness (distance opposed advance) or 3) Mission effectiveness. This is all discussed in Trevor Dupuy’s work and in War by Numbers.
To date, the only people I am aware of who have published their analysis of combat effectiveness is Trevor Dupuy, me (Chris Lawrence) and Niklas Zetterling. See: CEV Calculations in Italy, 1943 | Mystics & Statistics ( and his book Normandy 1944 (recently revised and republished). There is also a six-volume quantitative effort related to Operation Barbarossa by Nigel Askey, which I have never looked at. Everyone else has ignored quantifying this issue, although there are no shortage of people claiming units are good, bad or elite. How they determine this is judgment (and it is often uncertain as to what the basis is for this judgment).
Now, the original work on this was done by Trevor Dupuy in the late 1970s based upon his data collection and the QJM. Since that time the model has been updated to the TNDM. The engagements used for the QJM validation were then simplified (especially in weapons counts) and assembled into the LWDB (Land Warfare Data Base). The LWDB had around 70 engagements from the Italian Campaign. Since that time we have created the DuWar series of databases which includes the DLEDB (Division-Level Engagement Data Base). See: The History of the DuWar Data Bases | Mystics & Statistics ( We have doubled the number of Italian Campaign engagements to around 140.
There are a total of 141 Italian Campaign division-level engagements in the DLEDB. The first 140 engagements cover from September 1943 to early June 1944. There is almost 12 months of war not covered and not all units in the first part of the campaign are covered. With all the various nationalities involved (i.e German, Italian, U.S., UK, Free French, Moroccan, New Zealand, South African, Poland, Indian, Canadian, Brazilian, Greek, etc.), the Italian Campaign is a fertile field for this work. We are looking at stepping back into this. 
Units involved in engagements in the DELDB:
3rd PzGrD: 25 cases
15th PzGrD: 39 cases
16th PzD: 7 cases
26th PzD: 8 cases
29 PzGrD: 6 cases
65th ID: 5 cases
94th ID: 8 cases
305th ID: 4 cases
362nd ID: 3 cases
715th ID: 2 cases
4th Para D: 3 cases
HG PzGrD: 26 cases
LXXVI Pz Corps: 4 cases
12th Para Rgt: 1 case
1st AD: 3 cases
3rd ID: 19 cases
34th ID: 15 cases
36th ID: 12 cases
45th ID: 20 cases
85th ID: 7 cases
88th ID: 4 cases
509th PIB: 1 case
1st SSF: 1 case
7th AD: 6 cases
1st ID: 9 cases
5th ID: 2 cases
46th ID: 18 cases
56th ID: 24 cases

The History of the DuWar Data Bases

The original databases of battles was developed by Trevor Dupuy and HERO (Historical Evaluation and Research Organization) back in the 1980s. They were published in a six volume work in 1983 as the HERO Land Warfare Data Base. This is back in the days when a data base did not have to be computerized (paper database – how quaint) and database was two words. It is report number 95 listed here: TDI – The Dupuy Institute Publications. Descriptive link is here: Analysis of Factors that have Influenced the Outcomes of Battles and Wars ( Of significance, there is a detailed description of each engagement in these paper reports. It was republished in 1984, 1985 and 1986 as report numbers 100, 103 and 111 here: TDI – The Dupuy Institute Publications. The final publication named the database as CHASE. 

This effort was funded by CAA and was before my time. I came to work for HERO in 1987. There was then some back and forth between CAA, where HERO and CAA got to fighting over details of the content. One analyst at CAA sent 16 engagements out for comment. I did analyze that effort, although that file is now buried on an old Word Perfect DOS-era disk. He had four outside independent historians each analyze four engagements. The end result is the comments made corrections/improvements to 25% of the engagements, the comments did really did not change anything in 25% of the engagements, and the comments actually, if implemented, would have added error the engagements in 50% of the cases. This is fairly typical of outside comments, with 1-out-of-3 or 1-out-of-4 being helpful, and half of them would degrade the product. At that point, the project came to a griding halt, with much animosity between the arguing parties.

Then both HERO and CAA decided to independently computerize their databases. HERO added about four new engagements to their database, maybe corrected a few others, and the programmed it in a flat file called Reflex. It was 603 engagements (working off memory here) and called the LWDB (Land Warfare Data Base). CAA decided to computerize its version of 598 or 599 engagements and it was called the CHASE database. This became the CBD-90 that some people are still using. Neither of these versions included the extensive battle narratives as databases at that time could not handle large text files.

The computerized Reflex version of the LWDB was later purchased by Oak Ridge National Laboratories and published in the book by Dr. Dean Harley. It is a better version than the CBD-90. I did review the CBD-90 over twenty years ago. In the original database, there were a series of factors that were coded as to what degree they influenced the battle. In the CBD-90 about one-third of those factors (or one-third of the engagements that had those factors) – they were blanked out or mis-coded. It was a simple coding error, that as far as I know has never been corrected. 

In the meantime, around 1995 I decided we needed to reorganize and reprogram the database. We had a new database created by Jay Karamales in Access. It included text files. We loaded the old Reflex engagements in the database and then Susan Rich and I proofed the entire database back to the paper copies. Susan Rich then entered in all the narratives into the database. So this was now a complete and proofed version of the 1986 paper database. 

I then broke the database up. One of the problems with the original database is that it has engagements from 1600 next to engagements from 1973 next to a series of day-long division-level engagements from WWII next to some six-month long army-level engagements from the Great War next to battalion-level actions. While there are definitely some historical trends across all these, in some cases, depending on what you are analyzing, it is comparing apples to oranges. So, I took at mostly one-day battles from 1600-1900 and put them in a separate database (243 engagements – the  BaDB. I took all the large army-level engagements (like Battle of Verdun, Battle of the Somme) and put them into a Large Action Data Base – LADB. Basically, moved them out of the way. They were later used in part to help create the CaDB (Campaign Data Base). I put the smaller battalion-sized engagements into a separate battalion-level data base (BLODB). They left us with a core of around 300 engagements in a division-level database, mostly of 1-day engagements. All this work was done outside and independent of any contracted effort and therefore became a Dupuy Institute proprietary product. As with any proprietary product, you have to protect it.

We then expanded all these databases. In the case of the division-level database (the DLEDB), we ended up doing a series of studies for CAA on Enemy Prisoner of War capture rates in 1998-2001. We coded the division-level engagements by outcome and then using that to analyze capture rates based upon the outcomes of the battle. This effort included getting counts of the number captured and the number of deserters in each engagement. This is reports E-1 to E-8 here:  TDI – The Dupuy Institute Publications. The data used (but not the complete listing of the engagement) was included in appendices to these reports. CAA and the U.S. Army is still using these new rates.

We also added engagements to it from our urban warfare studies (CAA), reports U-1 to U-3. We used the database to analyze the urban versus non-urban combat. It was during that study we added engagements from the Channel Ports, Aachen and the three battles of Kharkov (1943). This study is discussed in two chapters in my book War by Numbers. We also took the time and put in 192 engagements from the Battle of Kursk (1943) based upon our work on the Kursk Data Base. All these Kursk engagements are listed (abbreviated) in my big Kusk: The Battle of Prokhorovka book. We also did a study on situational awareness for OSD Net Assessment (Andy Marshall’s old office). This is report SA-1 and also two chapters in my book War by Numbers. We ended up coding 295 division-level engagements based upon their knowledge of the enemy (by reviewing their intel reports of the divisions involved). We then reviewed what was the measurable combat advantage of improved situation awareness based upon real-world combat data. So, as in the EPW study, we took our original database and added additional filled-in fields so as to be able to do properly analyze the issue. This last expansion of the database was completed in 2004.

At that point, the division-level database had 752 cases in it. We had done some additional work on the old Italian Campaign engagements to clean them up and revise them. In particular Richard Anderson collected UK records from PRO and we cross-checked and revised all the UK engagements in the database and expanded the number of Italian Campaign engagements from about 70 to around 140. We then stopped work on the database in 2004.

During that time, we also expanded the battalion-level database to around 200 actions. We also had created a Campaign Data Base as part of our work, to examine operations above division-level and that last more than a few days. This was recently used for my presentation on Force Ratios that I gave at the second HAAC and in Norway in early November. See: The Schedule for the Second Historical Analysis Annual Conference (HAAC), 17 – 19 October 2023 | Mystics & Statistics ( In 2010 we created a small draft company-level database under contract with Boeing of 100 cases. A listing of most of these databases is here: TDI – The Dupuy Institute Publications. It does not include the company-level database, the Battle of Britain database nor the Dupuy Insurgency Spread Sheets (DISS) as we have not updated that page.

Obviously, people are going to ask: how can they get access to these databases. The answer is that you cannot until someone is willing to purchase them at a price that I willing to release them for. With the internet any single sale of the database will result in the release of the entire database to the world. So, any price would have to address the fact that these powerful and unique databases, which are proprietary to The Dupuy Institute, would be shared with the world. This includes potential business competitors. We still rely on contracts for our funding and these databases are part of our “product.” So, cost of giving away an exclusive competitive advantage? We would be willing to sell them to an organization if the price is right and they could then be publicly released. So far no one has made a significant concrete offer to us.


So other links:

Some Background on TDI Data Bases | Mystics & Statistics (

Dupuy Institute Data Bases | Mystics & Statistics

Cost of Creating a Data Base | Mystics & Statistics (

The Division Level Engagement Data Base (DLEDB) | Mystics & Statistics (

Battalion and Company Level Data Bases | Mystics & Statistics (

Other TDI Data Bases | Mystics & Statistics (

Using the DLEDB:

Average Losses per Day in Division-level Engagements on the Eastern Front in 1943 | Mystics & Statistics (

Density of Deployment in Ukraine | Mystics & Statistics (

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

Comparing Force Ratios to Casualty Exchange Ratios | Mystics & Statistics (

Comparing the RAND Version of the 3:1 Rule to Real-World Data | Mystics & Statistics (

Summation of Force Ratio Posts | Mystics & Statistics (

Amphitheater, 9 – 11 September 1943 | Mystics & Statistics (

Amphibious and River Crossing Engagements in the Italian Campaign 1943-44 | Mystics & Statistics (

The World War I Cases from the Division-level Database | Mystics & Statistics (

The World War II Cases from the Division-level Database | Mystics & Statistics (

Post-World War II Cases from the Division-level Database | Mystics & Statistics (

Force Ratios in the Arab-Israeli Wars (1956-1973) | Mystics & Statistics (

Other discussion:

Battles versus Campaigns (for Validation) | Mystics & Statistics (

Validation Data Bases Available (Ardennes) | Mystics & Statistics (

Validation Data Bases Available (Kursk) | Mystics & Statistics (

Other Validation Data Bases | Mystics & Statistics (

The Use of the Two Campaign Data Bases | Mystics & Statistics (

Measuring the Effects of Combat in Cities, Phase II – part 1 | Mystics & Statistics (

Presentations from HAAC – Urban Warfare | Mystics & Statistics (

The Battle of Britain Data Base | Mystics & Statistics (

Presentations from HAAC – Data for Wargames | Mystics & Statistics (

The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900 | Mystics & Statistics (

The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles | Mystics & Statistics (

Using the CBD:

The Key to Victory: Machine Learning the Lessons of History | Mystics & Statistics (

Presentations from HAAC – Machine Learning the Lessons of History | Mystics & Statistics (

There is more….

Phalanx Article: What We Have Learned from Doing Historical Analysis | Mystics & Statistics (

Advance Rates in Combat


Advance Rates in Combat:

                Units maneuver before and during a battle to achieve a more favorable position. This maneuver is often unopposed and is not the subject of this discussion. Unopposed movement before combat is often quite fast, although often not as fast as people would like to assume. Once engaged with an opposing force, the front line between them also moves, usually moving forwards if the attacker is winning and moving backwards for the defender if he is losing or choosing to withdraw. These are opposed advance rates. This section is focused on discussing opposed advance rates or “advance rates in combat.”

            The operations research and combat modeling community have often taken a short-hand step of predicting advance rates in combat based upon force ratios, so that a force with a three-to-one force ratio advances faster than a force with a two-to-one force ratio. But, there is not a direct relationship between force ratios and advance rates. There is an indirect relationship between them, in that higher forces ratios increased the chances of winning, and winning the combat and the degree of victory helps increase advance rates. There is little analytical work that has been done on this subject.[1]

            Opposed advance rates are very much influenced by 1) terrain, 2) weather and 3) the degree of mechanization and mobilization, in addition to 4) the degree of enemy opposition. These four factors all influence what the rates will be.

            In a study The Dupuy Institute did on enemy prisoner of war capture rates, we ended up coding a series of engagements by outcome. This has proven to a useful coding for the examination of advance rates. Engagements codes as outcomes I and II (limited action and limited attack) are not of concern for this discussion. The engagement coded as attack fails (outcome III) is significant, as these are cases where the attacker is determined to have failed. As such they often do not advance at all, sometimes have a very limited advance and sometimes are even pushed back (have a negative advance). For example, in our work on the subject, of our 271 division-level engagements from Western Europe 1943-45 the average advance rate was 1.81 kilometers per day. For Eastern Europe in 1943 the average advance rate was 4.54 kilometers per day based upon 173 division-level engagements.[2] These advance rates are irrespective of what the force ratios are for an engagement.

            In contrast, in those engagements where the attacker is determined to have won and is coded as attacker advances (outcome IV) the attacker advances an average of 2.00 kilometers in the 142 engagements from Western Europe 1943-45. The average force ratio of these engagements was 2.17. In the case of Eastern Europe in 1943, the average advance rate was 5.80 kilometers based upon 73 engagements. The average force ratio of these engagements was 1.62.

            We also coded engagements where the defender was penetrated (outcome V). These are those cases where the attacker penetrated the main defensive line of the defending unit, forcing them to either withdraw, reposition or counterattack. This penetration is achieved by either overwhelming combat power, the end result of an extended operation that finally pushes through the defenses, or a gap in the defensive line usually as a result of a mistake. Superior mechanization or mobility for the attacker can also make a difference. In those engagements where the defender was determined to have been penetrated the attacker advanced an average of 4.12 kilometers in 34 engagements from Western Europe 1943-45. The average force ratio of these engagements was 2.31. In the case of Eastern Europe in 1943, the average advance rates was 11.28 kilometers based upon 19 engagements. The average force ratio of these engagements was 1.99.

            This clearly shows the difference in advance rate based upon outcome. It is only related to force ratios to the extant the force ratios are related to producing these different outcomes.


            Also of significance is terrain and weather. Needless to say, significant blocking obstacles like bodies of water, can halt an advance and various rivers and creeks often considerably slow them, even with engineering and bridging support. Rugged terrain is more difficult to advance through and easier to defend and delay then smoother terrain. Closed or wooded terrain is more difficult to advance through and easier to defend and delay then open terrain. Urban terrain tends to also slow down advance rates, being effectively “closed terrain.” If it is raining then advance rates are slower than in clear weather. Sometimes considerably slower in heavy rain. The season it is, which does influence the amount of daylight, also affects the advance rate. Units move faster in daylight than in darkness. This is all heavily influenced by the road network and the number of roads in the area of advance.

            No systematic study of advance rates has been done by the operations research community. Probably the most developed discussion of the subject was the material assembled for the combat models developed by Trevor Dupuy. This included addressing the effects of terrain and weather and road network on the advance rates. A combat model is an imperfect theory of combat.

            Even though this combat modeling effort is far from perfect and fundamentally based upon quantifying factors derived by professional judgment, tables derived from this modeling effort have become standard presentations in a couple of U.S. Army and USMC planning and reference manuals. This includes U.S. Army Staff Reference Guide and the Marine Corps’ MAGTF Planner’s Reference Manual.[3]

The original table, from Numbers, Predictions and War, is here:[4]




                                                                                    Rates in km/day

                                                Armored          Mechzd.          Infantry           Horse Cavalry

                                                Division           Division           Division           Division or

                                                                                                or Force           Force

Against Intense Resistance

    (P/P: 1.0-1.1O)

Hasty defense/delay                4.0                   4.0                   4.0                   3.0

Prepared defense                    2.0                   2.0                   2.0                   1.6

Fortified defense                     1.0                   1.0                   1.0                   0.6


 Against Strong/Intense Resistance

    (P/P: 1-11-125)

Hasty defense/delay                5.0                   4.5                   4.5                   3.5

Prepared defense                    2.25                 2.25                 2.25                 1.5

Fortified defense                     1.25                 1.25                 1.25                 0.7


Against Strong Defense

    (P/P: 1.26-1.45)

Hasty defense/delay                6.0                   5.0                   5.0                   4.0

Prepared defense                    2.5                   2.5                   2.5                   2.0

Fortified defense                     1.5                   1.5                   1.5                   0.8


Against Moderate/Strong Resistance

    (P/P: 1.46-1.75)

Hasty defense                         9.0                   7.5                   6.5                   6.0

Prepared defense                    4.0                   3.5                   3.0                   2.5

Fortified defense                     2.0                   2.0                   1.75                 0.9


Against Moderate Resistance

    (P/P: 1.76-225)

Hasty defense/delay                12.0                 10.0                 8.0                   8.0

Prepared defense                    6.0                   5.0                   4.0                   3.0

Fortified defense                     3.0                   2.5                   2.0                   1.0


Against Slight/Moderate Resistance


Hasty defense/delay                16.0                 13.0                 10.0                 12.0

Prepared defense                    8.0                   7.0                   5.0                   6.0

Fortified defense                     4.0                   3.0                   2.5                   2.0


Against Slight Resistance

    (P/P: 3.01-4.25)

Hasty defense/delay                20.0                 16.0                 12.0                 15.0

Prepared defense                    10.0                 8.0                   6.0                   7.0

Fortified defense                     5.0                   4.0                   3.0                   4.0


Against Negligible/Slight Resistance


Hasty defense/delay                40.0                 30.0                 18.0                 28.0

Prepared defense                    20.0                 16.0                 10.0                 14.0

Fortified defense                     10.0                 8.0                   6.0                   7.0


Against Negligible Resistance

    (P/P: 6.00 plus)

Hasty defense /delay               60.0                 48.0                 24.0                 40.0

Prepared/fortified defense      30.0                 24.0                 12.0                 12.0


*Based on HERO studies: ORALFORE, Barrier Effectiveness, and Combat Data Subscription Service.

** For armored and mechanized infantry divisions, these rates can be sustained for 10 days only; for the next 20 days standard rates for armored and mechanized infantry forces cannot exceed half these rates.


                This is a modeling construct built from historical data. These are “unmodified” rates. The modifications include: 1) General Terrain Factors (ranging from 0.4 to 1.05 for Infantry (combined arms) Force and from 0.2 to 1.0 for Cavalry or Armored Force, 2) Road Quality Factors (addressing Road Quality from 0.6 to 1.0 and Road Density from 0.6 to 1.0), 3) Obstacles Factors (ranging from 0.5 to 0.9 for both a River or steam and for Minefields), 4) Day/Night with night advance rate one-half of daytime advance rate and 5) Main Effort Factor (ranging from 1.0 to 1.2). These last five sets of tables are not shown here, but can be found in his writings.[5]



[1] The most significant works we are aware of is Trevor Dupuy’s ORALFORE study in 1972: Opposed Rates of Advance in Large Forces in Europe (ORALFORE), (TNDA, for DCSOPS, 1972); Trevor Dupuy’s 1979 book Numbers, Predictions and War; and a series of three papers by Robert Helmbold (Center for Army Analysis): “Rates of Advance in Land Combat Operations, June 1990,” “Survey of Past Work on Rates of Advance, and “A Compilation of Data on Rates of Advance.”

[2] See paper on the subject by Christopher A. Lawrence, “Advance Rates in Combat based upon Outcome,” posted on the blog Mystics & Statistic, April 2023. In the databases, there were 282 Western Europe engagements from September 1943 to January 1945. There were 256 Eastern Front engagements from February, March, July and August of 1943.

[3] See U.S. Army Staff Reference Guide, Volume I: Unclassified Resources, December 2020, ATP 5-0.2-1, pages xi and 220; and MAGTF Planner’s Reference Manual, MSTF pamphlet 5-0.3, October 2010, page 79. Both manuals include a table for division-level advances which is derived from Trevor Dupuy’s work, and both manuals contain a table for brigade-level and below advances which are calculated per hour that appear to also be derived from Trevor Dupuy’s division-level table. The U.S. Army manual gives the “brigade and below” advance rates in km/hr while the USMC manual, which appears to be the same table, gives the “brigade and below” advance rates in km/day. This appears to be a typo.

[4] Numbers, Predictions and War, pages 213-214. The sixth line of numbers, three numbers were changes from 1.85 to 1.25 as this was obviously a typo in the original.

[5] See Numbers, Predictions and War, pages 214-216.



The actual paper this was drawn from is here: Advance Rates in Combat

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

Some Background on TDI Data Bases

The Dupuy Institute (TDI) are sitting on a number of large combat databases that are unique to us and are company proprietary. For obvious reasons they will stay that way for the foreseeable future.

The original database of battles came to be called the Land Warfare Data Base (LWDB). It was also called the CHASE database by CAA. It consisted of 601 or 605 engagements from 1600-1973. It covered a lot of periods and lot of different engagement sizes, ranging from very large battles of hundreds of thousand a side to small company-sized actions. The length of battles range from a day to several months (some of the World War I battles like the Somme).

From that database, which is publicly available, we created a whole series of databases totaling some 1200 engagements. There are discussed in some depth in past posts.

Our largest and most developed data is our division-level database covering combat from 1904-1991 of 752 cases: It is discussed here: The Division Level Engagement Data Base (DLEDB) | Mystics & Statistics (

There are a number of other databases we have. They are discussed here: Other TDI Data Bases | Mystics & Statistics (

The cost of independently developing such a database is given here: Cost of Creating a Data Base | Mystics & Statistics (

Part of the reason for this post is that I am in a discussion with someone who is doing analysis based upon the much older 601 case database. Considering the degree of expansion and improvement, including corrections to some of the engagements, this does not seem a good use of their time., especially as we have so greatly expanded the number engagements from 1943 and on.

Now, I did use some of these databases for my book War by Numbers. I am also using them for my follow-up book, currently titled More War by Numbers. So the analysis I have done based upon them is available. I have also posted parts of the 192 Kursk engagements in my first Kursk book and 76 of them in my Prokhorovka book. None of these engagements were in the original LWDB. 

If people want to use the TDI databases for their own independent analysis, they will need to find the proper funding so as to purchase or get access to these databases. 

More Force Ratio Posts

The last two posts I made on force ratios was drawn from my book War by Numbers. There are additional posts I did early last year on the subject based upon my in-process follow-on book More War by Numbers. They are summarized here:

Summation of Human Factors and Force Ratio posts | Mystics & Statistics (

I have been fairly diligent about making sure the “categories” that are listed on the right hand column of the blog are maintained. Therefore, clicking on Force Ratio will lead you to all 29 Force Ratio related posts on this blog. There are 1,129 posts on this blog (as of this post).



More Combat Results Tables from War by Numbers

Now, the purpose of War by Numbers was not to create Combat Results Tables (CRT) for wargames. Its real purpose was to test the theoretical ideas of Clausewitz, and more particularly, Trevor N. Dupuy to actual real-world data. Not as case studies, but as statistical compilations that would show what the norms are. Unfortunately, military history is often the study of exceptions, or exceptional events, and what is often lost to the casual reader it what the norms are. Properly developed statistical database will clearly show what the norms are and how frequent or infrequent these exceptions are. People tend to remember the exceptional cases, they tend to forget the norms, if they even knew what they were to start with.

Chapters 3, 4 and 5 of War by Numbers is primarily focused on measuring human factors (which some people in the U.S. DOD analytical community seem to think are unmeasurable, even though we are measuring them). As part of that effort I ended up assemble a set of force ratios tables based upon theater and nationality. The first of these, on page 10, was in my previous blog post. Here are a few others, from page 11 of War by Numbers.

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


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




Pacific Theater of Operations (PTO) Data, U.S. attacking Japanese, 1945


Force Ratio                          Result                                    Percent Failure   Number of cases

1.40 to 2.89-to-1.00             Attack succeeds                        0%                     20

2.92 to 3.89-to-1.00             Attack usually succeeds        21%                      14

4.35-to-1.00 and higher       Attack usually succeeds          4%                     26


Force Ratios and CRTs

Page 10 for War by Numbers includes the following table:

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


Many commercial wargames have something called a CRT or Combat Results Table. It is based upon force ratios. For example, this was one of the earliest CRTs used on Avalon Hill Games in the 1960s.

As can been seen from this Combat Results Table, at 1-to-1 the chances of an attack winning is one-in-three. At 2-to-1 odds the chances of the attacker winning is either the same as the defender winning or is a two-thirds chance of winning. At 3-to-1 odds, the attacker will always win.

Now the variable factor is the exchange result, which is defined that the defender removed everyone and the attacker removes as much as the defender. This usually results in an attacker win, if the attack has the right “spare change.” If the attacker was attacking with a single 7 strength unit against a 3 strength defender and they roll and exchange, then both units are eliminated.  

Compare that to the table from my book based upon 116 division-level engagements from the European Theater of Operations (1944-145).

Needless to say, some elements of my book War by Numbers are of interest to the commercial wargaming community. 

Their Wehrmacht was Better than our Army

Poking around the internet, I ran across an article from 1985 by the British journalist and historian Max Hastings, rather provocatively titled “Their Wehrmacht was Better than our Army.” It was published in the Washington Post. I had not seen it before (as I went to work for Trevor Dupuy in 1987):

A few highlights:

  1. The language in the first couple of paragraphs is also pretty provocative. 
  2. The discussion then goes to Liddell Hart.
  3. The discussion then goes to Trevor Dupuy and Martin Van Creveld.
  4. From Dupuy: “On a man for man basis, German ground soldiers consistently inflicted casualties at about a 50 percent higher rate than they incurred from the opposing British and American troops under all circumstances. This was true when they were attacking and when they were defending, when they had a local numerical superiority and when they did not, when they won and when they lost.”
  5. From Hastings: “A spirit of military narcissism, nourished by such films as “The Longest Day,” “A Bridge Too Far” and “The Battle of the Bulge,” was perpetuated mythical images of the Allied and German armies.”
  6. From Hastings: “Yet to be a soldier in America has never been the honorable calling, outside a few thousand Army families. It has traditionally been the route by which young men of modest origins…may aspire to build a career.”

It is worthwhile to read the entire article.

Now, these claims were controversial in the 1980s, and a number of U.S. Army officers and people out at Leavenworth personally and professionally went after Trevor Dupuy over this issue. There was a long unpleasant discussion of that story written up by the lawyer Thomas Nutter. He was going to turn into a book, but I gather that effort was never completed.

I do address the subject of the relative performance of armies in combat in Chapters 4 through 7 of my book War by Numbers. 


Summation of Human Factors and Force Ratio posts

The following five posts make up our discussion of the impact of Human Factors on Force Ratios.

Force Ratios at Kharkov and Kursk, 1943

Force Ratios in the Arab-Israeli Wars (1956-1973)

Measuring Human Factors based upon Casualty Effectiveness

Measuring Human Factors based on Casualty Effectiveness in Italy 1943-1944

The Performance of Armies in Italy, 1943-44

As a result of a comment by Tom from Cornwall, we ended up adding three posts to this discussion that looked at terrain and amphibious operations and river crossings in Italy:

German attacks in Italy by Terrain (1943-44)

Amphibious and River Crossing attacks in Italy 1943-44

Amphibious and River Crossing Engagements in the Italian Campaign 1943-44

The previous posts on this discussion on force ratios are presented here. These were the posts examining the erroneous interpretation of the three-to-one rule as presented in Army FM 6-0 and other publications:

Summation of Force Ratio Posts

We are going to end this discussion for now. There is some additional data from the European Theater of Operations (ETO) and Ardennes that we have assembled, but it presents a confusing picture. This is discussed in depth in War by Numbers (pages 32-48).

I am assembling these discussions on force ratios and terrain into the opening chapters for a follow-on book to War by Numbers.