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.

This entry was posted in Combat Databases, DuWar Databases, Force Ratios, Lessons of History, Modeling, Simulation & Wargaming, U.S. Military Doctrine, War by Numbers by Christopher A. Lawrence. Bookmark the permalink.

About Christopher A. Lawrence

Christopher A. Lawrence is a professional historian and military analyst. He is the Executive Director and President of The Dupuy Institute, an organization dedicated to scholarly research and objective analysis of historical data related to armed conflict and the resolution of armed conflict. The Dupuy Institute provides independent, historically-based analyses of lessons learned from modern military experience. ... Mr. Lawrence was the program manager for the Ardennes Campaign Simulation Data Base, the Kursk Data Base, the Modern Insurgency Spread Sheets and for a number of other smaller combat data bases. He has participated in casualty estimation studies (including estimates for Bosnia and Iraq) and studies of air campaign modeling, enemy prisoner of war capture rates, medium weight armor, urban warfare, situational awareness, counterinsurgency and other subjects for the U.S. Army, the Defense Department, the Joint Staff and the U.S. Air Force. He has also directed a number of studies related to the military impact of banning antipersonnel mines for the Joint Staff, Los Alamos National Laboratories and the Vietnam Veterans of American Foundation. ... His published works include papers and monographs for the Congressional Office of Technology Assessment and the Vietnam Veterans of American Foundation, in addition to over 40 articles written for limited-distribution newsletters and over 60 analytical reports prepared for the Defense Department. He is the author of Kursk: The Battle of Prokhorovka (Aberdeen Books, Sheridan, CO., 2015), America’s Modern Wars: Understanding Iraq, Afghanistan and Vietnam (Casemate Publishers, Philadelphia & Oxford, 2015), War by Numbers: Understanding Conventional Combat (Potomac Books, Lincoln, NE., 2017) , The Battle of Prokhorovka (Stackpole Books, Guilford, CT., 2019), The Battle for Kyiv (Frontline Books, Yorkshire, UK, 2023), Aces at Kursk (Air World, Yorkshire, UK, 2024), Hunting Falcon: The Story of WWI German Ace Hans-Joachim Buddecke (Air World, Yorkshire, UK, 2024) and The Siege of Mariupol (Frontline Books, Yorkshire, UK, 2024). ... Mr. Lawrence lives in northern Virginia, near Washington, D.C., with his wife and son.

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

  1. How is it possible for the attacker to win 83% of the time with a force ratio of 2.5 to 2.9 to his advantage while winning only 63% of the time with a much higher force ratio to his advantage?

    Would this data not suggest that there is a lot more which needs to be taken into consideration than just force ratios?

    • Of course.

      Also, it is highly variable data influenced by human factors, air support, positioning, terrain, surprise, force mix, etc. So, you actually need a much larger database to wash all these out or to properly address these subjects.

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