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. 

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Christopher A. Lawrence
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.

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  1. Chris, I hope that you have forwarded that message to the wargaming companies still in existence. (We’ll have to refight those battles for which your attacks defeated my defenses; of course, only for battles fought after you taught me to fight in battle lines rather than fight from strong points : – )

  2. Chris,
    I think this is a good point, but I have questions.

    1. How do you define attack “usually”? If it usually succeeds, then the ratio of attack/defeat could be succeeds? Or is that why you say the attack fails a certain percentage?
    2. A successful attack always advances because it seizes its objective. Does Attacker Advances mean he broke through or exploited?

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