There is a 3-to-1 rule that some people quote from somewhere. We have discussed this before: Trevor Dupuy and the 3-1 Rule | Mystics & Statistics (dupuyinstitute.org) and The 3-to-1 Rule in Histories | Mystics & Statistics (dupuyinstitute.org) and The 3-to-1 Rule in Recent History Books | Mystics & Statistics (dupuyinstitute.org).
Trevor Dupuy’s argument was always that it took a combat power advantage to advance (attack successfully). This combat power calculations considers weapons, terrain, posture, air support, human factors, etc. Because of the current artillery shell shortages for the Ukrainian Army, logistics may also be a factor.
This combat power advantage often happens at 1.5-to-1 or 2-to-1. Usually is happens by around 2-to-1 (my conclusions – see War by Numbers). For example, here is my chart of force ratios for division-level combat in the European Theater of Operation (ETO) in 1944 from page 10 of War by Numbers:
FORCE RATIO…………………..RESULT……………..PERCENTAGE OF 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….ATTACK ADVANCES……………………..0…………………………………..42
Notice that the attacker succeeds at force ratios between 1.15-to-1 to 1.88-to-1 in 79% of the 48 cases of division-level combat. It gets better from there. The book also has force ratios from other theaters and campaigns. Some of this has been discussed here before: More Combat Results Tables from War by Numbers | Mystics & Statistics (dupuyinstitute.org) and Force Ratios at Kharkov and Kursk, 1943 | Mystics & Statistics (dupuyinstitute.org) and Force Ratios in the Arab-Israeli Wars (1956-1973) | Mystics & Statistics (dupuyinstitute.org).
A rigidly defined 3-to-1 rule tends to create an officer corps of McLellan’s. This rule-of-thumb is doing more damage than good as constructed.
What got my attention is that some people are trying to apply some 3-to-1 rule in Ukraine, and then come to the conclusion that one or the other side cannot advance because they don’t have a 3-to-1 force ratio. Yet, people have been advancing. In fall of 2022 Ukraine re-took Kherson and surrounding areas (see: 2022 Kherson counteroffensive – Wikipedia) and achieved a breakthrough at Balakliya that took back a significant portion of Donetsk province (see: Battle of Balakliia – Wikipedia) and conducted a successful offensive around Kharkiv (see: 2022 Kharkiv counteroffensive – Wikipedia). In 2023 Russia did advance on Bakhmut and took it (see: Battle of Bakhmut – Wikipedia) and in 2023/2024 Russia did advance on Avdiivka and took it (see: Battle of Avdiivka (2023–2024) – Wikipedia). I think in three for those five cases the attacker did not have anything approaching a 3-to-1 advantage. Of course, I have no reliable manpower statistics for either side in any of these five battles, so this is sort of a guess, as is most of the analysis and expert opinions on this war.
I do not know how many troops Ukraine currently has. I am guessing at least 300,000 deployed. Some people throw out figures in the 600-700,000 range. I have no idea if that are total mobilized estimates or total deployed estimates. The same with Russia, where figures of 600-700,000 are also thrown out, but not sure that is what is actually deployed in Ukraine. I am guessing some number closer to 300,000. Don’t really know, and don’t know who does for certain (see the “Force Involved’ section of this post: The Russo-Ukrainian War – Day 699 | Mystics & Statistics (dupuyinstitute.org)).
Anyhow, I gather the two sides are somewhere near parity in force size. They can certainly concentrate forces to get a local advantage. With current modern intelligence gathering capabilities, concentrating forces is often seen while it is happening and opposing side can respond promptly. So not sure where anyone can get their 3-to-1 advantage.
I did do a test recently, comparing the force ratios in a database over 700 division-level combat engagements to the force-ratios in over 100 Army-level operations. The question was whether force ratios and the success from those force ratios was different at division-level vice army-level. My tentative conclusions were that force ratios for army level campaigns had the “Same patterns as for division-level combat.”
Now, I have not written this effort up. I did brief it last year at the Second HAAC and did brief it in Norway. I will be briefing it again on Thursday, July 11 at HADSS in York (see: Historical Analysis for Defence and Security Symposiums (HADSS), 8 – 11 July in York, England | Mystics & Statistics (dupuyinstitute.org)) and for one last time at the Third HAAC (see: Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8-10 October 2024 | Mystics & Statistics (dupuyinstitute.org)). After that, I may write it up, either as a blog post or as a chapter in a book called More War By Numbers, which will probably be delayed until 2026 (see: Current book release schedule | Mystics & Statistics (dupuyinstitute.org), which I probably need to update).
Anyhow, the point is, anyone doing analysis for the situation in Ukraine based upon some 3-to-1 rule probably needs to reconsider their analysis.
C.A.L: “I did do a test recently, comparing the force ratios in a database over 700 division-level combat engagements to the force-ratios in over 100 Army-level operations. The question was whether force ratios and the success from those force ratios was different at division-level vice army-level. My tentative conclusions were that force ratios for army level campaigns had the “Same patterns as for division-level combat.””
-I’d think that the wonders of differential concentration would allow an army-level attacker to gain a better force ratio at divisional level. I’m tempted to say there’s something wrong there, but I can’t argue that 700 is too small a sample size…
On this, I think 3:1 is probably about right for a company-level attack.
For something completely different that you might find entertaining: A few minutes ago, I looked myself up on MSN/Bing. Along with the web results, their AI does a run-down for you. Here are my AI results (be patient, it takes a while to get to the amusing part):
“James Dean Glick is a retired military personnel and historian. His research interests span various historical topics, including military campaigns and the ways historians shape our understanding of the past. Here are some notable aspects of his work:
Fort Donelson and Historical Revisionism:
Glick’s master’s thesis delved into the Battle of Fort Donelson, examining how historians construct narratives and interpret events. His research sheds light on the process of historical revisionism
1. He has explored the question of how much of what happened during the Fort Donelson Campaign was accurately recorded by historians.
2. Published Works:
“Kursk: The Battle of Prokhorovka”: A book that delves into the pivotal World War II battle at Kursk.
“America’s Modern Wars: Understanding Iraq, Afghanistan, and Vietnam”: An exploration of contemporary conflicts.
“War by Numbers: Understanding Conventional Combat”: A study of numerical aspects in warfare.
“The Battle for Kyiv”: A work that examines the battle for the Ukrainian capital.
“Aces at Kursk”: Focusing on the experiences of fighter pilots during the Kursk battle.
“Hunting Falcon: The Story of WWI German Ace Hans-Joachim Buddecke”: A biography of an ace pilot from World War I3.
“The Siege of Mariupol”: A detailed account of the siege of Mariupol.
3. Clarksville Civil War Roundtable:
Glick has been a speaker at the Clarksville Civil War Roundtable, sharing insights into historical events and challenging prevailing narratives.
James Glick’s contributions to historical research and his engagement with military history continue to enrich our understanding of the past.”
… #1 and #3 are right, and the conclusion might be a bit overblown, but fine. For a second, I couldn’t think of where anything in #2 came from, but then I remembered “Kursk”. AI can’t tell the difference between people who post on the same site. Isn’t that special?
VR,
JDG
Outstanding. Eight books published. That is impressive. Are they any good?
Anyhow, I am probably going to post up a few more force ratio posts. I do have a smaller battalion-level and a company-level data base. Right now I am trying to finish up a book, so if I want to get it done that has take priority.
C.A.L: “Right now I am trying to finish up a book, so if I want to get it done that has take priority…”
-Let me know when you finally publish one. 😉
Chris it would be interesting to see what is usually/historically accomplished by having at least a 3:1 ratio.
Since you tend to look at offensive successes in terms of whether the attacker advanced, what does your modeling tell you about the probability of advancing at 1:1, 2:1, 3:1, 4:1, 5:1, . . . ? You already do that for some ranges of force ratios, but how about giving probabilities for ranges such as or 0.1:1 – 1:0:1, 1.1:1 – 2.0:1, 2.1:1 – 3.0:1, 3.1:1 – 4.0:1, . . . ?
Would doing the same analysis to predict distance advanced at each force ratio range (all other explanatory variables held constant, then held constant at different values) be useful or would that not be useful because the desired distance to be advanced might differ from case to case (for example, attacker only trying to cross the river or to reach the next town or to capture the city or to take the high ground or . . . or to push the enemy back across the border)?
How useful is the 3:1 ratio rubric if the desired goal is the destruction of the enemy force (rather than advancing some distance)?
What is the success goal of those who promote the 3:1 ratio? Do different proponents have different success goals in mind? Do they even have a success goal in mind? Is it just a mindless “3:1 or better is good, less than 3:1 is bad” or a similar rubric?
Yes, I know, you might get to such analysis after you’ve worked on various book writing projects.