Category Force Ratios

People keep referencing us on the 3-to-1 Rule

Several people in their articles have referenced a 3-to-1 rule and then reference us as the source. The latest example is in a German article on Taiwan: Storming Taiwan by force of arms? | Telepolis

Of course, we are the people who are saying the 3-to-1 rule is really not correct. They obviously do not read that far.

This is the reference they use: The Source of the U.S. Army Three-to-One Rule – The Dupuy Institute. My final sentence in that article is “Are we training the next generation of George B. McCellans?”

 

Various links related to the 3-to-1 rule:

Trevor Dupuy and the 3-1 Rule – The Dupuy Institute

The U.S. Army Three-to-One Rule – The Dupuy Institute

The 3-to-1 Rule in Histories – The Dupuy Institute

The 3-to-1 Rule in Recent History Books – The Dupuy Institute

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

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

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

Summation of Force Ratio Posts – The Dupuy Institute

JSTOR, Trevor Dupuy, Combat Data and the 3:1 Rule – The Dupuy Institute

The 3:1 Ratio – The Dupuy Institute

Army- and Division-level force ratio posts – The Dupuy Institute

The 3-to-1 rule and the War in Ukraine – The Dupuy Institute

We have been talking about this for a while. It appears that some people are not listening.

 

 

 

Army- and Division-level force ratio posts

I did five posts on analyzing force ratios using the campaign database. They are here:

Analysis for Force Ratios using the Campaign Data Base (CaDB) – The Dupuy Institute

Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued – The Dupuy Institute

Analysis of Force Ratios using the Campaign Data Base (CaDB) – second continuation – The Dupuy Institute

Analysis of Force Ratios using the Campaign Data Base (CaDB) – third continuation – The Dupuy Institute

Analysis of Force Ratios using the Campaign Data Base (CaDB) – fourth and final continuation – The Dupuy Institute

 

I think this is actually kind of a big deal, and will be presenting it at HADSS in July: Updated Schedule for HADSS 2024 – The Dupuy Institute and at HAAC in October:  Next Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8 – 10 October 2024 – The Dupuy Institute

 

Now, as part of that presentation, I do compare it to the division-level engagements. I have posted about this before. They are here:

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

The World War I Cases from the Division-level Database – The Dupuy Institute

The World War II Cases from the Division-level Database – The Dupuy Institute

Post-World War II Cases from the Division-level Database – The Dupuy Institute

Force Ratios at Kharkov and Kursk, 1943 – The Dupuy Institute

Force Ratios in the Arab-Israeli Wars (1956-1973) – The Dupuy Institute

 

And a summary of force ratios and 3-to-1 rule posts:

Summation of Human Factors and Force Ratio posts – The Dupuy Institute

Summation of Force Ratio Posts – The Dupuy Institute

JSTOR, Trevor Dupuy, Combat Data and the 3:1 Rule – The Dupuy Institute

 

And more stuff:

Force Ratios and CRTs – The Dupuy Institute

 

and most recently here: 

The 3-to-1 rule and the War in Ukraine – The Dupuy Institute

 

And in the first few chapters of my book War by Numbers.

 

Anyhow, we have discussed force ratios at the division-level and have now addressed them at the army-level by using the campaign databases. We do have the ability to look at them at Battalion and Company-level, which I will probably do at some point in the future. We do have a couple of databases to address this. They are no where near as robust as our division-level data base (752 cases) but as they are the only thing out there like that, they will have to do.

Battalion and Company Level Data Bases – The Dupuy Institute

At some point this will all probably be assembled in my future book More War by Numbers, which is half-written. Probably won’t get serious about that book until 2025. 

Overview of the War in Ukraine going into the Spring/Summer Offensive Season

I am being told by “advisors” to start blogging again about the war in Ukraine. “That is what everyone really cares about, not the little things that you have been posting about.”

Anyhow, my last direct blog post on the war was day 699: The Russo-Ukrainian War – Day 699 | Mystics & Statistics (dupuyinstitute.org). A more detailed post was done for day 589: The Russo-Ukrainian War – Day 589 | Mystics & Statistics (dupuyinstitute.org). Since then, I have not blogged extensively about the war. In part, because the changes and shifts over time were incremental and in part because I was busy getting a book done on The Siege of Mariupol. It is now day 811 of this war (or 2.2 years or over 70 million seconds). 

So, let’s look at the war at the moment:

Ukrainian Forces Deployed: At least 300,000 are deployed along the front line. Last year Zelenskyy was saying that they have over 700,000 troops mobilized. There is a difference between people mobilized and people deployed. There is a difference between regular army and reserves and militia. What is actually deployed is a wild-eyed guess. We actually don’t know, and the people that do know are not saying.

Russian Forces Deployed: Probably about 400,000 or more. Putin said 617K and was immediately contradicted by Ukraine intelligence, which said 450K. I tend to believe the latter figure, except I suspect the tendency of the intel people is to overestimate. So, “more than 400,000” become the SWAG figure I used. 

So, Russia may have a 1.5-to-1 force ratio advantage (say 450K to 300K) or it may be roughly closer to 1-to-1 (say 400K to 400K). Not sure. Either way, this does not seem decisive: Analysis of Force Ratios using the Campaign Data Base (CaDB) – fourth and final continuation | Mystics & Statistics (dupuyinstitute.org). In particular look at Analysis for Force Ratios using the Campaign Data Base (CaDB) | Mystics & Statistics (dupuyinstitute.org) and Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued | Mystics & Statistics (dupuyinstitute.org).

Now what are Russia’s advantages:

  1. Artillery ammunition
  2. Air support *
  • Note that Russia still has 2,000+ aircraft and has maintained around 500 or so in the theater. This is more than enough to counteract the handful of F-16s that the Ukrainians have received. 

What are Ukraine’s advantages:

  1. Artillery (once ammunition issue is resolved)
  2. Air Support with Drones?
  3. Observation/Intelligence ?
  4. Morale
  5. Training
  6. Doctrine ?

Each of these is a long discussion. I may get to them later. These points are covered in three slides of my updated briefing I am doing on Force Ratios at HADSS in UK in July Schedule for HADSS 2024 | Mystics & Statistics (dupuyinstitute.org) and at HAAC in October: Next Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8 – 10 October 2024 | Mystics & Statistics (dupuyinstitute.org).

But Russia has been advancing. They have over the last few months taken Avdiivka (Battle of Avdiivka is dated 10 October 2023 to 17 February 2024). They have pushed out a little beyond that. This is not militarily significant terrain, but it is of political value, as Avdiivka is near the non-operational Donetsk International Airport, and has been in Ukrainian hands since 2014. So, it has some importance if the Russian political objective is to seize the rest of Donetsk province before the start of peace negotiations.

Now, the Russians have been advancing along the border next to Kharkiv. Kharkiv is a significant objective, being the second largest city in Ukraine and the largest Russian-speaking city in Ukraine. So, far, they have been advancing just along the border, it is not certain that these areas were even defended. This is either preparatory advances in anticipation of a major offensive, is an intended distraction, or is just taking some local territory because they can. So far, we have not seen what I would call a major offensive. Probably conditions are not quite right to start such: When does the campaign season start? | Mystics & Statistics (dupuyinstitute.org).

Still, regardless of army size, it does appear that both sides are spending roughly equally on this war: Dueling Defense Budgets | Mystics & Statistics (dupuyinstitute.org)

All evidence points to this war being stalemated, but for the last few months, Russia has been slowly advancing.

  1. Is this because Russian gained an advantage due to a proper build up of its armed forces over 2023/24, unlike what it did in 2022/23? This has probably helped.
  2. Is this because Ukraine failed to properly mobilize over 2023/24, taking its eye off the ball, to use a sports analogy? Maybe. This is what some people claim: Russia is exploiting Ukraine’s lack of manpower to thin out the front line and seek a breakthrough, military expert says (msn.com).
  3. Is this because Russian had an abundance of artillery shells (thanks to North Korea) and were outshooting the Ukrainians 5-to-1 or 10-to-1 according to Ukrainians sources (which I was never able to verify). Maybe. Theoretically, over time, this Russian advantage will disappear and may turn into a Ukrainian advantage. U.S. shell production was 25,000 a month and is now being ramped up to 125K a month. Europe has similarly ramped up its shell production. Once this is up to speed, then this may turn from a Russian advantage to a Ukrainian one.
  4. Is this because the U.S. congress held up the $61 Billion dollar aid package for six months? It may have had an impact. This is, of course, what many of the people opposed to the delay were saying. Have no idea how true that is. It is the nature of the political discourse that the effects of not doing something get overstated. For example, the delay in getting F-16s and 300km range ATACMs. So, don’t know how vulnerable the U.S. delays in the aid package made Ukraine, especially as there were no such delays in the European aid or Ukraine’s own defense expenditures. Still, the delay was hard to justify.

So, Russia may hold a slight advantage for now. I suspect that advantage does not result in any major breakthroughs. Over time, I suspect that the Russian advantages will disappear, and things will stabilize. After that, it will be up to Ukraine to see if they can develop any advantages that allow them to move forward. Needless to say, if Ukraine can start to steadily advance, this war will go in their favor. On the other hand, if Russia can get one significant breakthrough operations this spring/summer, it could be a very different story. We will have to see as it is hard to predict.

Territory Fought Over:

It appears that the fighting will be stretched from Sumy or Kharkiv down to Zaporizhzhia. This is a long line. It does not appear that it will include Kyiv (except for missile attacks). It does not appear that it will include Odessa, which is now well behind Ukrainian defensive positions. It does appear that Ukraine has won the Battle for the western Black Sea. Not only has it deprived Russia access to that area after sinking Russia’s largest ship on the Black Sea, and damaging several others, but it is now regularly moving tankers and cargo transports from the Bosporus Strait to Odessa and back. Russia is not intercepting these. Added to that Russia has replaced the admiral in charge. This does happen when you lose the largest warship on the Black Sea (the cruiser Moskva) in addition to losing control of the western half of the Black Sea. 

It also does not appear that Kherson and Kherson province is a major theater. The Dnieper or Dnipro River divides that province, with Kherson and the Ukrainian Army on the north bank and the Russian army on the south bank. And then there is large Kakhovka Reservoir to the east of that the cuts off a significant section of front (see map). It does appear the effective front starts to the east of the reservoir (near Zaporizhzhia).

Analysis of Force Ratios using the Campaign Data Base (CaDB) – fourth and final continuation

This is the fourth and final continuation of our previous four posts: Analysis for Force Ratios using the Campaign Data Base (CaDB) | Mystics & Statistics (dupuyinstitute.org) and Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued | Mystics & Statistics (dupuyinstitute.org) and Analysis of Force Ratios using the Campaign Data Base (CaDB) – second continuation | Mystics & Statistics (dupuyinstitute.org) and Analysis of Force Ratios using the Campaign Data Base (CaDB) – third continuation | Mystics & Statistics (dupuyinstitute.org).  It is a part of a briefing on forces ratios I will be giving at HADSS in UK: Schedule for HADSS 2024 | Mystics & Statistics (dupuyinstitute.org) and at HAAC near DC: Next Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8 – 10 October 2024 | Mystics & Statistics (dupuyinstitute.org)

All of this analysis of the CaDB was for a reason, it was to determine if odds (force ratios) play out difference at higher level of operations (meaning army level). Are they different at the operational level vice the tactical level of warfare. The answer appears to be no. I do not know of anyone who has actually specifically explored this issue before, so I am not sure there is an existing or countervailing opinions out there.

Of course, my real interesting in looking at this (which I did last year) was because of the war in Ukraine and the upcoming Ukranian spring/summer offensive in 2023. I did brief this at the Second HAAC (October 2023) and in Norway (November 2023). The question I had was does a minor advantage in force ratios or combat power ratios lead to a bigger advantage at the operational level of combat. The answer appears to be no, as this was reinforced by limited movement of the front line in Russo-Ukrainian War since the fall of 2022. 

My final slide in the briefing was “Does this relate to the fighting in Ukraine?” I then asked two questions:

  1. What are the odds?
    1. What is the strength of the deployed Ukrainian Army?
    2. What is the strength of the Russian Army deployed in Ukraine?
  2. What other advantages does the Ukrainian attacker have?
    1. Artillery
    2. Air Support? (Drones?)
    3. Observations/Intelligence
    4. Morale
    5. Training

Now, as it appears that Russia will be on the offensive this spring/summer, then I may need to restructure this slide and also add another point “artillery ammunition supply.”

 

I am probably going to do some more blog posts on this subject, looking at other levels of combat.

 

Analysis of Force Ratios using the Campaign Data Base (CaDB) – third continuation

This is a continuation of our previous three posts: Analysis for Force Ratios using the Campaign Data Base (CaDB) | Mystics & Statistics (dupuyinstitute.org) and Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued | Mystics & Statistics (dupuyinstitute.org) and Analysis of Force Ratios using the Campaign Data Base (CaDB) – second continuation | Mystics & Statistics (dupuyinstitute.org). It is a part of a briefing on forces ratios I will be giving at HADSS in UK: Schedule for HADSS 2024 | Mystics & Statistics (dupuyinstitute.org) and at HAAC near DC: Next Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8 – 10 October 2024 | Mystics & Statistics (dupuyinstitute.org)

This is a continuation of Section IV of the briefing titled “What is necessary to have a good chance of generating a breakthrough?”

Having put together a table in the last post of force ratios and exchange ratios by outcome, I decided to take a moment to look at each of these cases. Each of these 94 cases is a fully mapped out campaign, many that you have heard of.

First looking at the 29 cases that were coded outcome IV (attacker advances). The average force ratios were 2.69-to-1 and the average exchange ratios were 1.51-to-1:

Force Ratio    Notes

0.58                 HUSKY – US Invasion of Sicily (39 days)

1.05                 HUSKY – UK Invasion of Sicily (39 days)

1.15                 Ardennes Allied Counteroffensive South II (15 days)

1.22                SHINGLE – Allied Landing at Anzio (10 days)

1.23                The West Bank 1967 (3 days)

1.34                 Ardennes Allied Counteroffensive South I (9 days)

1.38                 Graziani’s Advance (6 days)

1.44                 Moselle-Metz (6 days)

1.50                 Ardennes Allied Counteroffensive North (15 days)

 

1.75 to 1.98     3 cases

2.02 to 2.32     4 cases

2.51 to 2.92     6 cases

3.63 to 4.94     5 cases

6.04 to 10.00   2 cases

 

What I was really looking for is to see if there is any pattern in these low odds cases. Do they represent particularly odd or unusual cases? They really don’t. It does help to look at the cases though.

I then looked at those 21 cases that were coded as outcome five (defender penetrated). The average force ratios were 2.75-to-1 and the average exchange ratios were 0.64-to-1. There did not seem to be any unusual pattern, although there are a number of Arab-Israeli cases in these low odd penetrations. That is because human factors matter (morale, training, experience, leadership, motivation, etc.). In fact, they matter a lot (and are not considered in most U.S. DOD combat models). 

Force Ratio   Notes

0.78                The Cauldron: Battle of Gazala (21 days)

0.80                The Sinai, 1967 (5 days)

0.93                Golan Heights, 1967 (2 days)

1.01                BUFFALO: Anzio Breakout (9 days)

1.50                KADESH: Israeli Attack in the Sinai (8 days)

1.57                PO Valley Breakthrough (UK) (22 days)

1.67                Battle of Normandy, US Army (31 days)

 

1.82 to 1.93    2 cases

2.10 to 2.49    3 cases

2.52 to 2.92    2 cases

3.47 to 4.54    5 cases

6.58 to 7.01    2 cases

 

By the way, if someone is looking for some 3-to-1 rule in this data, good luck. Warfare is more complex than that.

One more post to come on this series of force ratios for army-level operations. Debating what I should discuss next.

Analysis of Force Ratios using the Campaign Data Base (CaDB) – second continuation

This is a continuation of our previous two posts: Analysis for Force Ratios using the Campaign Data Base (CaDB) | Mystics & Statistics (dupuyinstitute.org) and Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued | Mystics & Statistics (dupuyinstitute.org). It is a part of a briefing on forces ratios I will be giving at HADSS in UK: Schedule for HADSS 2024 | Mystics & Statistics (dupuyinstitute.org) and at HAAC near DC: Next Revised Schedule for the Third Historical Analysis Annual Conference (HAAC), 8 – 10 October 2024 | Mystics & Statistics (dupuyinstitute.org)

Section IV of the briefing is titled “What is necessary to have a good chance of generating a breakthrough?”

We coded some (94), but not all, of the 196 Army-level operations as to outcome. The outcomes are defined as (see War by Numbers for a more detailed description):

  • Outcome I is limited action
  • Outcome II is limited attack
  • Outcome III is failed attack
  • Outcome IV is attack advances
  • Outcome V is defender penetrated
  • Outcome VI is defender enveloped
  • Outcome VII is other.

These definitions are used to create the following table:

Outcome             I        II      III        IV       V       VI       VII

Cases                15        9     10        29      21      8          2

Force Ratios   1.88   3.35   1.80    2.69    2.75   1.86   8.50

Loss Ratios    3.77   1.56   1.66    1.51    0.64   0.05   0.01

 

Now, I put seven of those numbers in bold. They are worth looking at.

For those 10 operations that were coded as “failed attack”, the average force ratio is 1.80-to-1 while the average loss exchange ratio is 1.66-to-1 (i,e. the attacker lost more than the defender).

For those 29 operations that were coded as “attack advances”, the average force ratio is 2.69-to-1 while the average loss exchange ratio is 1.51-to-1.

For those 21 operations that were coded as “defender penetrated”, the average force ratio is 2.75-to-1 while the average loss exchange ratio is 0.64-to-1 (meaning the defender lost almost twice as many people as the attacker. Note that casualties included kill, wounded, missing and captured). 

One notices that the loss exchange ratio gets even more favorable in mop-up operations (defender enveloped). These are often the operation after “defender penetrated.”

A few other observations:

  1. Failed attacks tend to be lower average odds than successful ones (i.e. 1.80 versus 2.69 and 2.75).
  2. Attackers suffer higher losses than defenders until they are penetrated (1.61 and 1.51 versus 0.64)
  3. These are the same patterns as for division-level combat.

This last point is significant. Are operations with bodies of 60 thousand plus people the same as operations with 10-20 thousand people? At least in the patterns of force ratios required, loss exchange ratios, etc., they are very similar.

More to come (my briefings are long). The obvious next work step would be to finish coding the outcome of the other 102 operations in the CaDB. This is several man-weeks of effort. Not going to take that on now (I am trying to finish up another book).

Analysis for Force Ratios using the Campaign Data Base (CaDB) – continued

This is the continuation of our previous post: Analysis for Force Ratios using the Campaign Data Base (CaDB) | Mystics & Statistics (dupuyinstitute.org)

In that post was a table showing the force and losses differences between battles won by the attacker, the defenders and those that are drawn. Below is a follow-up table, showing the force ratios for all the campaigns:

Force Ratio      Attacker wins   Defender wins *   Draws **   Notes

0.30                    1                                                                  Suomussalmi

0.52 to 0.73        6                         2

0.77 to 1.00        7                         5

1.01 to 1.25      14                         3                            1

1.27 to 1.50        8                         3                            1

1.55 to 1.75        9                         3

1.78 to 2.00       11                        5

2.02 to 2.50       10                        6                             2

2.51 to 2.92         8                                                       1 ****

3.01 to 4.00         8                      4 ***                       1 ****    Loos (3.97) – defender wins

4.02 to 4.94         8

5.79 to 7.33         5

10.00 to 11.21     2

 

 

Notes:

* Removed from this seven engagements coded as “limited action” and “limited attack.” Their ratios were 0.58, 1.51, 2.90, 2.90, 3.58, 6.55, 12.38

** Removed from this 15 engagements coded as “limited action” and “limited attack.”

*** Three World War one engagements (Festubert at 3.01, Chemin des Dames at 3.33 and Loos at 3.97) and First Cassino (US) at 3.12.

**** Gothic Line Stalemate I at 2.58 and Gothic Line Statement II (US) at 3.08

 

These are slides 19 and 20 of my briefing. Now, I do not make conclusions on this slide in this briefing or even observations, but…. there are a few that could be made looking at this table. First, a three-to-one rule doesn’t really apply. Second, the defender never wins above four-to-one. Third, clearly there are a lot of factors included in these campaigns beyond simple manpower counts, and…. fourth…. you tell me?

The next slide of my briefing goes into the Section III of the briefing:  “Influence of Human Factors on Combat.” This is all drawn from War by Numbers… so… read the book. I will skip that and my next post will pick up at Section IV of the briefing “What is necessary to have a good chance of generating a breakthrough.” Probably do that post next Tuesday.

Analysis for Force Ratios using the Campaign Data Base (CaDB)

We have not made much use of our Campaign Data Base. (See: The History of the DuWar Data Bases | Mystics & Statistics (dupuyinstitute.org)). We used it as part of the Enemy Prisoner of War (EPW) studies back in 2000-2001 and have not made use it in the last two decades. But, for a presentation I did last year on force ratios, I blew the dust off of it because I wanted to see if force ratios were different for army-level operations than for division-level engagements. I mean, in the ETO data we have (116 cases), in the force ratios ranging between 1.15-to-1 to 1.88-to1 the attacker won 79% of the time (so much for needing 3-to-1). See: The 3-to-1 rule and the War in Ukraine | Mystics & Statistics (dupuyinstitute.org). So the question became, is the pattern we see at army-level different than division-level?

The Campaign Data Base consists of 196 campaigns from 1905 to 1991. They from two days in length to 155 days in length. Only three were over 60 days in length. The problem is that the database is not complete. We assembled it, used it once and have not used it again. There are some holes. For example, we only had the starting strength ratios calculated for 163 cases, we only had the total casualty ratios calculated for 162 and only had the winner calculated for 156 cases. In most cases the missing data is available but has not been assembled. The database just needs a little tender loving care. 

The average attacker strength (99 cases) was 188,909. The average defender strength (96 cases) was 95,497. This comes out to a 1.98-to-1 ratio.

The average attacker losses (176 cases) was 36,076. The average defender losses (172 case) was 47,004. This comes out to a 1-to-1.30 ratio.

The average attacker percent losses per day (163 cases) was 0.69%. The average defender percent losses per day (162 cases) was 1.85%. This comes out to a 1-to-2.68 ratio.

The starting strength ratio (163 cases) was 2.24 (2.24-to-1). The total casualty ratio was (164 cases) 1.35-to-1.

Now, the holes in the database become an issue. This are holes that can be filled given time (read: budget). We have 97 cases where the attacker is coded as the winner, and 38 cases where the defender wins. We have draws in 21 other cases. The rest (40 cases) are currently not coded.

Anyhow, this all produces the following table:

                                                   Attacker   Defender   Draw 

Av. Attacker Strength               208,835    156,821     171,312

Av. Defender Strength                91,486    100,729       96,582

       Ratio                                   2.28           1.56           1.77

 

Av. Attacker Losses                    34,630      69,098       15,232

Av. Defender Losses                   52,466      64,271       12,632

      Ratio                                     0.66           1.08           1.21

 

Av. Attacker % per day              0.73           0.98           0.32

Av. Defender % per day             2.59           0.98           0.39

      Ratio                                      0.28          1.00            0.82

 

Starting Strength Ratio              2.42          2.24            1.79

Casualty Ratio                            1.04          2.51            1.22

 

Contemplate for a moment what this data is telling you. A few observations:

  1. There is a difference in force ratios between winning and losing engagements (2.28-to-1 vice 1.56-to-1).
  2. There is a difference in casualties between winning and losing engagements (0.66-to-1 vice 1.08-to-1).
  3. The data for these army-level operations does not look significant different than for a division-level operation. This is significant.

I will stop here for a moment. This is from slides 12 – 18 for my force ratios briefing. There is more to come (because my briefings, like some of my books, are never short).

 

The 3-to-1 rule and the War in Ukraine

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.

Top Ten Blog posts in 2023

Happy New Year to all. 2023 is over. Not the best year for many in the world. Wanted to take a moment to list out our top ten blog posts for 2023 (based upon number of hits). They are:

  1. Wounded-to-killed ratios in Ukraine in 2022 | Mystics & Statistics (dupuyinstitute.org)
  2. U.S. Tank Losses and Crew Casualties in World War II | Mystics & Statistics (dupuyinstitute.org) – a blog post by Dr. Shawn Woodford from 2016.
  3. How many brigades did Ukraine start with war with? | Mystics & Statistics (dupuyinstitute.org) – this is actually clipped from my book The Battle for Kyiv.
  4. Population over Time (US vs USSR) | Mystics & Statistics (dupuyinstitute.org) – a blog post from 2018. I suspect this gets so many hits because this was the initial entry point for a number of people who periodically check on this blog and they continue to use this post to direct them to our blog.
  5. German versus Soviet Artillery at Kursk | Mystics & Statistics (dupuyinstitute.org) – another 2018 blog post.
  6. New WWII German Maps At The National Archives | Mystics & Statistics (dupuyinstitute.org) – a 2017 blog post by Dr. Shawn Woodford.
  7. How Does the U.S. Army Calculate Combat Power? ¯\_(ツ)_/¯ | Mystics & Statistics (dupuyinstitute.org) – another 2017 blog post by Dr. Shawn Woodford.
  8. Tank Loss Rates in Combat: Then and Now | Mystics & Statistics (dupuyinstitute.org) – a 2016 blog post by Dr. Shawn Woodford.
  9. U.S. Army Force Ratios | Mystics & Statistics (dupuyinstitute.org) – a 2018 blog post.
  10. The Russian Artillery Strike That Spooked The U.S. Army | Mystics & Statistics (dupuyinstitute.org) – a 2017 blog post by Dr. Shawn Woodford. It was the second most popular blog post in 2022.

Honorable mentions:

13. Wounded-To-Killed Ratios | Mystics & Statistics (dupuyinstitute.org) – this 2016 blog post was our most popular blog post in 2022.

16. Where Did Japan Go? | Mystics & Statistics (dupuyinstitute.org) – this 2018 blog post was sort of the culmination of our series of demographic blog posts. May revisit this subject again this year.

18. The Russo-Ukrainian War – Day 560 | Mystics & Statistics (dupuyinstitute.org) – for a while we did post daily (then two-three times a week) about the war in Ukraine. This was our most popular one of those posts. We will probably restart these again sometime this winter, like when there is a danger of the front lines again moving.

 

Anyhow, the blog has been quieter for the last three months. This was in part because I was on travel and in part because I needed to finish up a book (The Siege of Mariupol). To date, I have not learned how to multi-task and complete a book, so the book has had the priority. Sorry to anyone I have not responded to as a result.

The Battle for Kyiv book will be available in the U.S. on Amazon.com come 18 January 2024.