Category European Theater of Operations (ETO)

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 ( and The 3-to-1 Rule in Histories | Mystics & Statistics ( and The 3-to-1 Rule in Recent History Books | Mystics & Statistics (

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:


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 ( and Force Ratios at Kharkov and Kursk, 1943 | Mystics & Statistics ( and Force Ratios in the Arab-Israeli Wars (1956-1973) | Mystics & Statistics (

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 (

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 ( 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 ( 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 (, 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.

Battlefield Tour of the Ardennes

Jay Karamales, the co-author of Against the Panzers and of the soon-to-be released Hunting Falcon, did record a video of his tour of the Ardennes in 1993. They are posted to YouTube. I just found out about it. So, the links to his YouTube videos are here:

Day 1, England to La Gleize (

Day 2, 3rd AD and Kauffman (

Day 2, Chateau Froid Cour and December 1944 Museum (

Day 2, Dom Bütgenbach (

Day 3, Peiper’s Route, Scheid to Stavelot (

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

American Thunder: U.S. Army Tank Design, Development and Doctrine in World War II

Just to give you a heads up, Richard Anderson, former researcher at TDI, is publishing the book American Thunder as of December 16, 2023. It will make for a great stocking stuffer for the right person. See: American Thunder: U.S. Army Tank Design, Development, and Doctrine in World War II: 9780811773812: Anderson, Richard: Books. This is his fourth book (American Thunder, Cracking Hitler’s Atlantic Wall, Artillery Hell, Hitler’s Last Gamble). He has been working on this last one for over fourteen years.

The table of contents are:

Introduction 1
Acknowledgements 4
U.S. Army World War II Procurement and Nomenclature 6
Part One: Organization, Development, and Production from Armistice Day to VJ Day 13
Chapter 1 Stagnation and Rebirth: The Lean Years from the End of the Great War to 1 September 1939 14
Chapter 2 State of the Art: The View Looking in, Sereno Brett and Arthur Hadsell 62
Chapter 3 Learning to Walk: 1 September 1939 to 30 June 1940 73
Chapter 4 State of the Art: The View Looking Out, the Spanish Civil War 94
Chapter 5 The Sleeping Giant Stirs: 1 July to 31 December 1940 107
Chapter 6 The Threat Perceived 129
Chapter 7 Explosive Growth…and Growing Pains: 1 January to 7 December 1941 137
Chapter 8 First Blood in the Pacific: The Fall of the Philippines, 1941-1942 161
Chapter 9 Giant Steps…and Stumbles: the First Year of the War, 1942 174
Chapter 10 Hard Knocks: The Battle of Happy Valley 223
Chapter 11 Learning Curve: the Second Year of the War, 1943 244
Chapter 12 More Hard Knocks: Early Lessons Learned 291
Chapter 13 Maturity: the Third Year of the War, 1944 303
Chapter 14 Europe: the Normandy Breakout 366
Chapter 15 Endgame, the Last Year of the War, 1945 383
Chapter 16 Europe: The Winter of Discontent 426
Chapter 17 Firestorm in the Pacific 456
Part Two: Controversies 484
Chapter 18 Death Traps? Myths of U.S. Tank Development in World War II 485
Chapter 19 The Great Tank Scandal? “It is said that it takes three of our Shermans to knock out a Tiger.” 494
Chapter 20 Bigger Guns? 506
Chapter 21 Where are the Tanks? The Real Tank Scandal 524
Chapter 22 What’s in a Name? 546
Conclusion 552
Appendix I: Other Ordnance Combat Vehicles 556
Tank Recovery Vehicles 556
Mine Clearing Vehicles 558
Flame Throwing Vehicles 564
Tank Rocket Launchers 572
Engineer Assault Vehicles 574
Remanufactured Tanks 576
Appendix II: Lend-Lease 578
Appendix III: Tank ‘T’ Numbers Assigned by Ordnance, 1926-1945 590
Appendix IV: Tank Model Year, ‘Mark’, and ‘M’ Numbers Assigned by Ordnance, 1928-1945 591
Appendix V: The Cost of Ordnance 592
Appendix VI: The Cost of War: U.S. Army Armored Personnel and Tank Losses in World War II 596
Appendix VII: Firing Tests 625
Shoeburyness Test, 23 May 1944 (1st ETOUSA Test) 625
Balleroy Test, 10 July 1944 (2d ETOUSA Test) 628
1st Isigny Test, 12-30 July 1944 (3d ETOUSA Test) 629
2nd Isigny Test, 19-21 August 1944 (4th ETOUSA Test) 632
703d Tank Destroyer Battalion Test, 5-9 December 1944 636
Bibliography 638
Primary Sources 638
Armored and Infantry School Student Papers 638
Other Primary Sources 638
Secondary Sources 650
Newspaper, Magazine, and Journal Articles 660
Websites 664
Videos 666
Table 1: Organization of the Cavalry Regiment (Mechanized) 1935. 25
Table 2: Tank Production 1921-1933 60
Table 3: Tank Production 1934-1 September 1939 61
Table 4: Tank Production 1 September 1939-30 June 1940 93
Table 5: Armored Force General Staff, June 1940. 107
Table 6: Organization of the Armored Force, July 1940. 108
Table 7: The National Guard Tank Battalions 112
Table 8: Organization of the Armored Division, 1940. 114
Table 9: Tank Production 1 July-31 December 1940 128
Table 10: Medium Tank M3/Grant I Production 146
Table 11: Medium Tank M3A1 Production 146
Table 12: Medium Tank M3A2 Production 147
Table 13: Medium Tank M3A3 Production 147
Table 14: Medium Tank M3A4 Production 148
Table 15: Medium Tank M3A5 Production 148
Table 16: Medium Tank M3-Series Production 148
Table 17: British Designations for the Medium Tank M3 Series 149
Table 18: Light Tank M3-Series Production 151
Table 19: Tank Production 1 January-31 December 1941 160
Table 20: Organization of the Armored Division, 1942. 182
Table 21:Medium Tank M4 (75mm) Production 191
Table 22: Medium Tank M4A1 (75mm) Production 192
Table 23: Medium Tank M4A3 (75mm) Production 194
Table 24: Medium Tank M4A4 (75mm) Production 195
Table 25: Medium Tank M4A5 (RAM) Production 198
Table 26: Medium Tank M4A6 (75mm) Production 198
Table 27: British Designations for the Medium Tank M4-series 199
Table 28: Light Tank M5-series Production 202
Table 29: British Designations for Light Tanks M3 and M5 203
Table 30: Tank Production 1 January-31 December 1942 222
Table 31: Production of the T10 Shop Tractor (CDL) 248
Table 32: The Armored Group Headquarters 251
Table 33: Unit Assignments to the Armored Divisions before the 1943 Reorganization 252
Table 34: Organization of the Armored Division, 1943. 253
Table 35: Reorganization of the Armored Regiments, 1943 253
Table 36: Unit Assignments to the Reorganized Armored Divisions 255
Table 37: Tank Loading Capacity of Allied Landing Craft and Ships 1945 278
Table 38: Light Tank T9E1 Production 279
Table 39: Tank Production 1 January-31 December 1943 290
Table 40: Organization of the 741st Tank Battalion for D-Day, 6 June 1944. 314
Table 41: Availability of Dozer Blades in the ETOUSA 316
Table 42: Allocation of 76mm and 105mm Armed Medium Tanks January- May 1944 328
Table 43: ‘Ultimate Design’ Medium Tank M4A3 (75mm) Wet Production 340
Table 44: ‘Ultimate Design’ Medium Tank M4-Series (76mm) Wet Production 341
Table 45: ‘Ultimate Design’ Medium Tank M4-Series (105mm) Production 342
Table 46: Status of ETOUSA Medium Tanks, 20 October – 20 December 1944 342
Table 47: Medium Tank T23 Production 344
Table 48: Light Tank M24 Production 345
Table 49: Medium Tank T25 and T25E1 Production 346
Table 50: Assault Tank M4A3E2 Production 355
Table 51: Losses of the Medium (Assault) Tank M4A3E2 358
Table 52: Heavy Tank T1-Series Production 361
Table 53: Tank Production 1 January – 31 December 1944 365
Table 54: Operational Tank Strength of VII Corps on the eve of Operation COBRA. 370
Table 55: Wartime Deployment and Inactivation of the Tank Battalions 384
Table 56: Organization of the Armored Division, 1945. 388
Table 57: Heavy Tanks T26E3 issued to 3d Armored Division 20 February 1944 396
Table 58: Status of T26E3 as of 14 April 1945 402
Table 59: Heavy Tank T26E3 allocations and on hand, April 1945 402
Table 60: Status of Heavy Tanks T26, 5 May 1945 403
Table 61: Light Tanks M24 “on hand” with 12th Army Group, 3 March – 11 April 1945 409
Table 62: Allocation of Light Tanks M24 to the 12th Army Group, 12 November 1944-213 April 1945 409
Table 63: Light Tanks M24 with 12th Army Group Units, 28 April 1945 410
Table 64: American 17-pdr Tank Conversions 412
Table 65: Medium Tank M4-Series Production by Manufacturer 417
Table 66: Total OCO-D and OMP Medium Tank M4-series Production 417
Table 67: Heavy Tank T26-Series Production 420
Table 68: Tank Production 1 January – 31 August 1945 424
Table 69: Tank Production 1 July 1940-31 August 1945 424
Table 70: Change in Tank Strength, 5th Armored Division, 2200 24 November-8 December 1944. 436
Table 71: Status of HVAP as of 14 February 1945 516
Table 72: Special Projectiles Manufactured for the 3-inch, 76mm, and 90mm guns (1,000’s). 516
Table 73: Principal Ordnance Tank Periscope Systems. 520
Table 74: Principal Ordnance Tank and GMC Telescopes. 521
Table 75: Known Medium Tank Deliveries to the ETOUSA, June-September 1944 531
Table 76: 12th Army Group Monthly Medium Tank Status 540
Table 77: Average Daily Medium Tank Strength in 12th Army Group 541
Table 78: First U.S. Army Tank Allocations Oct 44-Apr 45 543
Table 79: Third U.S. Army Tank Allocations Oct 44-Apr 45 543
Table 80: Ninth U.S. Army Tank Allocations Oct 44-Apr 45 543
Table 81: Fifteenth U.S. Army Tank Allocations Jan-Apr 45 543
Table 82: 12th Army Group Tank Allocations Nov 44-Jan 45 544
Table 83: Total Tank Allocations to 12th Army Group Oct 44-Apr 45 544
Table 84: On Hand and Redeployment of ETOUSA Tank Stocks 31 May-31 August 1945. 545
Table 86: Tank Recovery Vehicle Production 557
Table 87: Mechanized and Main Armament Flamethrower Production 572
Table 88: Medium Tank M4-series Remanufactured Production 576
Table 89: Light Tank M5, M5A1, and M3A3 Remanufactured Production 577
Table 90: Medium Tank M3 Allocation to the British Empire as of July 1942 579
Table 91: 21st Army Group Sherman Tank Holdings, 21 January 1945 581
Table 92: Lend-Lease Tank Deliveries to Britain according to Hunnicutt. 582
Table 93: Lend-Lease Tanks Deliveries to the UK according to ASF 583
Table 94: Canadian Tank Situation in Northwest Europe, May and December 1944 585
Table 95: Lend-Lease Tanks Shipped to the USSR 586
Table 96: Lend-Lease Tanks Shipped to the French 588
Table 97: Lend-Lease Tank Shipments by Type and Recipient as Recorded by the War Department 588
Table 98: Estimated Value of Army Ordnance Procurement of Combat Vehicles ($-thousands) 594
Table 99: Armored Division Total Personnel Losses 598
Table 100: U.S. Tank Casualties by Theater and Year as Calculated by ORO 599
Table 101: 5th Echelon Maintenance Awaiting Completion at ETOUSA Depots 600
Table 102: Total Work Orders by First U.S. Army Ordnance Maintenance 600
Table 103: 12th Army Group Tank Losses by Armies 601
Table 104: 12th Army Group Medium Tank Losses 601
Table 105: Armored Division and Tank Battalion Tank Losses 602
Table 106: Mechanized Cavalry Tank and Armored car Losses ETOUSA 604
Table 107: First U.S. Army Tank Loss by Type, 6 June 1944 – 8 May 1945 604
Table 108: First U.S. Army Strength and Losses, June-July 1944 605
Table 109: First French Army Medium Tank Losses 606
Table 110: U.S. Army Tank Losses in North Africa and Sicily 606
Table 111: U.S. Army Tank Losses in the Pacific 607
Table 112: U.S. Marine Corps Tank Losses in the Pacific 608
Table 113: U.S. Army Tank and Armored Vehicle Losses in the European Theater of Operations 609
Table 114: First Army Operational Tanks and Losses 615
Table 115: Third Army Operational Tanks and Losses 618
Table 116: Ninth Army Operational Tanks and Losses 620
Table 117: Fifth Army Tank Losses, Italian Campaign 623

The 88th Infantry Division Stole a Cake

Speaking of war crimes, I spotted this story today: US Army ‘returns’ cake to Italian woman for 90th birthday.

The 88th Infantry Division in Italy in 1944 in one of the units we have studied in some depth. There was a report done on it in 1981. See: 88. Performance of The 88th Infantry Division in World War II: Factors Responsible for its Excellence (1981) (MRA&L) – Pages: 120 at

This is also discussed on pages 114-121 of Trevor Dupuys Understanding War. He ended up conducting an analysis of the CEVs (Combat Effectiveness Values) of seven U.S. units, five UK units and 12 Germans units in Italy during WWII. This was done using his Quantified Judgment Method of Analysis (QJMA). Of those 24 units, the 88th Infantry Division was rated the fifth highest, based upon 4 engagements. It had a CEV of 1.14. It was the highest rated of all the allied units.

Ordering info is here:

Related posts:

Human Factors In Warfare: Combat Effectiveness | Mystics & Statistics (

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. 


Normandy 1944: German Military Organization, Combat Power and Organizational Effectiveness

Niklas Zetterling’s revised and update version of his excellent book Normandy 1944 is being re-issued. According to it will be available January 10, 2020. The link is here: Normandy 1944

It is set up to “look inside” so you can get some idea what is in there. It is of course, not another war story but a two part discussion on “Campaign Analysis” and “German Combat Formations.”

The “look inside” feature did not include an ability to search the text, so I was not able to check the really important stuff, like how many times Trevor Dupuy and I are mentioned in the book. I am graciously acknowledged in the introduction (as is Richard Anderson). Now, I did write an appendix for the original book. Always the gentleman, Niklas did ask my permission to remove it from this edition.

The book does include a discussion of the relative combat efficiency of the German forces compared to British and U.S. units, always a sensitive subject. We have never invested a lot of time in analyzing Normandy. Most of our analysis of this subject is from Italy 1943-44, Ardennes (Battle of the Bulge) 1944-45 and Kharkov and Kursk 1943 (and shown in War by Numbers). So this is a nice independent look at the subject using additional data from a different campaign by a different scholar.

The U.S. Army Three-to-One Rule

Various Three-to-one rules of thumbs have existed in the U.S. Army and in writings possibly as early as the American Civil War (1861-1865). These are fine as “rules of thumb” as long as one does not take them seriously and understands what they really mean. But, unfortunately, we have now seen something that is a loose rule of thumb turned into a codified and quantified rule. This is annoyingly overstating its importance and as given in U.S. Army manuals, is patently false.

The U.S. Army has apparently codified the “three-to-one rule” in its documentation and has given it a value. In the 2014 edition of FM 6-0, paragraph 9-103, it states that “For example, historically, defenders have over a 50 percent probability of defeating an attacking force approximately three times their equivalent strength.” This statement, on the surface, simply is incorrect. For example, the following table from my book War by Numbers is drawn from a series of 116 division-level engagements in France in 1944 against the Germans (see War by Numbers, page 10) They show the following relationship between force ratio and outcome:

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


Now these engagements are from fighting between the U.S., UK and Germany in France and Germany in 1944. These are engagements between forces of roughly equal competence. As can be seen, based upon 42 division-level engagements, in all cases of attacks at three-to-one (more specifically 2.71-to-1 and greater), the attacker advanced. Meaning in all cases of attacks at three-to-one, the attacker won. This directly contradicts the statement in FM 6-0, and contradicts it based upon historical data.

This is supplemented by the following two tables on the next page of War by Numbers. The first table shows the German performance when attacking Soviet units in 1943.

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


The next table shows the Soviet performance when attacking German units in 1943:

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


These charts are from the fighting around Kharkov in February, March and August of 1943 and the fighting during the Battle of Kursk in July 1943. It is 73 engagements between the German and Soviet armies.

Now, there is a clear performance difference between the German and the Soviet armies at this time. This is discussed in considerable depth in War by Numbers and will not be addressed here. But, what it amounts to is that the German Army has an advantage in the casualty exchange and that advantage also shows up in the outcomes of the battles, as show above. If they attacked at two-to-one odds are greater, they would win. The Soviets attacking at the same odds would win only 56 percent of the time. Clearly, at the division-level, in a unit to unit comparison, the Germans were two or three times better than their Soviet opponents.

Still, even in the worse case, which is the Soviets attacking the Germans, we do not get to the claim made in FM 6-0, which is the defender won 50% of the time when attacked at three-to-one. In fact, the Soviets managed to win 50% of the time when attacking at 1.20 to 1.65-to-1. Something is clearly wrong with the statement in FM 6-0.

Now, at the time I wrote War by Numbers, I was not aware of this sentence planted in FM 6-0 and so therefore did not feel a need to respond to the “three-to-one rule.” It is a rule of thumb, not completely without value, that had been discussed before (see Dupuy, Understanding War, pages 31-37). I thought this issue was properly understood in the U.S. analytical and defense community, therefore I did not feel a need to address it further. It turns out that I do. So, I will take a moment to tap into our databases and properly address this using all the resources at my disposal. This will be in subsequent blog posts.

Dupuy on D-Day

A LCVP from the U.S. Coast Guard-manned USS Samuel Chase disembarks troops of Company E, 16th Infantry, 1st Infantry Division (the Big Red One) at the Fox Green section of Omaha Beach on the morning of 6 June 1944. American soldiers encountered the newly formed German 352nd Division. During the initial landing, two-thirds of Company E became casualties.

Today is the 75th Anniversary of D-Day, the invasion of Normandy by U.S., British, Canadian and other allied forces. The American who announced the D-Day invasion on Tuesday, 6 June 1944 was the journalist, soldier and historian, R. Ernest Dupuy (1887-1975) of New York. The announcement from SHAEF can be heard here (Dupuy’s announcements starts at 2:00):

Under the command of General Eisenhower, Allied naval forces, supported by strong air forces, began landing Allied armies this morning on the northern coast of France.

He was the father of Trevor N. Dupuy, the founder of The Dupuy Institute.

R. Ernest Dupuy’s obituary is here: