Category Modeling, Simulation & Wargaming

How Attrition is Calculated in the QJM vs the TNDM

French soldiers on the attack, during the First World War. [Wikipedia]

[The article below is reprinted from December 1996 edition of The International TNDM Newsletter. It was referenced in the recent series of posts addressing the battalion-level validation of Trevor Dupuy’s Tactical Numerical Deterministic Model (TNDM).]

How Attrition is Calculated in the QJM vs the TNDM
by Christopher A. Lawrence

There are two different attrition calculations in the Quantified Judgement Model (QJM), one for post-1900 battles and one for pre-1900 battles. For post-1900 battles, the QJM methodology detailed in Trevor Dupuy’s Numbers, Predictions and War: Using History to Evaluate Combat Factors and Predict the Outcome of Battles (Indianapolis; New York: The Bobbs-Merrill Co., 1979) was basically:

(Standard rate in percent*) x (factor based on force size) x (factor based upon mission) x (opposition factor based on force ratios) x (day/night) x (special conditions**) = percent losses.

* Different for attacker (2.8%) and defender (1.5%)
** WWI and certain forces in WWII and Korea

For the attacker the highest this percent can be in one day is 13.44% not counting the special conditions, and the highest it can be for the defender is 5.76%.

The current Tactical Numerical Deterministic Model (TNDM) methodology is:

(Standard personnel loss factor*) x (number of people) x (factor based upon posture/mission) x (combat effectiveness value (CEV) of opponent. up to 1.5) x (factor for surprise) x (opposition factor based on force ratios) x (factor based on force size) x (factor based on terrain) x (factor based upon weather) x (factor based upon season) x (factor based upon rate of advance) x (factor based upon amphibious and river crossings) x (day/night) x (factor based upon daily fatigue) = Number of casualties

* Different for attacker (.04) and defender (.06)

The special conditions mentioned in Numbers, Predictions, and War are not accounted for here, although it is possible to insert them, if required.

All these tables have been revised and refined from Numbers, Predictions, and War.

In Numbers, Predictions and War, the highest multiplier for size was 2.0, and this was for forces of less than 5,000 men. From 5,000 to 10,000 is 1.5 and from 10,000 to 20,000 is 1.0. This formulation certainly fit the data to which the model was validated.

The TNDM has the following table for values below 15,000 men (which is 1.0):

The highest percent losses the attacker can suffer in a force of greater than 15,000 men in one day is “over” 100%. If one leaves out three large multipliers for special conditions—surprise, amphibious assault, and CEV—then the maximum percent losses is 18%. The multiplier for complete surprise is 2.5 (although this degraded by historical period), 2.00 for amphibious attack across a beach, and 1.5 for enemy having a noticeable superior CEVs In the case of the defender, leaving out these three factors, the maximum percent casualties is 21.6% a day.

This means at force strengths of less than 2,000 it would be possible for units to suffer 100% losses without adding in conditions like surprise.

The following TNDM tables have been modified from the originals in Numbers, Predictions, and War to include a casualty factor, among other updates (numbers in quotes refer to tables in the TNDM, the others refer to tables in Numbers, Predictions, and War):

Table 1/”2”: Terrain Factors
Table 2/“3″: Weather Factors
Table 3/“4″: Season Factors
Table 5/”6″: Posture Factors
Table 6/“9″: Shoreline Vulnerability
Table 9/”11″: Surprise

The following tables have also been modified from the original QJM as outlined in Numbers, Predictions, and War:

Table “1”: OLl’s
Table “13”: Advance Rates
Table “16”: Opposition Factor
Table “17”: Strength/Size Attrition Factors
Table “20”: Maximum Depth Factor

The following tables have remained the same:

Table 4/“5”: Effects of Air Superiority
Table 7/“12”: Morale Factors
Table 8/“19”: Mission Accomplishment
Table “14″: Road Quality Factors
Table “15”: River or Stream Factor

The following new tables have been added:

Table “7”: Qualitative Significance of Quantity
Table “8”: Weapons Sophistication
Table “10”: Fatigue Factors
Table “18”: Velocity Factor
Table “20”: Maximum Depth Factor

The following tables has been deleted and the effect subsumed into another table:

unnumbered: Mission Factor
unnumbered: Minefield Factors

As far as I can tell, Table “20”: Maximum Depth Factor has a very limited impact on the model outcomes. Table “1”: OLIs, has no impact on model outcomes

I have developed a bad habit, if I want to understand or know something about the TNDM, to grab my copy of Numbers, Predictions, and War for reference. As shown by these attrition calculations, the TNDM has developed enough from its original form that the book is no longer a good description of it. The TNDM has added in an additional level of sophistication that was not in the QJM.

The TNDM does not have any procedure for calculating combat from before 1900. In fact, the TNDM is not intended to be used in its current form for any combat before WWII.

Summation of Human Factors and Force Ratio posts

The following five posts make up our discussion of the impact of Human Factors on Force Ratios.

Force Ratios at Kharkov and Kursk, 1943

Force Ratios in the Arab-Israeli Wars (1956-1973)

Measuring Human Factors based upon Casualty Effectiveness

Measuring Human Factors based on Casualty Effectiveness in Italy 1943-1944

The Performance of Armies in Italy, 1943-44

As a result of a comment by Tom from Cornwall, we ended up adding three posts to this discussion that looked at terrain and amphibious operations and river crossings in Italy:

German attacks in Italy by Terrain (1943-44)

Amphibious and River Crossing attacks in Italy 1943-44

Amphibious and River Crossing Engagements in the Italian Campaign 1943-44

The previous posts on this discussion on force ratios are presented here. These were the posts examining the erroneous interpretation of the three-to-one rule as presented in Army FM 6-0 and other publications:

Summation of Force Ratio Posts

We are going to end this discussion for now. There is some additional data from the European Theater of Operations (ETO) and Ardennes that we have assembled, but it presents a confusing picture. This is discussed in depth in War by Numbers (pages 32-48).

I am assembling these discussions on force ratios and terrain into the opening chapters for a follow-on book to War by Numbers.

The Performance of Armies in Italy, 1943-44

 

Polish Sherman III after battle on Gothic Line, Italy, September 1944

Having looked at casualty exchanges from my book War by Numbers and in the previous post, it is clear that there are notable differences between the German and Soviet armies, and between the Israeli and Arab armies. These differences show up in the force ratio tables, in the percent of wins, and in the casualty exchange ratios. As shown above, there is also a difference between the German and the U.S. and UK armies in Italy 1943-44, but this difference is no where to the same degree. These differences show up in the casualty exchange ratios. They also will show up in the force ratio comparisons that follow.

The Italian Campaign is an untapped goldmine for research into human factors. In addition to German, American and British armies, there were Brazilian, Canadian, French, French Algerian, French Moroccan, Greek, Indian, Italian, New Zealander, Polish, and South African forces there, among others like the Jewish brigade. There was also an African-American Division and a Japanese-American battalion and regiment actively engaged in this theater. Also the German records are much better than they were in the second half of 1944. So, the primary source data these engagements are built from are better than the engagements from the ETO.

We have 137 engagements from the Italian Campaign. There are 136 from 9 September to 4 June 1944 and one from13-17 September 1944. Of those, 70 consisted of the Americans attacking, 49 consisted of armed forces of the United Kingdom in the offense, and 18 consisted of the Germans attacks, often limited and local counterattacks (eight attacks against the United States and ten attacks against the UK). So, let us compare these based upon force ratios.

American Army attacking the German Army, Italy 1943-44

(70 cases in the complete data set, 62 cases in the culled data set)

 

Force Ratio……………Percent Attacker Wins………………..Number of Cases

1.22 to 1.49……………………….42%………………………………………..26

    Culled…………………………………48…………………………………………21[1]

1.50 to 1.95………………………..43………………………………………….30

    Culled…………………………………48…………………………………………27[2]

2.02 to 2.23………………………100…………………………………………..4

2.58 to 2.96………………………..71…………………………………………..7

3.04…………………………………100…………………………………………..1

Gap in data

4.11 to 4.25………………………100……………………………………………2

 

There were seven cases of engagements coded as “limited attacks” and one case of “other”. These eight cases are excluded in the table above on those lines in italics.

Needless to say, this is a fairly good performance by the American Army, with them winning more than 40% the attacks below two-to-one and pretty winning most of them (86%) at odds above two-to-one.

 

British Army attacking the German Army, Italy 1943-44

(49 cases in the complete data set, 39 cases in the culled data set)

 

Force Ratio………………..Percent Attacker Wins………………..Number of Cases

0.85………………………………….0%……………………………………………….1

1.17 to 1.41………………………60…………………………………………………5

1.50 to 1.69………………………33…………………………………………………3

2.01 to 2.49………………………50……………………………………………….12

    Culled………………………………..86…………………………………………………7[3]

2.77……………………………….100………………………………………………….1

3.18 to 3.49………………………30………………………………………………..10

    Culled……………………………….43…………………………………………………7[4]

3.50 to 3.73……………………..80…………………………………………………..5

4.23 to 4.99……………………..42…………………………………………………12

    Culled………………………………50…………………………………………………10[5]

 

There were five cases of limited action and five cases of limited attack. These ten cases are excluded in the table above on those lines in italics.

This again shows the difference in performance between the American Army and the British Army. This is always an uncomfortable comparison, as this author is somewhat of an anglophile with a grandfather from Liverpool; but data is data. In this case they won 44% of the time at attacks below two-to-one, which is similar to what the U.S. Army did. But then, they only won only 63% of the time at odds above two-to-one (using the culled data set). This could just be statistical anomaly as we are only looking at 30 cases, but is does support the results we are seeing from the casualty data.

What is interesting is the mix of attacks. For the American Army 77% of the attacks were at odds below two-to-one, for the British Army only 23% of the attacks were at odds below two-to-one (using the culled data sets). While these 99 cases do not include every engagement in the Italian Campaign at that time, they include many of the major and significant ones. They are probably a good representation. This does probably reflect a little reality here, in that the British tended to be more conservative on the attack then the Americans. This is also demonstrated by the British lower average loss per engagement.[7]

The reverse, which is when the Germans are attacking, does not provide a clear picture.

German Army attacking the American and British Army, Italy 1943-44 – complete data set (18 cases)

Force Ratio…………………..Percent Attacker Wins…………………Number of Cases

0.72 to 0.84………………………….0%………………………………………………7

1.17 to 1.48………………………..50…………………………………………………6

1.89…………………………………….0…………………………………………………1

2.16 to 2.20………………………..50…………………………………………………2

Gap in data

3.12 to 3.24………………………..50…………………………………………………2

 

The Germans only win in 28% of the cases here. They win in 13% of the engagements versus the U.S. (8 cases) and 40% of the engagements the UK (10 cases). Still, at low odds attacks (1.17 to 1.48-to-1) they are winning 50% of the time. They are conducting 78% of their attacks at odds below two-to-one.

In the end, the analysis here is limited by the number of cases. It is hard to draw any definitive conclusions from only 18 cases of attacks. Clearly the analysis would benefit with a more exhaustive collection of engagements from the Italian Campaign. This would require a significant investment of time (and money).[8]

Regiment de Trois-Rivieres tanks entering the ruins of Regabuto, August 4th, 1943. Source: http://www.sfu.ca/tracesofthepast/wwii_html/it.htm

————————–

[1] There were four limited attacks that resulted in three defender wins and a draw. There was one “other” that was an attacker win.

[2] There three limited attacks that resulted in two defender wins and a draw.

[3] There were four “limited actions” that were defender wins and one “limited attack” that was a defender win.

[4] There as one “limited action” that was a defender win and two “limited attacks” that were defender wins.

[5] There were two “limited attacks” that were defender wins.

[6] The author’s grandfather was born in Liverpool and raised in Liverpool, England and Ryls, Wales. He served in the British merchant marine during World War I and afterwards was part of the British intervention at Murmansk Russia in 1918-1919. See the blog post:

Murmansk

[7] See War by Numbers, pages 25-27. The data shows that for the Americans in those 36 cases where their attack was successful they suffered an average of 353 casualties per engagement. For the 34 American attacks that were not successful they suffered an average of 351 casualties per engagement. For the UK, in the 23 cases where their attack was successful, the UK suffered an average of 213 casualties per engagement. Of the 26 cases where the UK attacks were not successful, they suffered an average of 137 casualties per engagement.

[8] Curt Johnson, the vice-president of HERO, estimated that it took an average of three man-days to create an engagement. He was involved in developing the original database that included about half of the 137 Italian Campaign engagements. My estimation parameter, including the primary source research required to conduct this is more like six days. Regardless, this would mean that just to create this 137 case database took an estimated 411 to 822 man-days, or 1.6 to 3.3 man-years of effort. Therefore, to expand this data set to a more useful number of engagements is going to take several years of effort.

Amphibious and River Crossing Engagements in the Italian Campaign 1943-44

Now, there were a few amphibious operations and major river crossing operations during the Italian Campaign. These are significant enough that we should examine them separately. Among the 141 Italian Campaign engagements there are three amphibious operations and 16 river crossing operations. These are outlined in our previous post:

Amphibious and River Crossing attacks in Italy 1943-44

This is a small number of cases, but does seem to show that the defender has an advantage when defending against amphibious assaults and river crossings. To compare them to the rest of the engagements:

 

Amphibious Operations Comparison – Italian Campaign 1943-44:

………………………………………………………………..Average..Average

……………………………………………………Percent…Percent…Attacker..Defender

………………………………….……..Cases….Wins…….Advance..Losses…Losses

U.S./UK Attacking – Amphibious…..3……….100………..100………..417……….105

UK Attacking – other RM…………….10………..40………….67…………382………152

U.S. Attacking – other RM…………..20………..65………….80…………341………430

 

………………………………………….……………Force….Exchange

………………………………….……..Cases…….Ratio…..Ratio

U.S./UK Attacking – Amphibious…..3……………3.45…….3.98-to-1

UK Attacking – other RM…………….10…………..1.94…….2.51-to-1

U.S. Attacking – other RM…………..20…………..1.69…….0.79-to-1

 

River Crossings Comparison – Italian Campaign 1943-44:

………………………………………………………………..Average..Average

……………………………………………………Percent…Percent…Attacker..Defender

………………………………….……..Cases….Wins…….Advance..Losses…Losses

UK Attacking – River Crossing……8………….63………….67………..169………154

UK Attacking – other FM…………….6………….50………….67………..306………284

U.S. Attacking – River Crossing…..6…………67………….67…………388……..112

U.S. Attacking – Other RM………..17…………59………….76…………374……..477

German Attacking – River Crossing..2……….50………..100…………955………507

German Attacking – Other FM………5………..40………….40…………756………805

 

………………………………………….……………Force….Exchange

………………………………….……..Cases…….Ratio…..Ratio

UK Attacking – River Crossing……8……………2.20…….1.10-to-1

UK Attacking – other FM…………….6……………1.71…….1.08-to-1

U.S. Attacking – River Crossing…..6…………..1.47…….3.47-to-1

U.S. Attacking – Other RM………..17…………..1.72…….0.78-to-1

German Attacking – River Crossing..2…………1.96…….1.88-to-1

German Attacking – Other FM………5…………1.39……..0.94-to-1

 

Now this is a very small number of cases for comparison, and just for balance I tried to match it across similar terrain types.[1] Still, even with this very limited data, there appears to be a clear pattern. In every case the exchange ratio more favors the defender. In the case of amphibious operations, this either 2.51-to-1 or 0.79-to-1 compared to 3.98-to-1 for amphibious operations. For river crossings this is 1.08-to-1 compared to 1.10-to-1 for UK river crossings, 0.78-to-1 compared to 3.47-to-1 for U.S. river crossings (or 0.78-to-1 compared to 0.82-to-1 if the two Rapido River engagements are left out), and 0.94-to-1 compared to 1.88-to-1 for German river crossings. Obviously a whole lot more cases would need to be examined to establish anything with certainty, but there are not a lot of amphibious operations over river crossings coded in the ETO or Kursk/Kharkov sections of the database. It would require a significant research effort to assemble such data.

Of course, what this really all points to is that the data needs to be more tightly prescribed and a whole lot more cases need to be assembled.

 

 

———

[1] In the case of U.S./UK Attacking – Amphibious, one engagement was done by the U.S. and the other two by the UK. In the case of UK Attacking – River Crossing there were 7 cases in flat mixed terrain and 1 case of rolling mixed terrain. In the case of U.S. Attacking – River Crossing there were 3 cases of rolling mixed terrain, one case of Rugged Mixed, and two cases codes as FB/M, meaning the terrain varied from flat bare to flat mixed. In the case of German Attacking – River Crossing, both engagements were in flat mixed terrain but one was against the U.S. and the other was against the UK. In the case of German Attacking – Other FM two engagements were against the U.S. and three were against the UK.

 

Measuring Human Factors based on Casualty Effectiveness in Italy 1943-1944

Then there is our analysis from the 137 engagements from the Italian Campaign. This was new analysis using the entire current version of the database.

………………………………………………………..Average………Average

Italian Campaign Data……………………………Force Ratio….Loss Ratio

All U.S. Attacks (70 cases)………………………..1.80-to-1………2.41-to-1

U.S. Low-odds Attacks (13 cases)……………….1.35-to-1………3.95-to-1

….1.20- to 1.50-to-1

All UK Attacks (49 cases)…………………………3.00-to-1……….3.17-to-1

UK Low-odds Attacks (7 cases)………………….1.29-to-1……….2.20-to-1

….0.85- to 1.50-to-1

All German Attacks (18 cases)………………….1.44-to-1……….1.14-to-1

German Low-odds Attacks (13 cases)…………1.02-to-1……….0.92-to-1

….0.72- to 1.48-to-1

 

In this case, when the U.S. was the attacker, they lost more than two men for every one the defending Germans lost. The UK lost about three men in the attack for every German loss. When the Germans attacked they lost about one for one. This was true even though the average force ratio of the U.S. and UK were higher than the German attacks.

The low odds attack data just reinforces this impression. When the Americans attack, they loose four men for every defending German lost. The UK low odds attacks are little better in that they loose two men for every defending German lost. When the Germans attacked at low odds, they lost fewer than one for one (from War by Numbers, pages 42-43).

………………………………………………………..Total…………….Total

Italian Campaign Data…………………………..Force Ratio…..Loss Ratio

All U.S. Attacks (70 cases)………………………1.65-to-1………..1.06-to-1

U.S. Low-odds Attacks (13 cases)……………..1.36-to-1………..1.43-to-1

…..1.20- to 1.50-to-1

All UK Attacks (49 cases)…………………………2.58-to-1………1.63-to-1

UK Low-odds Attacks (7 cases)………………….1.24-to-1………1.92-to-1

….0.85- to 1.50-to-1

All German Attacks (18 cases)…………………..1.27-to-1………0.84-to-1

German Low-odds Attacks (13 cases)………….1.03-to-1………0.63-to-1

….0.72- to 1.48-to-1

 

The Italian data, based upon weighted averages, show a different picture. Most significant is the casualty effectiveness of the U.S. attacks. The shift in the loss ratio from 2.41-to-1 down to 1.06-to-1 is caused a number of smaller engagements having very lopsided exchange ratios. For example the casualty ratios for one of the Rapido River operations were 48.12 to 1. These engagements clearly skewed the statistics. In fact, there is only one other engagement which has a casualty exchange ratio greater than 10.

Using these weighted statistics, if it harder to discern any difference in casualty effectiveness between the U.S. and the Germans. The U.S. had a 1.06-to-1 loss ratio when they attacked (average force ratio of 1.65-to-1), while the Germans had a 0.84-to-1 loss ratio with lower average odds (1.27-to-1). This supports the contention that combat effectiveness favored the Germans by 20 to 30 percent. These figures show the British slightly worse than the U.S., with a casualty effectiveness ratio some 50% worse than the U.S. (from War by Numbers, pages 44-45).

Measuring Human Factors based upon Casualty Effectiveness

This issue was addressed in multiple chapters of my book War by Numbers, so we will just present a few tables related to casualty effectiveness drawn from that book. They are simple comparisons of the average force ratios for attacks compared to the average loss ratios for these attacks. First, table compares the Soviet Union versus the German Army.

……………………………………………………….Average…………..Average

……………………………………………………….Force Ratio………Loss Ratio

All Soviet Attacks (18 cases)……………………..1.42-to-1…………..5.63-to-1

Soviet Low-odds Attacks (12 cases)…………….1.00-to-1…………..4.83-to-1

…..0.51- to 1.34-to-1

All German Attacks (31 cases)…………………..1.66-to-1………….0.30-to-1

German Low-odds Attacks (21 cases)…………..0.93-to-1………….0.41-to-1

….0.63- to 1.42-to-1

 

This shows a very significant casualty effectiveness advantage on the part of the Germans. When the Soviets attacked, they lost an average of 5.63 men for every German lost. When the Germans attacked, the lost .30 men for every man the Soviets lost, or inflicted 3.33 casualties for every 1 they lost. The difference between the effectiveness of the Germans when attacking versus defending is probably explained by the advantages of defense, terrain, etc. When the “odds are even,” which is roughly approximated by the low odds attacks, the Soviets attacked at an average odds of 1-to-1, yet lost almost five men for every one the Germans lost. The Germans attacks at less than 1-to-1, and caused almost 2.5 losses per one of their own (from War by Numbers, page 42)

Now these calculations were based on taking an average of the force ratios and the loss ratios (killed, wounded and missing). One can also sum up the total force ratios for all these attacks and compare them to the total losses for all these attacks. In the table below, the force ratio is the sum of the strength of all the cases, compared to the sum of the strength of the opposing forces, while the losses are the total losses for each side, compared to the losses on the opposing side.

………………………………………………………Total……………Total

Kursk Campaign Data…………………………..Force Ratio……Loss Ratio

All Soviet Attacks (18 cases)……………………..1.43-to-1………6.04-to-1

Soviet Low-odds Attacks (12 cases)…………….1.02-to-1………3.92-to-1

….0.51- to 1.34-to-1

All German Attacks (31 cases)………………….1.34-to-1……….0.30-to-1

German Low-odds Attacks (21 cases)…………0.99-to-1……….0.27-to-1

…..0.63- to 1.42-to-1

 

Notice that using the “weighted averages” did not change the numbers much. These figures still support the contention that there is a casualty effectiveness difference between the Germans and the Soviet of around 4 to 1 (from War by Numbers, page 44).

The 51 division-level engagements from the Arab-Israeli fighting show the following relationship:

………………………………………………………..Average………..Average

………………………………………………………..Force Ratio……Loss Ratio

All Israeli Attacks (33 cases)………………………1.29-to-1……….0.46-to-1

Israeli Low-odds Attacks (26 cases)……………..0.92-to-1……….0.43-to-1

….0.54- to 1.47-to-1

All Arab Attacks (18 cases)………………………..4.09-to-1………3.65-to-1

Arab Low-odds Attacks (2 cases)…………………0.96-to-1………4.91-to-1

….0.87- to 1.09-to-1

……………………………………………………….Total…………….Total

……………………………………………………….Force Ratio……Loss Ratio

All Israeli Attacks (33 cases)……………………..1.04-to-1……….0.31-to-1

Israeli Low-odds Attacks (26 cases)……………..0.89-to-1………0.28-to-1

….0.54 to 1.47 to 1

All Arab Attacks (18 cases)……………………….3.02-to-1………2.81-to-1

Arab Low-odds Attacks (2 cases)………………..0.95-to-1………3.87-to-1

….0.87 to 1.47 to 1

 

Now, there are probably performance differences between the Egyptian, Syrian, Jordanian, Iraqi and Palestinian forces, but for the sake of simplicity, all the Arab armies were lumped together. All the Arab attacks, with the exception of Mitla Pass in 1967, are from the 1973 war.

This fighting has the advantage that technologically there was not much difference between the opposing forces. The units were well armed and both sides had considerable armor. The Israeli’s had air superiority although in 1973, the Egyptians had very good air defense. It would appear that the major difference between the two armies was combat effectiveness.

One cannot help but note that the relative combat performance of the Israeli and the Arabs in 1956-1973 was similar in disparity to that between the Germans and the Soviets in 1943. This is not to say that the Germans and the Israelis performed at similar levels, as the only thing we are measuring is the relative combat performance between the two opposing forces. The German army in 1943 could have been superior to the Israeli Army of 1956-1973 and this would have meant that the Soviet Army in 1943 was also superior to the Arab armies in 1956-1973. We do not know if this is the case.

Trevor Dupuy’s analysis, using his model structure, but much of the same data, came to the conclusion that:

“The average Israeli combat effectiveness value (CEV) with respect to the Egyptians in 1967 was found to be 1.75; in other words, a combat effectiveness superiority of almost two-to-one. Following an identical procedure for the 1973 war, the average Israeli CEV with respect to the Egyptians for that war was 1.98…”[1]

As Trevor Dupuy’s combat effectiveness value is a force multiplier in his model of the combat power, then it is not directly comparable to exchange ratios, although it is related. In general, a force multiplier of two in his models will produce a casualty exchange rate of greater than two.[2] For all practical purposes, we are showing the same effect and the same results at roughly the same values.

Still these are forces that are at least competent or motivated enough to engage each other in a back-and-forth conventional engagement. There are many examples of truly one-sided results, like the 1991 Gulf War, and this seems to be typical of lots of operations of the post-World War II world (from War by Numbers, pages 50-51).

[1] Colonel T. N. Dupuy, Elusive Victory: The Arab-Israeli Wars 1947-1974 (HERO Books, Fairfax, VA., 1984), page 598.

[2] See the discussion in Chapter 16, “A New Square Law” in Col. T. N. Dupuy, Understanding War: History and Theory of Combat (Paragon House Publishers, New York, 1987), pages 221-235.

Force Ratios in the Arab-Israeli Wars (1956-1973)

An Egyptian Su-100 in Suez City, 1973

We see a similar disparity in results between the Israeli Army and the various Arab armies they engaged. The Arab armies include Egyptian, Syrian, Jordanian and Iraqi. To simplify we have just lumped the engagements involving these four armies together, although we are certain that there differences between these various armies. The data includes two engagements from 1956, 16 from 1967, one from 1968 and 32 from 1973 for a total of 51 division-level engagements. None of the engagements were coded as “limited action” or “limited attack.”

This database of only 51 engagements has 33 Israeli attacks and 18 attacks by Arab armies. It produces similar lop-sided results:

Israeli Army attacking the Arab armies (33 cases)

Force Ratio………………….Percent Attacker Wins ………………..Number of Cases

0.54 to 0.97………………………81%……………………………………………..16

1.00 to 1.47………………………90………………………………………………..10

1.51 to 1.99…………………….100………………………………………………….2

2.04 to 2.17…………………….100………………………………………………….2

2.90……………………………….100………………………………………………….1

Gap in data

3.50 to 3.96………………………..0………………………………………………….1

4.11 to 5.87………………………..0………………………………………………….1

 

As can be seen, the Israeli’s are wining 81% of the time that they attack at odds of less the one-to-one. Out of the 33 engagements where they are the attackers, they lose four and draw two. They are winning 82% of the time. Most of their attacks (79% of them) are at low odds, between 0.54- to 1.47-to-one. They win these attacks 80% to 90% of the time. They have two defeats at high odds, but in both cases, they advanced during the battle. At Jebel Libni in June 1967 they attacked at 3.60-to-one odds and advanced five kilometers. The engagement is coded as a draw because the Egyptian forces were able to successfully withdraw, as they were intending, while the Israeli forces had to rest and regroup. Both sides claimed victory. At Abu Ageila in October 1956, thee Israelis attacked at 4.57 odds and advanced 15 kilometers. This three-day engagement was coded as a defeat because the Israeli mission was to advance to Port Suez to support the Anglo-French operations there, and they were effective delayed by the Egyptians. The outcome of the engagement was coded as “attack advances” even though is a defender victory based upon the mission accomplishment scoring. The data in these tables could change slightly depending on how one chooses to code or interpret the outcome of the engagements.

When the Arab armies attacked, the results were very different.

Arab armies attacking the Israeli Army (18 cases)

Force Ratio…………………….Percent Attacker Wins…………………Number of Cases

0.87……………………………………..0%………………………………………………..1

1.05……………………………………..0…………………………………………………..1

1.75 to 1.80…………………………..0…………………………………………………..2

2.22 to 2.25…………………………..0…………………………………………………..2

Gap in data

3.03 to 3.49…………………………..0…………………………………………………..2

3.50 to 3.96…………………………33…………………………………………………..3

4.11 to 5.87…………………………50…………………………………………………..4

6.06………………………………….100…………………………………………………..1

8.12 to 12.18……………………..100…………………………………………………..2

 

One notes that the Arab armies lose all engagements below 3.94-to-1. This is some ten of the 18 engagements. Overall, they win only one-third of the time (six engagements out of 18). All victories are at roughly four-to-one odds or higher and even then they win 71% of time. This cannot more sharply demonstrate the performance differences between some armies. This was also examined in my previous book, primarily looking at casualty exchange ratios.

Finally, there is a 1991 Gulf War, where the differences in the performance between the two armies were far greater than either the German army versus the Soviet Union in 1943, or the Israeli Army versus the various Arab armies. We have 11 engagements from the odds of 0.64- to 3.26-to-one. The U.S., UK and French win them all. We have four Iraq attacks from odds of 0.21- to 3.00-to-1. All the Iraqi attacks fail. The Gulf War is a very unusual case.

An Israeli M4A3 Sherman near Suez, 1973

Force Ratios at Kharkov and Kursk, 1943

T-34 Tanks near the Derzhprom building during brief Soviet re-occupation of Kharkov, February 1943. Source: https://thecharnelhouse.org/

Now, some of the data provided in the previous posts were muddied by the fact that there were serious differences in the performances of the opposing armies. This is true for the German Army versus the Soviet Army in 1943, the Israeli Army versus the Arab armies in 1956-1973, and for the U.S. Army, USMC and allied armies versus the Iraqi Army in 1991. To a much lesser extent, it is also true for the German Army versus the U.S and UK armies up through the middle of 1944. This is discussed in some depth in my book War by Numbers.

As such, this seems like also a good time to again briefly address this issue. We need to break down the force ratio tables by which nationality is attacking. First let us look at the Eastern Front World War II data:

World War II, Kharkov and Kursk 1943 (180 cases)

German Army attacking the Soviet Army – culled data set (100 cases)

Force Ratio…………………Percent Attacker Wins……………..Number of Cases

0.49………………………………..0%…………………………………………….1

0.58 to 0.95………………………90……………………………………………..10

1.01 to 1.49……………………..100……………………………………………..30

1.52 to 1.96………………………95……………………………………………..19

2.09 to 2.42…………………….100……………………………………………….6

2.57 to 2.87…………………….100……………………………………………….7

3.00 to 3.45…………………….100……………………………………………….8

3.60 to 3.79…………………….100……………………………………………….2

4.31 to 5.85………………………92……………………………………………..13

6.48 to 6.63…………………….100……………………………………………….2

8.60 to 11.41…………………..100……………………………………………….2

 

In these hundred battles, when the Germans are on the offensive, they win 96% of the time. That is a pretty impressive result. The full data set with another 28 cases that include “limited action” and “limited attack” are listed below.

German Army attacking the Soviet Army – complete data set (128 cases)

Force Ratio………………….Percent Attacker Wins…………………Number of Cases

0.49…………………………………….0%…………………………………………….1

0.58 to 0.95…………………………..47…………………………………………….19

1.01 to 1.49…………………………..88…………………………………………….34

1.52 to 1.96…………………………..77…………………………………………….26

2.09 to 2.42…………………………..86………………………………………………7

2.57 to 2.98…………………………100………………………………………………9

3.00 to 3.45…………………………100………………………………………………8

3.60 to 3.79…………………………100………………………………………………3

4.31 to 5.85…………………………..71…………………………………………….17

6.48 to 6.63…………………………100………………………………………………2

8.60 to 11.41……………………….100………………………………………………2

 

Out of these 128 battles, when the Germans attack they win 79% of the time. This is still impressive by any standard. Because of the additional cases being “limited action” and “limited attack” there are a lot of drawn engagements in this data set. The “culled” data set has three defender victories and one draw (and 96 attacker wins). This one has five defender victories and 22 drawn engagements. Now, let us look at how the Soviets do in response. These are the opposing forces on the same battlefield, similar terrain, similar weather, and often on the same day

Soviet Army attacking the German Army – culled data set (41 cases)

Force Ratio…………………Percent Attacker Wins…………………Number of Cases

0.40 to 0.43……………………..67%………………………………………………..3

0.51 to 0.99……………………..18…………………………………………………11

1.02 to 1.46……………………..25…………………………………………………16

1.53 to 1.96……………………..50…………………………………………………..4

2.08 to 2.31……………………..50…………………………………………………..4

2.79 to 2.89……………………..33…………………………………………………..3

 

This is a very different result than what we see for the Germans. Out of the 41 attacks, the Soviets win 13 times or 32%. If I compare the German results of their attacks at odds below three-to-one, I have the Soviets succeeding 32% of the time while the Germans are succeeding 96% of the time (70 out of 73 attacks). Hard to argue that there is not a performance difference as the two armies in 1943 were roughly equivalent in armament and the mix of armaments. Each of the engagements from Kursk are presented in considerable detail in my books on the battle.[1]

The same data, but including “limited action” and “limited attack” is shown below:

Soviet Army attacking the German Army – complete data set (52 cases)

Force Ratio…………………Percent Attacker Wins………………….Number of Cases

0.40 to 0.49……………………..50%…………………………………………………4

0.51 to 0.99……………………..14………………………………………………….14

1.01 to 1.46……………………..19………………………………………………….21

1.53 to 1.96……………………..40……………………………………………………5

2.08 to 2.31……………………..50……………………………………………………4

2.66 to 2.89……………………..25……………………………………………………4

 

With this data set, out of 52 engagements the attacker still only won 13 times, or 25%.

 

 

[1] See Lawrence. Kursk: The Battle of Prokhorovka (2015) and The Battle of Prokhorovka (2019). The first book lays out all 192 engagements from the offensive in the south while the second book provided the detailed data for 76 of the engagements. Each engagement has a separate engagement sheet that lays out the forces involved, their strength and their losses. There is a detail narrative of their operations in the text of the books. If anyone has any questions over the accuracy or interpretation of this data, it is presented in these books, developed primarily from the unit records of both sides (primary sources).

The Source of the U.S. Army Three-to-One Rule

Oddly enough, 1991 was when this rule was first published, that we are aware of. It was published in the CGSC (Command and General Staff College) Student Text 100-9: Techniques and Procedures for Tactical Decision Making dated July 1991. There may have been work or materials prepared before then that we are not aware of.

The actual statement in that publication is that “Historical experience has shown that a defender has approximately a 50-50 probability of successfully defeating an attacking force approximately three times his equivalent strength.” The publication then goes on to recommend that for planning purposes that they “Therefore, as our start part, we will attempt to defend on each avenue of approach with, roughly, a 1-to-3 force rations expressed as a US unit defending against the next higher level enemy unit. For example, a US battalion would defend against an enemy regiment. There are only tools for the plan. Table 3-2 shows the preferred minimum planning ratios used to initially array forces.” The key here is the words “initially” and “to start with.” When deploying out a force, seeing up a blocking force that may be initially outnumbered three-to-one in an planned deployment does not mean that it will be outmatched in combat power by three-to-one as the battle develops. It is possible to reinforce the unit, provide it with artillery or air support, or withdraw to a more favorable position. So, the guidance that forces should be arrayed one level lower than the expected opposition is not bad guidance, even though one of the arguments made in that 1991 document supporting this is clearly wrong. The problem is that this rule is now repeated in other army documents without fully clarifying that this is just a planning factor for initial dispositions. It is also serving as the basis for charts in manuals and informal casualty estimation and modeling procedures. The army now commonly publishes the following table (from the proposed ATP 5-0.2, 31 July 2019):

Historical minimum planning ratios

Friendly Mission                     Friendly: Enemy

Hasty defend                          1:2.5

Deliberate defend                   1:3

Hasty attack                            2.5:1

Deliberate attack                     3:1

Delay                                       1:6

Counterattack                         1:1

Penetration (lead element)      18:1

 

This table, as shown by the data leave the impression that you need to have three-to-one odds to attack and that one-to-three odds is sufficient for defense. This would be the wrong impression to give. To claim that it is “historical” gives it more authority than it deserves, as the historical data in fact does not support this table. They are “minimum planning” factors, and that needs to properly stressed.

The bigger problem is that you fight as your train. So, if the officer corps is trained that you need at least a three-to-one force ratio to have a 50% chance of winning, then what kind of war planning and offensive action is now being envisioned? In World War II, the most common attack in our database are those at odds 1.00- to 1.49-to-one and they win 63% of the time. In the post-World War II engagements, the most common attack is done at 0.54- to 0.97-to-1 and the attacker wins 75% of the time (20 cases). So to what reality are we training our officers? Are we training the next generation of George B. McCellans?

Post-World War II Cases from the Division-level Database

We have 66 engagements in our database from after World War II. There are 51 cases from the Arab-Israeli Wars and 15 cases from the 1991 Gulf War.

Arab-Israeli Wars 1956-1973 (51 cases)

Force Ratio…………………Percent Attacker Wins………………..Number of Cases

0.54 to 0.97-to-1……………….76%…………………………………………….17

1.00 to 1.47-to-1……………….82……………………………………………….11

1.51 to 1.99-to-1……………….50…………………………………………………4

2.04 to 2.25-to-1……………….50…………………………………………………4

2.90-to-1……………………….100…………………………………………………1

3.03 to 3.59-to-1…………………0…………………………………………………2

3.50 to 3.96-to-1……………….25…………………………………………………4

4.11 to 5.87-to-1……………….40…………………………………………………5

6.06-to-1……………………….100…………………………………………………1

8.02 to 12.18-to-1…………….100…………………………………………………2

 

Now, this data is highly variable, with the largest number of attacks being conducted at less than one-to-one odds and the attacker winning 76% of the time. This is because of a significant difference in the combat capability of Israeli forces compared to the Egyptians, Syrians and other Arab armies that they are engaged with. This difference is well documented and discussed in more depth in my book War by Numbers. Of the 17 attacks at less than one-to-one odds, 16 were conducted by the Israelis and only one attack was conducted by the Arab armies. The Iraqi attack at those low odds was resoundingly defeated (Tel el Hara, 11 October 1973).

There is a similar performance disparity between the German and the Soviet armies in 1943. This also affects the force ratio data from World War II. We will separate these cases out by who the attacker is just to clarify the results. In the case of the Gulf War, the difference in morale, motivation and performance of the two armies were extremely disparate. This is a fairly extreme case, although not the only such case in history.

Gulf War (1991):

Force Ratio…………………..Percent Attacker Wins…………………Number of Cases

0.20 to 0.21…………………………0…………………………………………………..2

0.64 to 0.93………………………..67…………………………………………………..3

1.10 to 1.16………………………100…………………………………………………..2

None between 1.16 and 2.47

2.47……………………………….100………………………………………………….1

2.60 to 2.86………………………100………………………………………………….5

3.00 to 3.26………………………..50………………………………………………….2

 

One is hesitant to draw any conclusions from this data. The one attack that failed at three-to-one was the Iraqi Army attack at Khafji 29 January – 1 February 1991. In fact, all four failed attacks in the data set occurred when the Iraqis were attacking.

Anyhow, these databases can certainly be expanded and further analysis can be done, but good luck finding the three-to-one rule in this data that results in the defender winning 50% of the time. It is clear that from 1600 to 1991 that the attacker won more often than not at two-to-one odds or even lower, depending on the period and the forces involved. There is really no historical evidence supporting the Army version of this rule that I know of. I have been in this industry for over three decades and have not seen such evidence. I am not aware of any databases the size, depth or range of ones used here. If this historical data does not establish the rule, then where is the historical data that does?