Monthly Archives: November 2019

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

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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

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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).

Summation of Force Ratio Posts

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I think the following posts make the cases that the three-to-one rule as presented in Army FM 6-0 and other publications is incorrect (50% chance of the defender winning at 3-to-1). If there is any historical evidence that supports this claim, then I would ask that TRADOC, which is responsible for these manuals, to produce such evidence. I strongly suspect there is no such evidence. I would hope that we will see corrective action from TRADOC.

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

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

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

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

The World War I Cases from the Division-level Database

The World War II Cases from the Division-level Database

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

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

My next few blog posts are going to address the impact of “Human Factors” on these force ratios.

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

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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

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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?

The World War II Cases from the Division-level Database

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There are 576 cases from World War II in our division-level database. There are no engagements from 1939, only two from 1940, seven from 1941, one from 1942 and the rest are from 1943-45.

World War II (576 cases) – complete data set

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

0.25 to 0.49………………………22%………………………………………………..9

0.50 to 0.98………………………30…………………………………………………50

1.00 to 1.49………………………55……………………………………………….128

1.50 to 1.96………………………61……………………………………………….117

2.01 to 2.49………………………73…………………………………………………48

2.52 to 2.99………………………82…………………………………………………44

3.00 to 3.49………………………76…………………………………………………41

3.50 to 3.98………………………85…………………………………………………26

4.06 to 5.86………………………68…………………………………………………59

6.17 to 7.90………………………87…………………………………………………15

8.20 to 17.87……………………100…………………………………………………20

 

This clearly makes our point in spades about the U.S. Army three-to-one rule. Above one-to-one odds the attacker wins over half the time and above two-to-one odds the attacker wins over 70% of the time. This is the un-culled data set. The culled data set with 102 cases removed that are “limited action,” limited attack” or “other” consists of only 474 cases. It shows the following:

World War II (474 cases) – culled data set

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

0.25 to 0.49……………………..25%………………………………………………..8

0.50 to 0.98……………………..43………………………………………………….35

1.00 to 1.49……………………..63………………………………………………..111

1.50 to 1.96……………………..68………………………………………………..102

2.01 to 2.49……………………..83………………………………………………….41

2.52 to 2.99……………………..82………………………………………………….39

3.00 to 3.49……………………..79………………………………………………….33

3.50 to 3.98……………………..84………………………………………………….25

4.06 to 5.86……………………..77………………………………………………….48

6.17 to 7.90……………………..87………………………………………………….15

8.20 to 17.87…………………..100………………………………………………….15

22.84-198.69…………………..100…………………………………………………..2

 

Again, no surprises in this data, and of course, it parallels the patterns seen in the previous data sets.

The World War I Cases from the Division-level Database

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There are several major periods of covered by this 752 cases division-level database, so let us separate them out. The periods covered are:

Era ………………………………………………Number of Cases

Russo-Japanese War (1904-1905)……………….3

The Balkan Wars (1912)……………………………1

World War I (1914-1918)…………………………25

Between the wars (1938)………………………….1

World War II (1939-1945)………………………576

Arab-Israeli Wars (1956 – 1973)………………..51

Gulf War (1991)………………,………………….15

 

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

Now, both World War I and World War II are so massive that with a diligent research effort, thousands of engagements could be assembled. This does take time. Our post-World War II includes almost every significant division-level engagement from the Arab-Israeli fighting of 1956, 1967, 1968 and 1973. The Gulf War category includes every significant division-level engagement from 1991. Let us look at each of them in turn:

World War I and others (30 cases)

 

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

0.67 to 0.99-to-1………………..29%…………………………………………..7

1.01 to 1.47-to-1………………..11……………………………………………..9

1.58 to 1.80-to-1………………….0……………………………………………..2

2.00 to 2.13-to-1………………..67……………………………………………..3

2.50 to 2.80-to-1………………..67……………………………………………..3

3.00 to 3.20-to-1………………..33……………………………………………..3

4.04 to 4.38-to-1………………..50……………………………………………..2

6.32-to-1………………………..100……………………………………………..1

 

Note that the attacker is winning to majority of the time at two-to-one odds and higher. The 33% wins in the three-to-one category consists of one victory and two drawn engagements (Bazentin Ridge from the Somme and First Dardanelles Landing from Gallipoli). In both of these cases the attacker advanced, although the engagement is coded as a draw. These three cases do not make a strong argument. This data collection is too small to draw any real conclusions from. The database could certainly be expanded to thousands of cases given time and effort. We also have a collection of engagements from World War I at brigade- and battalion-level and a number of engagements above division-level. These will be explored later.

TDI Friday Read: Battalion-Level Combat Model Validation

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Today’s Friday Read summarizes a series of posts detailing a validation test of the Tactical Numerical Deterministic Model (TNDM) conducted by TDI in 1996. The test was conducted using a database of 76 historical battalion-level combat engagements ranging from World War I through the post-World War II era. It is provided here as an example of how such testing can be done and how useful it can be, despite skepticism expressed by some in the U.S. operations research and modeling and simulation community.

Validating A Combat Model

Validating A Combat Model (Part II)

Validating A Combat Model (Part III)

Validating A Combat Model (Part IV)

Validating A Combat Model (Part V)

Validating A Combat Model (Part VI)

Validating A Combat Model (Part VII)

Validating A Combat Model (Part VIII)

Validating A Combat Model (Part IX)

Validating A Combat Model (Part X)

Validating A Combat Model (Part XI)

Validating A Combat Model (Part XII)

Validating A Combat Model (Part XIII)