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Q: IIRC there was a reference in a TDI Forum thread to the effect that the Dupuy methodology's results had been corroborated by one or two other studies which reached the same (or very close) results with their own methodologies. If the previous is substantially correct; are you able to direct me to these "other studies"?

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Our independent non-TNDM/QJM collaboration of Dupuy's CEV values was covered in depth in our report on Enemy Prisoner of War Capture Rates:

E-4. Capture Rate Study Phases I and II Final Report (March 6, 2000) (CAA) (2 Vol.) - Pages: 222

The results of this specific issue were presented by me in a breifing at the 2000 ISMOR (International Society of Military Operational Reseach):

E-5. Measuring Human Factors in Combat - Part of the Enemy Prisoner of War Capture Rate Study (August 31, 2000), (CAA) - Pages: 45

We also look at the issue in our post-WWII report:

E-6. Capture Rate Study: Phase III: Post-World War II Capture Rates (November 10, 2000), (CAA) - Pages: 77

All of these rely on simple statistical compilations of the results of primiarly division-level engagements to measure human factors differences.

Also, David Roland, the noted English operational researcher, did considerable work on human factors, which came to similar conclusions to Dupuy's work. I do not have specific citations in front of me for his work, but was always disappointed that he only published his conclusions, not his data. Therefore, it was hard to check or confirm the validity of what he did.

Finally, Niklas Zetterling, of the Swedish War College, has done some independent analysis using the TNDM.

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"As promised here is a short version of some of what is wrong with Dupuy and his 1.2 to 1 German superiority factor:

Pg 13: "Technology and Rates of Advance"

In this subheading Dupuy only addresses average rates of advance as applied to entire campaigns. He ignores the value of instantaneous rates of advance (first derivative values). By doing so, he is able to demonstrate that advance is unimportant. This plays well with attrition style battles but does nothing for a maneuver campaign. More on this later.

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This criticism demonstrates a lack of understanding of the methodology. The table in question is to illustrate that opposed rates of advance are not driven primarily by technology. It has no direct relationship to the model. The fact that Trevor did not actually list the advance rates for each engagement in Numbers, Predictions and War (NPW) has probably lead to this confusion in understanding.

The model does provide a predicted rate of advance, along with outcome, for each engagement. These are then compared to the historical rates of advance as part of the CEV calculation. The rates of advance for historical battles are relatively easy to measure, but not always easy to precisely measure. These advance rates are for an actual engagement....and they are "opposed" advance rates. It has nothing to do with "campaign advance rates".

I do not know what are "instantaneous rates of advance (first derivative values)."

The claim that Trevor "is able to demonstrate that advance is unimportant." is incorrect and contrary to anything that he has stated or written.

I infer from his last statement that the questioner believes that there is two schools of warfare ("attrition" versus "manuever"). I consider this dichotomy to be absurb.

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Pg 23: "9. Punishment factor

This is just one of a great many values going into the TLI formula. My intent here is to demonstrate using this particular one (there are many others that can be demonstrated to be just as erroneous) that Dupuy's underlying values are incorrect. As the TLI is the basis of the OLI, which in turn, makes the foundation for the QJM by having demonstrable flaws in the TLI the QJM results are flawed.
The punishment factor uses the weight of an AFV as its value. The formula Dupuy gives can be reduced to ". APC's, assault guns (e.g. Sturmgeschultz, JgPz like the Jadgtiger etc.) are weighted by .5 of their full value. Aircraft are likewise given a value.
Better yet, by applying the WW II dispersion factor (3000) we can reduce the punishment equation (for that period) to . The equation Dupuy gives is just unsimplified. By reducing it to its most basic form we find that it is just drawn from thin air rather than on the basis of any reasoned, objective analysis.

Some results:

Vehicle Weight Punishment factor
Char B1 35.27 222169
T34/76 35.27 222169
T55 39.68 265114
Tiger I 55 432633
M1Abrams 54.5 426747
Matilda 29.68 171503
M60A3 52.6 404627

Now, if a Tiger I is truly capable of taking more punishment than an M1 Abrams, I (and no doubt the US Army) would like to know about it. Of course, the Char B1 is also likely to be as protected as a T34 and more so than a Matilda.....NOT!
Also, see note 8. This states the formula includes a value for dispersion (3000 as given by Dupuy). This value is a duplication of the dispersion factor used in the QJM later. Thus, AFV are considered to be far more dispersed than other targets even though they are generally considered a point target.

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First, one must keep in mind the TNDM/QJM bases its weapon effects on a scoring system. These are called OLI's (Operational Lethality Index). Over the years, several scoring systems have been developed by different groups, including the "Firepower Scores", WEI/WUVs, etc. One common disadvantage to all of these scoring systems is that they were based upon an individual judgement or scoring for each system. As such, the scoring tended to be inconsistently applied. Trevor Dupuy's major contribution was to create a standard formula for scoring of weapons. This has the advantage, whether one agrees or disagrees with the details of the formula, of providing a consistent scoring of weapons. This is discussed in depth in Dr. James Taylor's article "Consistent Scoring of Weapons and Aggregation of Forces" in The International TNDM Newsletter Volume 2, Number 2.

Scoring systems are not only used for the TNDM/QJM, but also by RAND's combat model, which is used for the US Army War College. RAND's continued use of "inconsistent" WEI/WUVs is a conceptional flaw in their RSAS and JICM models.

The actual scoring system for mobile fighting platforms uses 21 factors, or which the punishment factor is one of them.

The basing of the punishment factor on vehicle weight is a perfectly rational methodology, up until the development of composite armor. As damage to tanks come from multiple weapons platforms, from many directions, a general measurement of robustness needs to be derived. This can be done by "judgement" (which is inconsistently applied), some exhaustive test procedures (which I cannot figure out what the might be), or using vehicle weight. It seems that vehicle weight does the tirck, and although not perfect, gives a reasonable approximation of robustness.

The issue of composite armor is addressed in the corrections to the OLIs made in TNDM. As the book he is quoting from was published in 1977, the formula had naturally not yet accounted for the new armor developments.

The punishment factor based primarily on weight does have a weakness in that it does not account for vehicle size, slope of armor etc. The underlying assumption is that the vehicles being measured are equally well designed. This is not always the case early in WWII, and of course his example for the Char B1 compared to the T34 is an example of this weakness.

The TNDM armor formula does take into account length and height of vehicle. This degree of sophistication, while nice, does not significantly change most values relative to each other.

The point that the critic seems to studiously ignor is that a slight error in the punishment factor is not going to make a noticable difference in the overall outcome of an engagement in the model. The combined OLIs of a division consists of it tanks, artillery, infantry weapons, air support, etc. The minor errors caused by a simplified punishment factor are simply not going to change any model result by more than a percent or two.

His comment on dispersion is irrelevent, as it is a multiplier (not a divider) to an index number. All it does is place the number at a value to make it combatable with the other data. As discussed in depth in my article in the Newletter, Volume I, No. 3, "Dispersion is Not Played in the TNDM", dispersion is a theoretical construct, not something that is actually used within the model to create any effect.

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Pg 35: "Mobility"

The equation Dupuy gives includes the value Wi that integrates the weapons effects into the equation. This essentially doubles the value of weapons in the QJM. Also note that Md (defender's mobility) is always set at 1. As the Germans are the defender in most of the HERO database this gives them a constant rather than a variable in this area. Additionally, where the Germans are lacking mobility, this will improve their outcome scores.

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The mobility equation produces a final number that is a multiplier of the OLIs (like a value of 1.1). As such, the claim that it double counts weapons can only be made if the critic did not understand this point. Obviously, being a multiplier, nothing is being counted twice.

Second, the mobility equation divides the attacker score by the defender score. The equation addresses both sides in one equation. As such, the multiplier addresses the defender's lack of mobility, as well as the attacker's mobility. It can be a value less than 1, if the defender has superior mobility. As such, the defender value was set at one so as to not double the effect of the mobility equation.

Both of the critics comments are completely irrelevent as he simply did not take the time to understand the math.

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Pg 38: "Time and Space"

"...we are convinced that unopposed, or only partially opposed, rates of advance of units across space over extended periods of time are not relevant...."

Tell this to the French or Germans in 1940, the Russians facing the Germans in 1941 or, the Japanese in 1945 or, any other army using maneuver as a weapon.

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The full qoute is:

"Time and Space. Time and space are major factors in combat, both seperately and in combination. They are two of the three basic "coins" of war (the other being military manpower).
However, at present we believe it is neither possible nor necessary to express directly the impact of the passage of time, or the effect of timing as factors affecting combat outcomes, since these are reflected indirectly in various other factors, principally mobility, and are of course inherent in leadership. Furthermore, time is represented directly in most dynamic models and simulations.
The concept of utilization of space is also inherent in leadership. So, too, is space considered with respect to advance or retrograd movements in combat, and thus as an element contributing both to force substitution calculations and to calculation of the quantifiable outcome of an engagement. For reasons to be shown later, we are convivnce that unopposed or only partially opposed, rate of advance of units across space over extended periods of time are not relevent to assessments of combat power, or vice versa."

The bold is mine. The critic's decision to delete the direct object from his copy of the quote appears intellectually dishonest. It is clear from the overall quote, especially the first sentence, that Trevor N. Dupuy considered time and space important. The final sentence refers to measurement of combat power, for the sake of the model attrition calculations (after all, this is in the section on "Identifying and Representing Combat Variables").

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"Momentum"

"...it does not warrant expression in a calculation of combat power."

I'm sure everyone from Sun Tzu to Patton would disagree with that one. Momentum is critical to maneuver warfare. It is unimportant in attrition. The best quantitative model of this is a wave motion one using an integration of the instantaneous rates of advance. This model produces something looking like a variable sine wave where the period is determined by the frequency of combat and the amplitude by its severity. In maneuver wars the result
has high amplitude and a low frequency. In attrition warfare it has a high frequency and low amplitude.

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"Momentum. Momentum is an intangible comprised of both space and time factors. However, it does not seem to warrant expression in a calculation of relative combat power. In circumstances in which momentum might be a factor, the difference in combat power of the opposing forces is probably already too great to be affected significantly by a relatively modest bonus value."

Unfortunately, I do not understand the critics remark, so it is somewhat difficult to respond to them.

Of course, Sun Tzu and Patton were not involved it trying to design a model that generated four outputs 1) Winner, 2) Personnel attrition, 3) Equipment attrition, 4) Opposed advance rate. Critic's response appears to entirely miss what the model is producing.

By his comment that "Momentum is critical to maneuver warfare. It is unimportant in attrition." it would appear that he is indeed agreeing with Trevor N. Dupuy that putting Momentum into his attrition calculations is not significant. As such, it is hard to fathom what his criticism is....unless he has somehow or the other decided the Trevor N. Dupuy and the model represent some "Attrition School of Warfare" (which would be a gross mis-representation of Trevor Dupuy's writing).

His discussion on the "best quantitative model" being a "wave motion one using an integration of the instantaneous rates of advance." completely mystifies me. I have not seen such a model. If such a model actually exists, then I would be interested in knowing how it was designed, what was the source of formula's and data used for the model, and how does the model perform when tested to real world data (validation).

Until we see such a model validated to real-world data, I do not believe that anyone can claim that it is the "best".

The discussion on "variable sine waves" appears to be fanciful. His discussion of that maneuver wars "result
has high amplitude and a low frequency" while "attrition warfare it has a high frequency and low amplitude" appears to be a data-less construct that describes the world as he wishes it would appear.

I have yet to see any study or analysis (not that I have seen them all) that actually defines, and mathematically compares and contrasts "manuever warfare" with "attrition warfare". First, one would have to assemble a set of battles, campaigns or operations that clearly fit these definitions. That might prove to be quite a challenge, as all operations usually include both manuever and attrition to some degree.

Once one has created such a data collection, then one could test them to his "sine wave model". I suspect the results would not be very satisfactory.

Unless this work has already been done and been tested by proper validation to real-world data, then one is criticizing an existing funtioning (and tested model) to a hypothetical construct, and declaring that this hypothetical construct must be the "best" model. This is intellectual leap far more breath-taking and courageous than I could make.

By the way, what is an "instantaneous rates of advance."? I never knew anything in the military to be "instantaneous"

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Originally posted by Chris Lawrence:

By the way, what is an "instantaneous rates of advance."? I never knew anything in the military to be "instantaneous"

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This is a very puzzling expression. In the second post on this page, it is also said that "instantaneous rates of advance" are first order derivatives. One wonders of what.

Also, he writes that "integration of the instantaneous rates of advance" is part of his wave motion model. If we integrate the derivate, we will get back to the original (except an added constant), which makes it even more reasonable to wonder what he actually makes the first derivative of.