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ADM-A278 401
111111111K/DSRD-598

FORECASTING

TECHNOLOY

RELATIVE COMBAT EFFECTIVENESS
A Feasibility Study

DTIC

SAPR22 19940 z z
F

I

ri

an

Bader
R.

Jonathian Morstorn
John RL Brinkedholf

JULY 1991
jTbb doa jr-n

94-12170

DEPARIneT NF ENERG

DISCL.AMMER

This report was prepared as an account of work sponsored by an agency of the
United States Government Neither the United States Government nor any agency
thereof, nor any of their employees, makes any warranty, express or Implied, or
assumes any legal liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process disclosed, or
represents that its use would not Infringe privately owned rights. Reference herein
to any specific commercial product process, or service by trade name, trademark,
manufacturer, or otherwise, does not necessarily constitute or imply its
endorsement, recommendation, or favorng by the United States Government or any
agency thereof. The views and opinions of authors expressed ht-rein do not
necessarily state or reflect those of the United States Govemment or any agency
thereof.

KIDSRD-M

FORECASTING RELATIVE COMBAT E.FJ-ECTIVENESS
A Feasibility Study

Dean S. Hartley III
Martin Marietta Energy Systems, Inc.
Keith J. Posen
Brian R. Bader
Jonathan Morstein
John R. Brinkerhoff
Data Memory Systems, Inc.
Subcontract No. 15K-CR504C

Acce~ioo For

NTIS

CGA&I
•1AP,

LI

U , :a .:: ,,;::.c e d

EJ

01

By

B .... y .........................

July 1991

Dist ibiutlo'lI
Ava~iabihity unoles

prepared for

Office of Net Assessment
Office of the Secretary of Defense
DOE Interagency Agreement No. 1950-1612-Al
Prepared by
Data Systems Research and Development Program
Applied Technology
Located at the
Oak Ridge K-25 Site
Oak Ridge, TN 37831-7170
Managed by
MARTIN MARIETTA ENERGY SYSTEMS, INC.
For the
U.S. DEPARTMENT OF ENERGY
under contract DE-ACO5-840R21400

Dist

Avail

3:•

Or

ii

EXECUTIVE SUMMARY

Using computer models to predict combat outcomes requires assembling large amounts of
authoritative data. Yet, describing all of the factors that influence combat outcomes cannot be
done without explicitly representing the quality of opposing forces. Unfortunately, reliable
empirical methods for measuring troop quality do not currently exist.
To address this critical issue, this feasibility study examined one methodology for developing
values of relative troop quality. The methodology sought to compare historical levels of combat
effectiveness (troop quality) with basic measures of societal conditions. If strong relationships
between the societal factors and the level of combat effectiveness could be established, then
such measures might be useful for predicting combat effectiveness in other cases.
By using the Quantified Judgment Model and historical data on World War I and World War II
combat engagements, values for relative combat effectiveness were established for Germany, the
United States, the United Kingdom, and Russia/Soviet Union. Archival research produced data
for numerous societal measures for the corresponding time periods. Using statistical analyses,
the relationships between the societal factors and the level of relative combat effectiveness were
examined.
The analyses found that measures indicating the degree of industrialization were most closely
related to the level of relative combat effectiveness. That is, in World War I and World War II, by
knowing the degree of industrial sophistication, the level of relative combat effectiveness for the
major participants could be predicted. This may not be surprising, because the conditions and
characteristics that lead to industrial growth - advanced education, technological and economic
development, cultural work ethics and motivations, etc. - are in many ways critical to successful
modern combat operations. From this conclusion itwas possible to develop predictive equations
and estimate the recent US/USSR combat effectiveness ratio as about 1.75 to 1.0 in favor of the
US. This result does not appear to be beyond the range of plausibility.
The feasibility study was not pursued in enough detail and breadth to ensure its validity,
generality, and applicability to other nations. It simply demonstrated that it may be possible to
do so with further study that generates enough quality data on combat engagements and
societal factors. This study serves as promising Initial research that offers useful results if
pursued on a larger scale.

liii

iv

CONTENTS

LIST OF TABLES ........................................................

vii

LIST OF FIGURES .......................................................

vii

1. INTRODUCTIO N ......................................................
1.1 PURPOSE OF THE STUDY .......................................
1.2 PURPOSE OF THE REPORT ......................................
1.3 ASSUM PTION .................................................
1.4 ORGANIZATION OF THE REPORT ..................................

1
1
1
1
1

2. BACKGROUND .......................................................
2.1 THE CONCEPT OF RELATIVE COMBAT EFFECTIVENESS ................
2.2 THE COMBAT POWER RELATIONSHIP ..............................

3
3
5

3. METHODOLOGY ....................................................
3.1 CALCULATING COMBAT EFFECTIVENESS VALUE RATIOS PRIOR TO
CO MBAT ...................................................

9

3.2 COMBAT EFFECTIVENESS VALUE RATIOS AND SOCIETAL CONDITIONS ...

3.3 STAGES INTHE PROCESS ......................................

9
9

10

4. ESTIMATING HISTORICAL RELATIVE COMBAT EFFECTIVENESS ................

11

5. SELECTION OF HISTORICAL INDEPENDENT VARIABLES .....................

15

6. ANALYSIS OF DATA ..................................................
6.1 CORRELATION ...............................................
6.2 FACTOR VERSUS MEAN
EFFECTIVENESS VALUE CORRELATION
RESULTS .................................................
6.2.1 Industrial Production ....................................
6.2.2 Transportation and Communications ........................
6.2.3 Agricultural Production ...................................
6.2.4 Educational System .....................................
6.2.5 Vital Statistics and Health .................................
6.2.6 Financial Activity .......................................
6.3 ADVANCED STATISTICAL ANALYSIS ...............................
6.3.1 Correlation Using All Engagements .........................
6.3.2 Correlation Using All Engagements and Logarithms .............
6.3.3 Comparing Correlation Results .............................
6.3.4 Multiple Regression .....................................
6.3.5 Another Possible Analysis ................................

17
17

7. ESTIMATING COMBAT EFFECTIVENESS VALUES ...........................

35

6COMBAT

V

17
19
21
22
24
24
26
26
26
27
29
30
33

39
8. CONCLUSIONS .
8.1 RESULTSS....................................................39
40
8.2 COMMENTS ON THE METHODOLOGY .............................
41
8.3 OUTLOOK FOR CONTINUED ANALYSIS ............................
BIBLIOGRAPHY ........................................................

43

APPENDIX A. DATA ON COMBAT ENGAGEMENTS ............................

A-1

APPENDIX B. SUMMARY OF PLANNING CONFERENCE ........................

B-1

APPENDIX C: PER CAPITA FACTOR VALUES .................................

C-1

APPENDIX D: NORMALIZED PER CAPITA FACTOR VALUES .....................

D-1

vi

LIST OF TABLES
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table

Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table

1. Number of Combat Engagements and Battles ..........................
2. Mean Combat Effectiveness Value Ratios for Opponents .................
3. Categories of Factors Affecting Relative Combat Effectiveness .............
4. Categories of Societal Factors ......................................
5. Presentation of Factor Data ........................................
6. Presentation of Combat Effectiveness Value Ratio .......................
7. Correlation of Industrial Production Factors and Combat Effectiveness Values
8. Correlation of Transportation and Communications Factors and Combat
Effectiveness Values ..........................................
9. Correlation of Agricultural Production Factors and Combat Effectiveness
Values .........................................................
10. Correlation of Educational System Factors and Combat Effectiveness
Values .........................................................
11. Correlation of Vital Statistics and Health Factors and Combat Effectiveness
Values .........................................................
12. Correlation of Financial Activity Factors and Combat Effectiveness Values ....
13. Alternative Correlation Coefficients ..................................
14. Regression Results and Equations for CEVod./13 ,. ....................
15. Estimating Combat Effectiveness Values .............................
16. World War I: Germany vs United States .............................
17. World War 1: Germany vs United Kingdom ...........................
18. World War I: Germany vs Russia ..................................
19. World War II: Germany vs United States .............................
20. World War II: Germany vs United Kingdom ...........................
21. World War Ih: Germany vs USSR ...................................
22. Planning Conference Participants ..................................
23. World War I (1913) societal factor values .............................
24. World War 11 (1938) societal factor values ............................
25. Current (early 1980s) societal factor values ...........................
26. World War I (1913) normalized (to Germany) societal factor values .........
27. World War 11 (1938) normalized (to Germany) societal factor values .........
28. Current (early 1980s) normalized (to Germany) societal factor values ........

12
12
15
15
18
18
19
21
22
24
25
26
30
32

37
A-1
A-1
A-2
A-2
A-3
A-3
B-1
C-1
C-2
C-3
D-1
D-2
D-3

UST OF FIGURES
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.

1.
2.
3.
4.
5.
6.

Electrical production vs mean Combat Effectiveness Value .................
Number of pigs vs Mean Combat Effectiveness Value ......................
Infant mortality vs Mean Combat Effectiveness Value .......................
Electrical production vs Mean and All Combat Effectiveness Values ...........
Electrical production vs Natural Log of All Combat Effectiveness Value .........
US/USSR Combat Effectiveness Value trend .............................

vii

20
23
25
28
29
38

LIST OF TABLES
Table 1. Number of Combat Engagements and Battles ..........................
Table 2. Mean Combat Effectiveness Value Ratios for Opponents .................
Table 3. Categories of Factors Affecting Relative Combat Effectiveness .............
Table 4. Categories of Societal Factors ......................................
Table 5. Presentation of Factor Data ........................................
Table 6. Presentation of Combat Effectiveness Value Ratio .......................
Table 7. Correlation of Industrial Production Factors and Combat Effectiveness Values
Table 8. Correlation of Transportation and Communications Factors and Combat
Effectiveness Values ...............................................
Table 9. Correlation of Agricultural Production Factors and Combat Effectiveness
Values .........................................................
Table 10. Correlation of Educational System Factors and Combat Effectiveness
Values .............................
...........................
Table 11. Correlation of Vital Statistics and Health Factors and Combat Effectiveness
Values ......
.................................
..............
Table 12. Ci,,,.,;ation of Financial Activity Factors and Combat Effectiveness Values ....
Table 13. Alternative Correlation Coefficients ..................................
Table 14. Regression Results and Equations for CEVo•,/G,,,,w* ....................
Table 15. Estimating Combat Effectiveness Values .............................
Table 16. World War 1: Germany vs United States .............................
Table 17. World War 1: Germany vs United Kingdom ...........................
Table 18. World War 1: Germany vs Russia ..................................
Table 19. World War II: Germany vs United States .............................
Table 20. World War II: Germany vs United Kingdom ...........................
Table 21. World War I1: Germany vs USSR ...................................
Table 22. Planning Conference Participants ..................................
Table 23. World War I (1913) societal factor values .............................
Table 24. World War 11 (1938) societal factor values ............................
Table 25. Current (early 1980s) societal factor values ...........................
Table 26. World War I (1913) normalized (to Germany) societal factor values .........
Table 27. World War 11 (1938) normalized (to Germany) societal factor values .........
Table 28. Current (early 1980s) normalized (to Germany) societal factor values ........

12
12
15
15
18
18
19
21
22
24
25
26
30
32

37
A-1
A-1
A-2
A-2
A-3
A-3
B-i
C-1
C-2
C-3
D-1
D-2
D-3

LIST OF FIGURES
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.

1.
2.
3.
4.
5.
6.

Electrical production vs mean Combat Effectiveness Value .................
Number of pigs vs Mean Combat Effectiveness Value ......................
Infant mortality vs Mean Combat Effectiveness Value .......................
Electrical production vs Mean and All Combat Effectiveness Values ...........
Electrical production vs Natural Log of All Combat Effectiveness Value .........
US/USSR Combat Effectiveness Value trend .............................
vii

20
23
25
28
29
38

1. INTRODUCTION
Using computer models to predict combat outcomes requires assembling large amounts of
authoritative data. Yet, describing all of the factors that influence combat outcomes cannot be
done without explicitly representing the quality of opposing forces. Unfortunately, reliable
empirical methods for measuring troop quality do not currently exist.
1.1 PURPOSE OF THE STUDY
This initial feasibility study was commissioned to determine if it is possible to establish a general
method of estimating current relative combat effectiveness values among the armed forces of
various nations using current societal data as a predictor. If this general approach were
determined to have some merit, it could be applied to make estimates of relative combat
effectiveness in planning for future combat with potential adversaries.
12 PURPOSE OF THE REPORT
This report provides an overall view of the way in which the study was accomplished and a
summary of the results that were produced. As is appropriate for a feasibility study, the report
illustrates measures and estimates of relative combat effectiveness for the armed forces of the
nations used to test the method, but results are not presented as definitive.
1.3 ASSUMPTION
This study was based on an understanding of combat effectiveness that was developed in
conjunction with the Quantified Judgment Model (QJM).1 The QJM's Combat Effectiveness
Value (CEV) is seen as a reasonable proxy measure for the impact of behavioral factors on
overall combat outcomes. No other combat model assesses combat effectiveness in this way.
The authors postulate that QJM-derived CEVs reflect first order effects reasonably well.
1.4 ORGANIZATION OF THE REPORT
The report is organized into nine major sections. Section 2 is a background discussion of the
concept of combat effectiveness. Section 3 is a general discussion of the methodology of the
study. Section 4 describes how the combat engagements were selected for inclusion and
presents the relative combat effectiveness values estimated from the results of those
engagements. A listing of selected characteristics of these engagements is appended. Section
5 describes the independent variables chosen for the study and the values of those variables.
'The Quantified Judgment Model (QJM) is proprietary to Data Memory Systems, Inc. (DMSi),
and has been licensed for use by several organizations, including the Office of Net Assessment,
Office of the Secretary of Defense (OSD), the sponsors of this study.

2
Section 6 presents the results of the statistical analyses of the variables and their relationship
with relative combat effectiveness values. Section 7 uses the results to predict US versus Soviet
CEVs. Section 8 presents the conclusions and findings from the work accomplished. Section 9
consists of the Appendices, containing the data and a summary of the project planning
conference.

3
2. BACKGROUND
Relative Combat Effectiveness is a term used to describe the abilities and fighting quality of a
military unit or force compared to an opposing unit or force. While relative combat effectiveness
in general may be considered a function of the totality of factors - including strength, weapons,
and tactics - it is most often restricted to those Intangible or human factors that cause some
troops to stand and fight while other troops break and run. This work was done using the
narrower, limited sense of combat effectiveness as a human or behavioral matter.
2.1 THE CONCEPT OF RELATIVE COMBAT EFFECTIVENESS
Most modem military analysts have recognized the importance of relative combat effectiveness
in determining combat outcomes. Napoleon implied that the "moral is to the physical as three
is to one." Military historian Trevor N. Dupuy goes further and says that the moral is the
equivalent of the physical squared.2 Whatever the exact nature of the relationship, it is possible
that relative combat effectiveness is as important - and may be more important - than
technology, weapons effectiveness, or sheer numbers in influencing combat outcomes.
History provides numerous examples of smaller forces defeating larger adversaries through sheer
determination, fighung ability, or enthusiasm. The Spartans at Thermopylae defeated a larger
Persian force, and they died doing it. The small but well-disciplined and well-trained light cavalry
of Genghis Khan defeated larger European armies. A few English bowmen at Crecy defeated
a larger number of French heavy cavalry. Some of these victories by smaller forces are the result
of superior technology - the long bows at Crecy, for example. But many of these battles have
been fought between forces employing the same technology and the same tactics, and in these
instances, the quality of the troops. - their relative combat effectiveness - was clearly the
deciding factor. What other explanation can there be for the ability of the German Army in World
Wars I and IIto fight outnumbered and win consistently - even though losing the war in the end
because of lack of resources or sheer numbers of the foe? How else can the ability of the Israeli
Army in 1947, 1956, 1967, and 1973 to defeat well-equipped and more numerous foes be
explained? it is clear that relative combat effectiveness is an important element in the outcomes
of combat engagements.
However, it is not clear what is responsible for better relative combat effectiveness. Though
many of its components may relate to the quality and depth of military training, experience, and
preparedness, it seems reasonable to believe that basic societal characteristics have an effect
on CEV or at least move in coincident directions and therefore will reflect a high degree of
correlation with CEV. Economic and technological development, educational achievements,
cultural and historical legacies and motivations, and political or religious ideology and
participation may all have some impact on how well the people of a nation will perform in
combat. In fact, many of these basic societal conditions may be responsible for superior military
training and preparedness, given that these factors have both direct and indirect influences on
2 Trevor

N. Dupuy, UnderstandingWar, Paragon House Publishers, New York, 1987, p. 11 and
p. 23. Dupuy explicitly modifies the Napoleonic statement.

4
relative combat effectiveness. It remains an open question in regard to which of these factors
has the most overall influence and is therefore the best predictor of a nation's expected combat
effectiveness.
If, as most believe, the quality of the troops is an important factor In combat, knowing In advance
the relative combat effectiveness of the various combatants would be of great value in planning
and waging war. Military planners could use knowledge of greater relative combat effectiveness
to economize on the number of troops and weapons used against a particular foe. This could
be applied to mass overwhelming force in another sector of the battlefield or theater of war. It
could be used as a "force multiplier" to secure victory with smaller forces. It could be used as
a margin of safety when planning campaigns or fighting battles. Knowing how well troops will
perform against opposing troops would be a great advantage.
Military commanders have been estimating relative combat effectiveness since war began.
Indeed, one of the major aspects of the art of the general has been the ability to assess the
relative strengths and weaknesses of the opposing troops realistically. A lot of mistakes have
been made in these assessments. Because of the intangible nature of the factors comprising
relative combat effectiveness, attempts to make this estimation in a scientific manner have not
been very successful.
In recent years much has been written on relative combat effectiveness. Most authors address
the subject in qualitative terms from a sociological or psychological viewpoint. 3 The leading
proponent of quantifying relative combat effectiveness has been Trevor N. Dupuy, 4 who used
the QJM to estimate the relative combat effectiveness of the German Army in World Wars I and
II against the United States Army and the British Army. Martin van Creveld essentially used the
Dupuy quantitative results as a starting point for his explanation of the reasons for German
superiority against the Americans in World War 11.5 Although van Creveld and Dupuy agree that
the Germans fought better than the Americans, their reasons differ. Dupuy has also applied the
QJM to estimate the relative combat effectiveness of the Israeli Army against the Egyptian and
Syrian armies during the 1967 and 1973 Arab-Israeli Wars. 6 The Dupuy approach to quantifying
relative combat effectiveness has been used in this feasibility study.

3 Typical of these are William Darryl Henderson, Cohesion: The Human Element in Combat,

National Defense University, Washington, DC, 1985; and Sam C. Sarkesian, Editor, Combat
Effectiveness: Cohesion, Stress, and the Volunteer Military, Sage Publications, Beverly Hills and
London, 1980.
4 See A Genius for War: The German Army and General Staff, 1807-1945, HERO Books,

Fairfax, VA, 1985.
5 Martin Van Creveld, Fighting Power: German and US Army Performance, 1939-1945,
Greenwood Press, Westport, CT, 1982.
6 Trevor N. Dupuy, Elusive Victory: The Arab-IsraeliWars, 1947-1974, HERO Books, Fairfax,
VA, 1985.

5
2.2 THE COMBAT POWER RELATIONSHIP 7
Mankind has been fighting since the earliest days, and military analysts have been trying to
define the nature of combat from about the same time. A formula or equation for describing the
mechanics and outcomes of combat would be advantageous, because it would then be possible
to know exactly the number of troops, numbers of weapons, and the supplies needed to assure
victory in combat. Deriving such an equation has also proven to be most difficult because
combat is a complex matter in which chance and human factors play as much or even more of
a role than mere numbers of troops or weapons. Although the dynamics of combat do not
reduce well to a single, simple equation, they can be represented by some general mathematical
forms for which factors values can be derived empirically.
While there is no one formula that represents the equation of combat, it is reasonable to express
the relationship between two adversaries as a ratio of their relative combat power. One simple
statement of this ratio is shown in Eq. (1).

Where:

P
S
F
0

P1

SlxFlxQ1

P2

S,

(1)

,X2,

= Combat Power
= Force Strength
= Factors Affecting the Combat
= Quality of the Troops

Force Strength, S, is a function of the number of troops, the numbers and types of their
weapons, and their intrinsic mobility. The environmental and operational factors affecting
combat, F, include weather, terrain, mission or posture (attack, defend, delay), surprise achieved,
and preparations (e.g., fortifications). The quality of the troops, 0, is a function of behavioral
factors, such as morale, esprit de corps, training, leadership, and will of the troops.8
The product of these three quantities - S, F, and 0 - is the Combat Power, P, for each side.
The ratio of the combat power of the two sides is an indicator of the way in which combat has
or will proceed. The side with the greater combat power will inflict more casualties, move or hold
more successfully, and accomplish the assigned mission. In simplified terms, the side with the
greater combat power will "win.0 The extent of the ratio of combat power will determine the
extent of the victory. Thus, if a combat power ratio could be calculated for any combat
engagement or battle, the outcome could be predicted.

"7The discussion in this paragraph is based on two books by T. N. Dupuy, Understanding
War; and Numbers, Predictions,and War, HERO Books, Fairfax, VA, 1985.
a These behavioral factors seem to be derivative of the larger societal conditions that underlie
the country and therefore implicitly include these more basic conditions. For example, the
degree of military training is, in part, a function of the country's educational system, cultural
legacy, and economic and technological sophistication.

6
All methods of calculating the force strength (S) of adversaries in combat engagements use
various counting schemes that assign weights to different kinds of weapons and munitions. The
aggregation schemes derive from engineering data and the physical characteristics of weapons.
Defining force strength is a matter of aggregating the combatants' physical resources. In this
analysis, the QJM method for calculating force strength based on Operational Lethality Indices
(OLls) was used.
Similarly, it is possible to estimate the impact of the environmental factors (F) - weather, terrain,
cloud cover, etc. - or operational factors - mission, posture, fortifications, etc. - on combat
outcomes. This can be done using an engineering approach or a historical approach.
It is far more difficult to estimate the quality of the troops. This is because the quality factor
depends almost exclusively on human factors that are generally believed to be difficult to
quantify. This would require introduction of substantial analytical judgment in subjectively
estimating the aggregate impact of these factors.
In theory, the estimation of troop quality could be based on an ideal standard of troop
proficiency. Each nation's forces could be measured against this standard and rated accordingly
to produce values for Q. While an absolute measure of troop quality may be possible and
certainly would be desirable, no empirical method using objective data currently exists for
authoritatively measuring troop quality in this manner.
Because war is a two-sided (at least) affair, it is the relative combat power for a particular combat
engagement that is important. This is also true for the quality of the troops. The resulting
estimate of relative troop quality is the ratio of their respective qualities, which is defined as their
relative combat effectiveness value, CEV. (The symbol CEV,,, is used because it is the ratio of
side 1 to side 2, generally attacker over defender.) This definition is shown in Eq. (2).

Q2

If the two absolute values of troop quality could be estimated independently, the ratio of the
respective quality estimates would be the CEV and could be expressed as a single number.
The Combat Power relationship may be rewritten to reflect the single-number ratio of CEV as the
measure of relative quality, as shown in Eq. (3).

P..1 = S•F
ý xCEV
-

T2

S ~F
2

1/

(3)
(3)~x

Given the methodology described above, the CEV can be calculated for historical engagements.
The numbers of troops and numbers and types of weapons are known, so that the force
strength, S, may be calculated for each side. The environmental and operational conditions of
the engagement are known, and the proper values assigned to F for each side. The historical

7
combat outcome is known and can be translated (using the QJM) mathematically so that a
combat power ratio that led to that outcome may be estimated as well. Working from these
known quantities, it is possible to estimate the relative CEV that existed for that particular
historical engagement from the equation below. Until a method Is devised to estimate an
absolute value of troop quality, Q, this is the only practical method for quantifying combat
effectiveness that does not rely exclusively on judgment or subjective measures. The calculation
is shown in Eq. (4).
CEV

S2 xF2XP

SlxF xP2

(4)

This method was used in this study to develop relative combat effectiveness values for historical
combat engagements. For predicting future combat outcomes, however, a CEV ratio is required
in advance as one of the combat power equation inputs. This leads to the search for a
methodology to calculate or estimate CEV ratios prior to combat. When a CEV ratio can be
derived, it can be plugged into Eq. (3). Note that when predicting combat outcomes, P, and P2
are calculable only as an overall ratio of P1/P2 , not as separately and independently derived
values.

B

9
3 METHODOLOGY
By using the QJM and historical data on World War I and World War II combat engagements,
values for relative combat effectiveness were established for Germany, the United States, the
United Kingdom, and Russia/Soviet Union. Archival research produced data for numerous
societal measures for the corresponding time periods. Using advanced statistical analysis, the
relationships between the societal factors and the level of relative combat effectiveness were
examined.
3.1 CALCULATING COMBAT EFFECTIVENESS VALUE RATIOS PRIOR TO COMBAT
There are essentially three methods that can be used to develop numbers for CEV ratios
between two adversaries.
1.

Recent Direct Combat Experience: Historical analysis has shown that CEV ratios tend
to have a rough constancy over time. Therefore, CEV ratios determined from recent
previous combat between two nations can be used for predictions of future combat
between those same nations. However, the currency of such ratios is uncertain because
basic societal conditions that affect troop quality do fluctuate over time.

2.

Recent Indirect Combat Experience: The same process as above can be used in cases
where two nations have previously fought against a common opponent. The common
opponent effectively becomes a constant and the difference in CEV ratios for the two
target nations can be used to estimate what a direct matchup would be.

3.

Indirect Measures of Combat Effectiveness: For predicting the CEV ratio between two
potential future combatants, there are often no recent direct or indirect combat
experiences applicable to the countries selected. More indirect measures of troop quality
must be found so the CEV ratio can be estimated. It Is not unreasonable to expect that
some independent variables of societal or national characteristics would correlate closely
with, and thus suggest or indicate, a country's relative troop quality versus an adversary.

This study examined the indirect measures method in greater detail. To pursue this method, it
was necessary to analyze a historical data base of combat outcomes and societal conditions.
Analysis helped to determine if there were significant relationships between any societal
measures and relative combat effectiveness values. It was a question of how much societal
issues and which specific factors are at the root of combat effectiveness differentials.
3.2 COMBAT EFFECTIVENESS VALUE RATIOS AND SOCIETAL CONDmONS
The basic assumption underlying this study is that there is a close relationship between certain
characteristics or conditions of both the nation and the nation's armed forces, especially with
regard to the combat effectiveness of the armed forces. The study was designed to be a
pioneering effort in interdisciplinary research involving military science, historical analysis of
combat, military sociology, economics, psychology, and mathematical analysis to determine if

10

presumably independent societal conditions could be used as indicators of a military's combat
effectiveness. All of these disciplines played a role in the initial feasibility study.
The general approach was to estimate relative combat effectiveness between several pairs of
opponents, establish military and societal factors to serve as independent variables, and compare
the two sets of numbers to determine if there are any relationships. The concept was to
determine which factors appear to be most influential in determining relative combat
effectiveness.
3.3 STAGES IN THE PROCESS
The work was accomplished in four general, overlapping stages as follows:
1.

Estimates of relative combat effectiveness for historical combat were obtained using the
QJM. Data for both sides of the combat engagements were compiled to include troop
strength, weapons, environmental conditions, operational circumstances, and outcomes.
The outcomes were defined in terms of mission accomplishment, attrition of personnel
and weapons, and opposed distance advance. Where possible, data were obtained from
existing data bases maintained by Data Memory Systems, Inc. (DMSi). In a few cases,
additional historical research was performed.

2.

The next step was to select several factors as independent variables. These had to
satisfy the criteria of relevance and availability. The method used to compile the list of
potential independent variables was to consult recognized experts in several fields and
obtain their judgments in a structured manner. Archival research was accomplished to
provide values for factors to be used in the initial feasibility study.

3.

The CEVs and independent variables were correlated statistically to determine if there
were any relationships. Strong correlation would indicate co-variation between
independent and dependent variables, indicating that a significant relationship might exist
between them. Some more sophisticated analyses were performed to indicate the type
of results possible with a larger data base.

4.

Finally, some general conclusions were drawn with regard to the pros and cons of the
methodology and the general feasibility of using this approach to provide estimates of
future relative combat effectiveness.

11
4. ESTIMATING HISTORICAL RELATIVE COMBAT EFFECTIVENESS
Although the study could have used any reasonable set of combat engagements to derive CEV
ratio data, It was decided to use major participants in World War I (WW I) and World War II
(WW 11).9 Using combat engagements and relative combat effectiveness scores from both wars
provides a larger set of engagements from which to draw and would allow testing with two sets
of independent variables rather than one set only. This would serve as a partial validation of any
results if they were found to be consistent across both wars. It also offered the added advantage
of providing the opportunity to examine US and UK forces vs the Russians/Soviets using the
indirect combat experience method outlined In Sect. 3.1 above.
QJM analysis of historical combat requires detailed knowledge of the circumstances of combat
on both sides. Accurate data for much of the US, UK, and German experience is available in
archives, and the DMSi Land Warfare Data Base includes numerous combat engagements
between US and German forces and UK and German forces for both world wars. However,
accurate data on Russian or Soviet experience is hard to obtain, and there is a general lack of
QJM engagements between German and Russian (WW I) or Soviet (WW II)forces. So one of
the challenges of the feasibility study was to obtain adequate data on Russian and Soviet combat
engagements. This was done by consulting leading experts on the Soviet Army and performing
additional research on the Eastern Front in World War I. The difficulty in obtaining division level
data for the Russian and Soviet experience explains why some of the combat events analyzed
are corps- or even army-level battles lasting many days.
For the feasibility study, QJM analyses were conducted for a total of 56 combat engagements,
arrayed as shown in Table 1. Some details of these combat engagements are provided in
Appendix A, including the CEV ratio for each.

9 Historical analysis of combat is performed preferably at the level of combat engagements.
The term "combat engagements' is defined as a combat event involving units from company to
division size lasting one to five days. This is in accordance with the hierarchy of combat
presented in Dupuy's Understanding War (page 67). In this terminology, a battle is a larger
combat event consisting of several engagements, Involving larger units up to army corps and
extending over a longer period of time up to several weeks. Most of the combat events used in
this study are combat engagements, however, some of the combat events for Germany vs US
(WW I) and Germany vs Russia/USSR (WW II) are battles because data on individual
engagements are not yet available.

12
Table 1. Number of Combat Engagements and Battles
Germany vs
Germany vs US

Germany vs UK

Russia/USSR

WWl

10

9

9

WW II

10

9

9

For one set of analyses, the results of these engagements were condensed into a single CEV
ratio that represented the overall CEV ratio for those two opponents for the entire war. After the
CEVs were calculated for each engagement, the arithmetical mean was computed for use as the
representative CEV for each war and pair of opponents. The mean CEVs computed for each
pairing are shown in Table 2.
Table 2. Mean Combat Effectiveness Value Ratios for Opponents
Germany vs
Itself

Germany vs
Germany vs US

Germany vs UK

Russia/USSR

WW I

1.0

0.492

1.219

3.154

WW II

1.0

1.227

1.540

2.848

To simplify the analysis and presentation, all CEVs are shown for Germany relative to the other
nations. Though QJM CEVs are generally presented as attacker over defender, this would
provide confusing results because there was no consistency in which side was attacking.
However, since CEV is a ratio (QjQd), it can be inverted when necessary to allow for consistency
in presenting the results and still correctly reflect the magnitude of the ratio. Therefore, CEVs are
shown as 00,1.o
regardless of which side was attacking or defending.
A CEV of greater than 1.0 means that the Germans (in this case) had higher combat effectiveness
than their opponent; a CEV of less than 1.0 means that the Germans had lower combat
effectiveness than their opponent. The size of the number also represents the size of the combat
effectiveness disparity. To be able to include German societal data in the statistical analysis, a
hypothetical German vs German CEV ratio was included for each war. This ratio was assigned
as 1.0 to 1.0 and increases the number of pairings (cases or dependent values) to eight for
performing correlation analysis.

13
The mean CEVs were calculated to provide a simple comparative measure that could easily
demonstrate the analytical concepts under study. They show that the Germans had higher
combat effectiveness than their opponents in both wars, except against the United States in
World War 1.10 It also shows a rough constancy of CEV ratios for the UK and USSR across both
wars. However, more advanced statistical analyses are possible using the individual CEVs for
all 56 combat engagements and battles (plus hypothetical German vs German cases).

'o This result may be explained by the circumstances of the combat between Germany and
the US in WW I. The first engagement used in this study between US and German troops was
in June 1918, after the Germans had just barely failed to win victory by a massive offensive and
only five months before the Armistice. The German troops were dispirited and certain of defeat;
the US troops were fresh and eager to fight.
Clearly this explanation causes problems with certain of our assumptions: the Q,,., value
is assumed constant to allow estimation of Qus/QJ,,I etc., and the use of the same Q.,.,,. for
WW I and WW II might cause statistical errors. However, for the purposes of this study feasibility - these effects are ignored. A more detailed study would need to address this issue.

14

15
5. SELECTION OF HISTORICAL INDEPENDENT VARIABLES

Selection of suitable independent variables that might establish or influence relative combat
effectiveness was accomplished by convening a multidisciplinary panel of experts at a Planning
Conference on October 11, 1989. The group of military analysts and experts, including
sociologists and Soviet experts, drew up a list for use in the study. A summary report of the
conference proceedings and a list of participants is in Appendix B. After considerable
discussion, general agreement was reached that relative combat effectiveness would depend on
the six general categories listed in Table 3.
Table & Categories of Factors Affecting Relative Combat

e

Societal Factors
Manpower Quality
Military Leadership
Military Doctrine and Theory
Military Training
Readiness for Combat

For the purposes of this initial feasibility study, it was decided to investigate only the category
of Societal Factors. Although the other categories of independent variables may be equally valid
for measuring and explaining relative combat effectiveness, the consensus was that societal
factors were more fundamental - in some sense primary factors - and provided the basis for the
other categories.
It was hypothesized that a nation's capacity to wage war - its overall performance in combat was demonstrably related to or influenced by a number of discrete societal factors for which
numerical data could be compiled. In general, these factors fell into six distinct categories as
listed in Table 4. A total of 33 separate factors were used. Other factors were investigated but
discarded because of a lack of authoritative data.
Table 4. Categories of Societal Factors
Industrial Production
Agricultural Production
Transportation and Communications
Educational System
Financial Activity
Vital Statistics and Health

16
For the initial feasibility study it was decided to use data for a single year just prior to the
outbreak of each war. The year chosen for World War I was 1913 and for World War II, 1938.
To eliminate differences due to sheer size, the factors were calculated on a proportional basis
of the total population of each nation in the year of measurement. These are expressed as a per
capita number, the number of items per one million population. Per capita values of the factors
used in the analysis are provided in Appendix C.

17
6. ANALYSIS OF DATA
Several statistical techniques were used to analyze the data. Simple correlations were used to
Identify potentially important factors. More complex techniques were used to indicate
methodologies that could be used for a complete Investigation of the problem.
6.1 CORRELATION
Correlation is a statistical method for measuring the degree of linear co-variation between the two
variables being analyzed. This means that as one variable changes, the other changes
proportionately. The more closely the two co-variate, the stronger the relationship.'1 The
strength of the relationship is indicated by the correlation coefficient. Ifthere Is no connection
(random association) between the values for the two variables, they will not co-variate and will
have a low correlation coefficient. Iftwo variables have a high correlation, then it means that by
knowing the value for one variable, a confident prediction can be made as to the value for the
second variable.
A correlation coefficient of 1.0, either positive or negative, indicates a perfect relationship between
the two variables. A correlation coefficient of 0.0 indicates no relationship. The closer the
correlation coefficient is to either 1.0 or -1.0, the stronger the relationship. A positive correlation
coefficient indicates a direct relationship and a negative coefficient indicates a negative direct
relationship (one variable increases proportionally as another decreases).
The relationship being analyzed can also be represented graphically using a scatterplot. In a
scatterplot the values for each pair of variables are plotted on an XY chart. The alignment of the
points indicates visually if a relationship exists. For each set of points, a "best fit" line can be
drawn that minimizes the total squared distance that all of the points lie off of the line. In a
perfect correlation of 1.0 (or -1.0) all of the points would fit precisely on the line. The value of the
correlation coefficient indicates how closely the points come to lying exactly on the best fit line.
The positive or negative sign indicates whether the best fit line has a positive or negative slope,
respectively. Ifthe correlation is low, then the points should appear to be randomly distributed
on the graph.
62 FACTOR VERSUS MEAN COMBAT EFFECTIVENESS VALUE CORRELATION RESULTS
In the first stage of the analysis, each of the societal factors (independent variables) was
correlated with the mean CEVs (dependent variable) for that war. To facilitate the correlation
analysis, the data were utilized in two ways. First, data for each war were separately analyzed
with four cases for each war (Germany, UK, US and Russia/USSR). To validate the significance

"1'A well-known statistical adage is that "correlation does not prove cause and effect."
However, a strong correlation suggests that the analyst should at least investigate the possibility
of causal linkage or other form of relationship.

18
of relationships that were found and to show consistency across both wars, a correlation that
combined all eight cases into one data set was used.
Inthis combined effort, the data for each factor were "normalizedo according to Germany, so that
the German values served as a standard for each war. For the independent variables,
normalization allows data to be utilized without regard to specific units of measurement because
it converts all absolute data into ratios. In these ratios, the value for Germany is set at 1.0 and
data points for other nations are calculated based on their relative value vs Germany. Therefore,
a value less than 1.0 for another nation indicates real values lower than Germany's and
normalized values greater than 1.0 mean values higher than Germany's. Table 5 Illustrates this
process.
Table 5. Presentation of Factor Data
Steel Production per Capita

WWI:

Germany
Russia

Absolute

Normalized

270.9
35.1

1.00
0.13

For CEVs, normalization effectively inverts the CEV ratios because it sets Germany's Q value to
1.0. This process is illustrated in Table 6.
Table 6. Presentation of Combat Effectiveness Value Ratio

Original
WWI:

CEV",•,f,

=3.14
1.00

CV

=.318

Normalized
1.000
0.318

T1.00

Normalization allows combining data from both wars because it eliminates disparities or
distortions that might exist because of wide variance in absolute data values. Normalization
allowed for correlation of all eight cases at once, though the two German cases were identical
with all values equal to 1.0. Factors for which data could not be found for both wars were not

19
used in the combined correlation effort. Normalized per capita factor values can be found in
Appendix D. Presentation of individual factor correlation coefficients follows below.
6.2.1 IndustrIal Production
There appears to be a general, strong positive relationship between per capita industrial
production and relative combat effectiveness, as shown in Table 7. Nations with greater per
capita industrial output tended to be the nations with the higher CEVs. The question as to
whether and how this industrial production advantage translated into better performance from
the troops remains to be answered. Figure 1 shows the normalized correlation scatterplot for
electrical production vs mean CEV.
Table 7. Correlation of Industrial Production Factors and Combat Eei

s Values

Correlation Coefficients
Independent Variables (per

World War I

World War II

Combined

capita)

Coal Production

.394

.735

.564

Iron Production

.931

.108

.539

Steel Production

.872

.926

.783

Sulfuric Acid Production

.725

.931

.712

Electrical Production

.990

.823

.921

Motor Vehicles Registered

n/a

.360

n/a

20
Correlation With Values Normalized to Germany
3.0
0

2.5
u

0

0

1.5

S•
S•

.921

R
00

1.0

U

0.0.5

1.0
Mean

15

CEV Normalized

2

0

2.5

to Germany

Fig. 1. Electrical prouction vs mean Combat Effecdiveness Vu•.

3.0

21
6.2.2 Transportation and Communications
Authoritative data for transportation and communications factors were difficult to obtain and
therefore limit the generalizations and conclusions that can be drawn. To the degree that these
factors relate to industrial activity, they should have the same high correlations with CEV. The
actual correlations are shown in Table 8.
Table 8. Correlation of Trnportation and Communications Factors and Combat Effectivenes
Values
Correlation Coefficients
Independent Variables (per

World War I

World War II

Combined

capita)

Railway Mileage
Rail Passengers

.942
n/a

.591

Ships, Numbers

.292

Shipping Tonnage

-.259

Mail Items, Numbers
Telegrams, Numbers

.342

n/a

n/a

n/a
n/a

.060
.606

.071

.720

.195

.119
n/a
-.050

22
6.2.3 Agricultural Production
Agricultural production comparisons send a mixed message. Table 9 shows the correlations.
Nations with extensive effort and production of cereal grains show a contradictory relationship
with combat effectiveness. Conversely, nations with large numbers of livestock, show modest
positive relationships with combat effectiveness. Except for pigs, there is also a distinct
difference with respect to livestock between the two wars. On this basis, it would be imprudent
to conclude that a high per capita level of agricultural production in general is a positive factor
in having high combat effectiveness. Use of a single factor such as pigs, though it shows a
strong correlation across both wars, could be of suspect value as it may easily be an anomaly
that will not be consistent across time and space. Figure 2 shows the scatterplot for the number
of pigs factor.
Table 9. Correlation of Agricultural Production Factors and Combat Effectiveness Values
Correlation Coefficients
Independent Variables (per

World War I

World War II

Combined

capita)

Wheat Hectares

.142

-.542

-.070

Barley Hectares

-.553

-.540

-.418

Oats Hectares

.328

-.354

-.032

Wheat Output

.276

-.509

.106

Barley Output

-.720

.446

-.273

Oats Output

.399

.251

.271

Horses, Numbers

.477

-.365

.399

Cattle, Numbers

.912

.269

.666

Pigs, Numbers

.867

.760

.796

Sheep, Numbers

.145

-.532

-.086

23
Correlation With Values Normalized to Germany
i

2.5

0

2.0

i

IqP . 796

0
hi

1.0

0

a.,
0.5
.4

0

00.5

1.0

.5

2.0

2.5

Meant CEY Niormalized t~o Germany

Fig. 2- Number of pigs vs Mean Combat E-11tvee

Value.

3.0

24
6.2.4 Educatonal System
Relatively incomplete data on national educational systems show little consistent pattern of
relationship with combat effectiveness (Table 10). The relationships for World War I are positive
and strong. The relationships for World War II are largely reversed. Though in both wars there
are relatively strong correlations, their inverse nature reduces their validity as predictors of CEV.
The normalized value for primary school pupils shows that these inverse values tend to cancel
out when combined.
Table 10. Correlaton of Educational System Factors and Combat Effectiveness Values

Correlation Coefficients
Independent Variables (per
capita)

World War I

Primary School Pupils
Primary Teachers

.842
n/a

Secondary School Pupils
University Students

Combined

-.721
-.906

.528
n/a

World War II

n/a

.152
n/a
n/a

.054

n/a

6.2.5 Vital Statistics and Health
There is a strong negative correlation between the vital statistics and combat effectiveness, as
shown in Table 11. Whereas high values for industrial production indicate national strengths,
high values for infant mortality and death rate indicate national weaknesses (e.g., poor health
care system). Therefore, the negative direct relationship shows that a better health care system
is related to better combat effectiveness. The strong negative correlation between birth rate and
CEV may reflect the trend that as nations industrialize, their birth rates tend to decrease. In
general, these societal conditions closely match the level of industrialization. Figure 3 shows the
scatterplot for the infant mortality rate factor.

25
Table 11. Correlatlon of VRtal Statistics and Health Factors and Combat EFOPdivenee Values
Correlation Coefficients
Independent Variables (per
capita)

World War I

World War II

Combined

Infant Mortality Rate

-.751

-.825

-.628

Death Rate

-.451

-.732

-.427

Birth Rate

-.690

-.842

-.627

Correlation With Values Normalized to Germany
0

3.0

0

2.5

2.0

P

a$4

-. 628

0
Z

1.5

40

,.5
S0.5
0.4J0

..

S:S
05

0

0.5

1.0

1.5

2.0

2.5

HIean CEY Normalized to Germany

Fig. 3. Infant mortality vs Mean Combat Effectiveness Value.

3.0

26
6.2.6 FInandal Activity
There is a consistent and moderate positive relationship shown in Table 12 between measures
of financial prosperity (money flow and spending) and combat effectiveness. On the other hand,
there Is a moderate negative relationship shown between high taxes and combat effectiveness.
Table 12. Correlation of Financial Activity Factors and Combat Effectiveness Values
Correlation Coefficients
Independent Variables (per

World War I

World War II

Combined

capita)

Banknote Circulation

.688

.124

.421

Bank Deposits

.896

.472

.451

Government Spending

-.388

Tax Revenues

-.320

n/a
-.842

n/a
-.354

6.3 ADVANCED STATISTICAL ANALYSIS
The simple correlations shown above demonstrate the ability of statistically comparing mean
CEVs with broad national factors. However, the small sample sizes (four or eight cases) provide
low confidence in the results and makes the correlation unduly affected by even one outlying
value. This tends to skew the results unnecessarily; however, more advanced procedures can
help to reduce this impact.
6.3.1 Correlation Using All Engagements
Determining the mean CEV for a pair of nations for a given war is useful for making simple
comparisons, but the process of calculating the mean discards valuable information. This
information can be retained by using the individual CEVs from all of the combat engagements
as the cases of dependent values. So instead of having a total of only eight cases from both
wars, the analysis used 58 cases. (This includes the 56 separate combat engagements/battles
plus two additional cases representing a German baseline case for each war.12 ) As was done
for the mean CEVs, each war could have been examined separately, but this was not done

This does imply a constancy of German CEV across both wars, but there is no basis for
assuming otherwise. Making an assumption of this kind cannot be avoided if data from both
wars are to be Included in a single analysis.
12

27
because of the desire both to increase the data set being used for added confidence and validity,
and to find the best results across both wars for the sake of generality.
The calculated CEVs shown In Appendix A demonstrate a spread, or variance, around the mean
values. This variance may be based on one or more of several factors. One factor is error,
common to all measurements. If this were the only factor, it could be assumed that there is one
true CEV for all engagements between two nations in one war and that the mean is the best
approximation to this value. Another possibility is that the CEVs fluctuate during a war, perhaps
because of the progress of the war or special circumstances of given battles or campaigns. If
this is the case, It is probably better to use all of the individual CEVs in the correlation analysis.
Correlations using mean CEVs did not use the information contained in CEV variances, though
they could have. Generally speaking, correlations based on the complete data will be lower than
for the means alone because the spread of data is greater. Figure 4 illustrates this concept. The
top portion of the figure is a replication of Fig. 1 where the mean CEV value was used against
normalized values for electrical production. However, the bottom portion shows all of the CEV
values for a given opponent in a given war, rather than just the mean. Thus each point in the
top portion is expanded to a row of points at the same level of electrical production in the bottom
portion. The spread of data shows the uncertainty in the CEV value, which is important for
predicting CEVs from societal data.
6.3.2 Correlation Using AN Engagements and Logarithms
Not only does Fig. 4 show the variance of CEVs, but It shows an apparent nonlinear trend. The
arcing dashed line indicates a possible curve that has a better "fit" than the straight line. If this
is true, and that curve can be defined, then it would serve as a better predictor of points than the
equation of the straight line.
An examination of the variables yields a possible explanation for the apparent curvilinear nature
of the relationship between electrical production and CEVs. The CEV range covers all possible
positive numbers, but in some sense a CEV of 1.0 is the center of the range because this
indicates equality of effectiveness. This causes all of the instances of low CEV to clump together
between 0 and 1.0 and all instances of high CEV to spread from 1.0 to infinity. A way to adjust
for this uneven spreading is to use the natural logarithm of CEV. This would tend to equalize the
spread of CEV values above and below 1.0 and straighten out the curve from Fig. 4.
Figure 5 shows the correlation scatterplot of the natural logarithm of CEV (called LnCEV) vs
electrical production. This produces a clearly more linear trend and higher correlation coefficient
than shown in the bottom of Fig. 4. In a larger data base, it might make sense to use the natural
logarithm of the normalized values for the independent variables as well because their
normalization tends to produce the same Vclumping" problem.

213
Correlation Using Mean CEVs
*

3.0

Z.5

u
0.

S2.0

a,
o 0a,
u
0

w

0

ta

3.092
15



1,

0.
U
305

4)

e

00

u

0.5

4

0

751

10 0

~.a
4.

0..

0

U

I

""
o

0

S•

,f

0.5

o



0U

- WWII

•UK

-

-

WWIan

u
-

,

--. m=

USSR
m

m

Immmmm3.0.

ap

0

i

0 Fee

0.5

1.305

,

L
Z0

,

n

CEV By Engagement Normalized

Fig. 4. Ejeclcal p

.

n
3.

RUS
.45
5.0

to Germany

ucorr a Mion andgA Combas Effectiem Vale.

-WWII

WWV
I

29
Normalized Values For Both Wars

S3.0

0

2.5

r4
a

2.0

0

0

a

*

R = .786

,4

a.
be

A,

USA - VVII
0
0 .5

0

Ntr. L

S

of

GermanN

e

UK

ga
,

0.5

-

VaII

-

ve

U

o

USSR

-

VII

U

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

Natural Log of CE-V Normalized to Gernany
Note:
&&3 Coplf 4

As
exlie

Wado

Values above 1.0 for electrical production and above
ResultsV

0 for LnCEV indicate performance better than Germanyv

abve th

corlto

coficet

Fig 5. Electrica production vs

fo caehnteC

rmalcma

atrlLog of AR Combat EecinssValue.

6.3.3 Comparing Correlation Results
As explained above, the correlation coefficients for cases when the CEVs from all combat
engagements are used will generally be lower than when the mean CEV was used. However,
use of the natural logarithm of CEV should generally produce stronger correlation coefficients
than without doing so, and may even produce a stronger correlation coefficient than when using
the mean CEV. A full list of correlation coefficients for all three methods is provided in Table 13.

30
Table 13. Alternative Correlation Coefficients
Normalized CEVs for Both Wars
Normalized Societal
Factors
Coal Production
-Iron Production
Steel Production
Surf Acid Production
Electrical Production
Wheat Hectares
Barley Hectares
Oats Hectares
Wheat Output
Barley Output
Oats Output
Horses
Cattle
Pigs
Sheep
Railway Mileage
Shipping Tonnage
Telegrams
Prim School Pupils
Infant Mortality Rate
Death Rate
Birth Rate
Banknote Circulation
Bank Deposits
Tax Revenues

CEV Means
.564
.539
.783
.712
.921
-.070
-.418
.032
.106
-.273
.271
.399
.666
.796
-.086
.720
.119
-.050
.152
-.628
-.427
-.627
.421
.451
-.354

All Battles CEVs
.426
.436
.637
.580
.751
.016
-.313
.079
.167
-.251
.199
.421
.555
.664
.027
.658
.162
-.037
.121
-.509
-.322
-.495
.317
.375
-.241

Log of All CEVs
.563
.561
.767
.748
.786
-.158
-.509
-.049
-.037
-.401
.104
.220
.528
.640
.143
.670
.268
.185
.167
-.668
-.528
-.689
.274
.557
-.326

The lack of consistency as to the method producing the strongest correlations prevents drawing
a firm conclusion about the nature of the general relationship between CEVs and societal factors.
While the tendency of strc ng correlations between natural logarithms of CEVs and societal
factors (when using all of the individual cases) suggests that the general relationship is nonlinear,
it would take more data and more cases to confirm this.
6.3.4 Multiple Regression
Correlation is not the last step in the analytical process because it is not the most advanced
statistical tool that could help to predict CEVs given societal data. This is because correlation
considers only one factor at a time and is insufficient if it is believed that several factors are at

31
work simultaneously to explain CEVs. Regression analysis can be used to overcome these
limitations.
Whereas correlation analysis provides only the strength of co-variation between two variables,
regress!on analysis provides a linear equation that allows calculation of dependent variable
values given data for the independent variable(s). The calculation of this best fit line is based
on the principle of least squares, which means that the squared distance between all of the data
points and the line is at a minimum. Similar to correlation analysis, the regression coefficient, R2,
indicates the "goodness" of fit for the line and varies from 0 to 1.0 with 1.0 being a perfect fit.
Another way to look at the R2 value is through the concept of explained variance. The
dependent variable, in this case CEV levels, has a range of values that is known as its variance.
The challenge is to determine what accounts for this spread in values. In theory, the more that
is "known" about the dependent variable, the more of the variance that can be explained. Data
on related independent variables provide this increased knowledge about the dependent variable.
The R2 value indicates just how much of the variance in the dependent variable is explained by
the independent variable(s) used. If the independent variable(s) have a complete and direct
relationship to the dependent variable then all of the variance is explained and R2 equals 1.0.
One problem in using regression analysis is the tendency for several independent variables to
correlate highly with each other. But if two or more independent variables correlate well with
each other, then they may not be able to explain much more variance than any one can alone
because they simply serve as proxies for each other. The key is to find two or more independent
variables that explain different portions of CEV variance so that their simultaneous inclusion
through regression analysis provides stronger results than using either separately.
When provided with a large number of independent variables for possible inclusion in a
regression equation, the procedure of stepwise regression offers the ability to test each variable
and select the best combination of variables to explain the variance in the dependent variable.
First the process finds the variable that explains the most variance on its own, then it seeks the
variable that explains the most additional variance, and so on. The process is stopped when no
further statistically significant increase in variance explanation is achieved by adding an additional
variable.
Regression analysis is the primary means by which current values for CEVs can be estimated.
it is also possible to use these equations to validate historical mean CEVs. Regression analysis
was performed for all three sets of independent variables used in the correlation analysis: mean
CEVs, individual CEVs, and natural logarithms of individual CEVs. For the analysis, data for the
variables were in normalized form so that both wars could be Included. Table 14 shows the
equations that are the results of the regressions.

32
Table 14. Regiression Result and Equations for CEVwwmw,w
Using Mean CEVs:
Explained Variance: R2 = 0.92
Best Fit Une:
CEV - 0.1902 + 0.7528xELECT

(5)

Using Individual CEVs:
Explained Variance: R2 = 0.69
Best Fit Une:
CEV = 0.33 + 0.98xELECT + 0.15xSHIPS - 0.169xTELEGRAMS

(6)

Using Natural Logarithm of Individual CEVs:
Explained Variance: R2 = 0.72
Best Fit Une:

ln(CEV)

-

-1.19 + 0.83xELECT + 0.16xSHIPS

(7)

Or
CEV = e-.1X&xeLECrxe16xSH'PS

(8)

(Notice that to calculate a CEV, the factors are now multiplied, rather than added.)

The exceptionally strong RFresult and the use of only one independent variable in the regression
equation for the mean CEV approach reflects the fact that use of the mean reduces the spread
of CEV values so that it is easier to explain the variance in CEVs. When CEVs from individual
engagements are used, they are more spread out making a good "best fit" line (high A2 value)
harder to obtain. In the other approaches, two or three independent variables were included
because the additional variables - ships or telegrams - tended to supplement electrical
production by explaining different pieces of CEV variance. Although the R2 value for the latter
two approaches is not as high as that for the mean CEV approach, inclusion of further variables
will not yield statistically significant explanations of any additional variance.
However, it is clear that the regression results are relatively strong for all three methods and that
electrical production is an important variable in all three cases. Because of co-variation, use of
other variables representing industrial production in place of electrical production would show
similar results.

33
6.3.5 Another Possible Analysis
All of the above approaches to correlation and regression use the societal variables as separate
factors for study. Though the point of the study was to determine which, If any, of these
variables could perform as good predictors of CEVs, there is a danger in relying on just one or
two key Indicators. The problem is that it is possible that those indicators, while valid for the
nations and wars under study, might not be equally reliable for different times or different nations.
To develop results with more generality - applicable across a wider range of places and times
- it might be more useful to develop aggregated measures as independent variables. Instead
of using the level of electrical production, the predictor would be a broader measure of industrial
production that included electrical production, steel production, and other relevant factors.
Use of simple composite variables - such as additive measures of agricultural production - was
attempted in the regression analysis. However, the regression results were higher when using
the individual variables as opposed to the composites. Part of the problem was the small data
set that did not offer enough cases or variables to make these types of manipulations useful.
Another problem was that aggregating variables often requires weighting schemes to ensure that
variables with small values or ranges do not get "masked" by other variables. This adds a level
of complexity that was deemed to be unjustified at this time, though the approach may prove to
be significant in future efforts of this type. In theory, composite variables seem to present the
best case for producing an equation for predicting CEV that could be applied to many nations.

34

35
7. ESTIMATING COMBAT EFFECTIVENESS VALUES
Though the results of the statistical analysis suggest a good predictive ability for determining
current CEVs, the actual predictive ability of societal factors - at this time - to estimate current
and future CEV ratios Is limited. The method Is sound, but more data need to be accumulated
and analyzed before there is high confidence that the results are valid and can be used for other
countries. For illustrative purposes, the CEV ratio between the US and USSR have been
estimated using the analyses of this study.
For historical battles, there are two ways to do estimate the CEV ratios. One is to use the
experienced mean CEV values relative to Germany, where a US/USSR mean CEV can be
estimated by using the German mean CEV as a constant baseline13 :
CEVIUSS

(9)

=3"154 -=6.411:1
0.492

(10)

CEVusDsR

=

CEV",,WILj

This would produce the following values:
World War 1:
CEVwIsuSSR

World War Ih:
CEVu~s/usR = 2"848 - 2.321 •1

(1

1.227
The other method, and the only method applicable for predicting current (or future) CEVs, would
be to use the equations that were generated during the regression analysis. These can also be
compared to experienced CEVs that were calculated as means from the historical combat
engagement data from World Wars I and II. The calculated CEVs are also extended to the most
current data."'
This, however, assumes that the German component of CEV is constant against both
sides. Especially in the WW I case this may not be entirely accurate. The German/Russian
battles date from 1914 and the German/US battles date from 1918. During this time the German
Army was exhausted through four years of hard combat and had lost most of its early cadre of
top forces. Its quality in 1918 almost undoubtedly was less than in 1914, but the exact amount
of degradation in German combat effectiveness during those years is unknown.
13

Additional research provided current (early-i 980s) data for factors used in the regression
equations. Data are shown in Appendices C and D. Telephones per thousand was substituted
for telegrams, since the latter data were not readily available (or may not have been applicable).
14

36
Table 15 shows the various CEV estimates. The "Experienced CEV" entries for Germany/US and
Germany/USSR entries are the mean value CEVs. The experienced CEV entries for US/USSR
are those calculated in Eqs. (10) and (11). The CEVs calculated from the means were derived
using Eq. (5) in Table 14. The CEVs calculated from "All" were derived using Eq. (6) in Table 14.
The CEVs calculated from "Log All" were derived using Eq. (8) in Table 14.
The derivations of the entries involve four steps.
I.

The appropriate (normalized) values were substituted into the equations for Germany, the
US, and Russia/USSR.

2.

Because the equations produce CEVs for the given country over Germany, they are
inverted in step 2.

3.

Because the equations are approximations, the calculated CEVs for Germany over
Germany are not 1.0. To maintain the normalization convention, the calculated CEVs are
renormalized by dividing by the calculated Germany over Germany CEVs.

4.

The US/USSR CEVs are calculated using Eq. (9).

Interestingly, the results generated from all three methods are remarkably close for US/USSR
CEVs, with the exception of the value of 21.24 for World War I using the logarithm method. This
abnormally and unrealistically high value may be the result of the peculiar behavior of exponential
mathematics where seemingly small variances in data values (outliers) can become especially
magnified and produce large values. Overall, the results as shown in Fig. 6, indicate a trend (the
average line) where US/USSR CEV has fallen from around 7.65:1 in WW I (excluding the
logarithm data) to about 2.75:1 in WW II to about 1.82:1 for the mid-1980s.1 5 This trend and
the similarity between methods provides a degree of validity to the overall approach, especially
since this seems to be largely in concert with expected results.
There is a cautionary note in this process. Although electrical production was the single
strongest correlation and regression factor for explaining CEV variance, other factors of industrial
production were also strong and co-varied closely with electrical production in the historical data.
However, the historical realities of industrialization have undercut some of this co-variation.
Because of this, had some of these other factors been used in the regression equations instead
of electrical production, the projected CEV ratio for the current period between the US and the
USSR would have come out much different. For example, while US electrical production per
capita is nearly double Soviet levels, current US coal production per capita is only 70% greater
than Soviet coal production and the Soviets actually outproduce the US in steel per capita by
nearly two-to-one. Use of steel values, therefore, would have suggested that the US/USSR CEV
ratio should be seen to favor the Soviets.

15

In general, Quantified Judgment Model rules cap CEV ratios at 6.0:1.0, and it would

probably be difficult to come up with historical cases that demonstrated higher CEV ratios than
that. The calculated WW I figures for US/USSR CEV should be understood in that context.
Though it does seem clear that the US would have had a significant adv&ntage against the
Russians, it would likely not have been above the 6.0:1.0 cap.

37
Table 15. Estinmatin Combat E09sc(dvwnsm Values

Germany/
World War I

Germany/US

Russia

US/Russia

Experienced CEV:
CEVs Calc From Means:
CEVs Calc From All:
CEVs Calc From Log All:

0.49
0.52
0.36
0.10

3.15
3.73
3.35
2.21

6.41
7.20
9.30
21.24

Average:
Average Without Log:

0.37
0.46

3.11
3.41

11.04
7.64

World War II

Germany/US

Germany/USSR

US/USSR

Experienced CEV:
CEVs Calc From Means:
CEVs Calc From All:
CEVs Calc From Log All:

1.23
0.80
1.05
0.63

2.85
2.36
2.57
2.07

2.32
2.96
2.43
3.29

Average:

0.93

2.46

2.75

Current (Mid-i 980s)

Germany/US

Germany/USSR

US/USSR

CEVs Calc From Means:
CEVs Calc From All:
CEVs Calc From Log All:

0.64
0.71
0.58

1.17
1.07
1.22

1.84
1.52
2.10

Average:

0.64

1.16

1.82

38
Four Methods of Calculation

10:1

S

A

Experienced

9:1

*K Calc
Kean

8:1

Ave
7:1

=7.

From
CEVs

65: 1

*K

Calc From
All CEVs

6:1

Caec From
Logarithms

o

5:1

Average

a
S4:1

3:1 3:

Ave =1. 82,1

Ave= 2. 75: 1.
2:1

1:1

0
World War I

World War
W

II

Current

(1980s)

*0

Period

S Logarithm

value

## No Experienced

discarded as outlier

value since no historical

combat

Fig. 6. US/USSR Combat Effectiveness Value trend.

In further studies, regression analysis using more countries and more engagements (needed for
higher confidence of the results) might yield different factors as being more stable predictors.
The instability of single factors reinforces the value of using composite factors that should limit
the chance that nonrepresentative factors could skew the results.

39
8. CONCLUSIONS
The feasibility study was not pursued in enough detail and breadth to ensure its validity,
generality, and applicability to other nations. The study simply demonstrated that it may be
possible to produce valid, general, and widely applicable results with a further study that
generates enough quality data on combat engagements and societal factors.
8.1 RESULTS
Analysis of the correlation and regression results between CEVs and the societal factors selected
for the initial feasibility study shows limited conclusions. Factors related to Industrialization, such
as electrical production, generally showed strong positive correlations with (R = .90+) and
implied good predictive ability for relative combat effectiveness. Other factors, particularly those
related to agriculture, showed inconsistent and inconclusive results. The CEV/industrialization
link is not surprising because many of the characteristics necessary for military prowess are also
important in industrial activities and vice versa.
The three different analytical approaches produced differing results, but the most advanced
approach (and arguably the most reliable and accurate) using logarithmic values for CEVs still
produced significant results (A 2 = .72) for the nations and wars under study. In fact, it would
have been surprising if the societal factors could explain even more CEV variance than was
observed since it is assumed that some portion of CEV derives from military factors (like training)
that should not be directly related to or subsumed by the societal factors under study.
The analysis also illustrates the different types of statistical techniques that could be used and
the kinds of answers they would prov.ide in studies of this type. It is premature to conclusively
attempt to select the best among these approaches. it does seem that a model for predicting
CEVs with relatively high accuracy could be developed over time.
This initial feasibility study has produced several tentative methods for calculating (and crossvalidating) CEV ratios for combatant nations given key societal data about those nations. Using
recent data, these methods were applied to develop estimates for the CEV ratio that existed
between the US and the USSR during the mid-1 980s. There is no reason this method could not
be used to forecast or project future CEV ratios as well as to measure current ratios. The
significant needs are forecasts, projections, or estimates of values for the key independent
variables, such as per capita electrical production. In instances where only projection ranges for
this data are practical, then CEV ratio ranges can be derived as well. Because of remaining
unexplained variance in CEVs (R2 <1.0) it may be best to express all projected or estimated CEVs
in range format. (There is a statistical procedure for calculating confidence ranges for regression
equations.) In broadest terms, the project indicates the possibility of ascertaining relative combat
effectiveness values by exploring the underlying state of the adversarial nations.
Overall, the study produced some interesting results for the particular cases examined and hinted
at some important relationships that may exist. Drawing more general conclusions about the
basis of troop quality and combat effectiveness from this small effort would appear to be
premature without substantial validation through further study. The high correlations that were


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