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OCR for page 105
Appendix B
Force Exchange Ratio, Historical Win
Probability, and Winning with
Decisive Force
FORCE EXCHANGE RATIO AND
HISTORICAL WIN PROBABILITY
For a number of years the Center for Army Analysis (CAA) analyzed
historical combat data to determine the relationship between victory and
casualties in land combat. The historical data, contained in the CAA Data
Base of Battles (1991 version, CDB91) is from a wide range of battle
types durations ranging from hours to weeks, dates ranging from the
1600s to the late 20th century, and forces involving a variety of nationali-
ties. Based on the analysis of these data (and some motivation from
Lanchester's square law formulation), it has been demonstrated (see Center
for Army Analysis, 1987, and its references) that:
· the probability of an attacker victory1 is related to a variable called
the "defenders advantage" or ADS, where ADVis a function of force
strengths and final survivors; and
· ADV~ in (FER)
Since N= threat forces and M= friendly coalition forces in our defini-
tion of the force exchange ratio (FER), Figure B-1 depicts the historical
relationship between the FER and the probability of winning, regardless of
Probability of a defender victory is the complement.
105
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106
IMPROVED OPERATIONAL TESTING AND EVALUATION
1
0.8
0.6
0.4 -
0.2 -
, - ~
I
0~ 1 1 1 1 1 1 1 1 1
0 1
4 5 6
Force Exchange Ratio
7 8 9 10
FIGURE B-1 Historical relationship between force exchange ratio and Prkwin).
SOURCE: Adapted from Thompson (1992) and Helmbold (1992~.
whether the coalition is in defense or attack mode. Additionally, the rela-
tion between FER and friendly fractional casualties is depicted in Figure
B-2 (see CAA, 1992 and VRI, 19921.
FER is not only a useful measure of effectiveness (MOE) to indicate
the degree to which force imbalance is reduced, but it is also a useful his-
torical measure of a force's warfighting capability for mission success.
FER AND "DECISIVE FORCE"
Following the demise of the Soviet Union and Operation Desert
Storm, the U.S. National Military Strategy (NMS) codified a new military
success objective: "Apply decisive force to win swiftly and minimize casual-
ties." The NMS also implied that decisive force will be used to minimize
risks associated with regional conflicts. The FER is a MOE that is useful in
defining and quantifying the level of warfi~htin~ canabilitv needed to meet
this objective.
Figure B-3 has been derived from a scatterplot of results from a large
number of simulated regional conflicts involving joint U.S. forces and coa-
lition partners against a Southwest Asia regional aggressor. The coalition's
~ ~ . ,
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APPENDIX B.: FORCE EXCHANGE RATIO
.12—
REIN .10 —
o
,i, .08—
Ct
t~ .06—
Ct
,~ .04—
. _
107
\
\
\
-
2 3
Force Exchange Ratio
4 5 6
FIGURE B-2 Force exchange ratio/casualty relationship.
SOURCE: Adapted from Thompson (1992) and Helmbold (1992~.
Objectives are to conduct a defense to prevent the aggressor from capturing
critical ports and airfields in Saudi Arabia and to then conduct a counterof-
fensive to regain lost territory and restore national boundaries.
The FER-coalition casualty relationship shown in the figure is based
on simulation results, in which the FER is the ratio of the percentage of
enemy losses to the percentage of coalition losses. Except for the region in
which the coalition military objectives were not achieved (FER < 1.3) be-
cause insufficient forces arrived in the theater, the relationship between
FER and coalition casualties is similar to that shown in Figure B-2, which is
based on historic data. The relationship between FER and the probability
of win in Figure B-3 is based on the analysis of historic data.
As shown in Figure B-3, a FER= 5.0 is defined to be a "decisive"
warfighting capability. This level comes close to achieving the criterion of
minimizing casualties, since improvements above that level only slightly
reduce casualties further. This level of FER also minimizes risk in that a
force with a FERof 2.5 will win approximately 90 out of 100 conflicts (lose
10 percent of the time) but will lose less than 2 percent of the time with a
FER= 5.0.
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108
to
. _
to
o -
.~
o
~ -
._
to
Pr (win) = .505
IMPROVED OPERATIONAL TESTING AND EVALUATION
Aggressor achieves military objectives
Coalition objectives achieved,
casualties high
1.0 2.0 3.0 4.0
.846 .937 .968 .981
Force Exchange Ratio
FIGURE B-3 Force exchange ratio and decisive warfighting capability.
SOURCE: Adapted from Thompson (1992) and Helmbold (1992~.
Coalition objectives
achieved, casualties
. reduced
Decisive
ODS
5.0 50.0 100.0
Representative terms from entire chapter:
exchange ratio
