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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