IT'S NOT THE SIZE OF THE ARMY; it's how you use it. That's the conclusion of a recent study by Patricia Sullivan, a professor at the University of Georgia, who has devised a simple yet effective statistical formula that correctly predicts the outcome of 78% of the conflicts plugged into it.
Pr = probability that an intervening nation will achieve its goals
Limited goals mean better odds. Sullivan calculates the U.S.'s chances of success in Vietnam were 22%. The 1991 Gulf War had a 93% chance of succeeding. The invasion to overthrow Saddam had a 68% chance of working; as for routing insurgents and installing democracy, chances of success are 1 in 5.
x, y = variables
ß = magnitude and direction of variables' effects
Sullivan's formula has several variables, including war aims, troop levels, alliances, and length of conflict. She found that as troop levels increase, the probability of successfully achieving political aims through force decreases.
Pr(yi=1|xi) = 1/(1 + exp(-xi ß))
i = intervention in question
Sullivan tracked 122 military interventions involving the U.S., Russia, China, France, and the U.K. between 1945 and 2003. Overthrowing governments is easy, but using military intervention to get nations to do what you want has only a 17% chance of success. Propping up foreign regimes works just 40% of the time.