In short, war involved a lot of uncertainties, and if the systems analyst failed to take at least the most important ones into account (and who knew just what those were in any particular case?), the conclusions and recommendations might be way off the mark.
This realization marked the discrediting of one of Paxson’s first and most ambitious pieces of systems analysis at RAND—his attempt to design the “best” bomber for the U.S. Air Force to use in a strategic atomic-bombing campaign against the Soviet Union. In many ways, it was an impressive effort. Using a combination of economic and mathematical analysis, Paxson drew up a list of the 100 “best” industrial target complexes to hit inside the U.S.S.R. He pulled together more than a dozen variables describing features and profiles of a bombing campaign and a bomber, put them into a single analysis and demonstrated how they interacted with each other, trying out different combinations to see which performed the best under a variety of circumstances. And he devised a way of defining effectiveness, a standard by which one weapon might be judged “better” than another. His measure was simply the number of targets a bomber could destroy for every million dollars spent. This was a new and unique way of taking into account, simultaneously, the war plan and the defense budget. You could ask, “If I have a fixed budget, which bomber could destroy the most targets?” or “If I must destroy a fixed number of targets, which bomber can do the job most cheaply?”
Paxson concluded that the Air Force should build a turboprop airplane rather than one with a turbojet engine. Not going with a jet meant sacrificing some quality in performance, but performance was merely a means to the end of bombing Soviet targets. And Paxson calculated that for the same price a larger number of fairly cheap turboprop bombers would do more damage than a smaller number of highly expensive turbojet bombers.
Air Force officers, almost all of whom were pilots, hated the study. They didn’t care about systems analysis. They liked to fly airplanes. They wanted a bomber that could go highest, farthest, fastest. And that obviously meant some sort of turbojet model. Some at RAND felt the same way, especially those in the aircraft and engineering divisions who sympathized with the Air Force.
But there were others who felt there was something else wrong with that Paxson study, something more fundamental. And that was where Albert Wohlstetter entered the picture. As a mathematical logician, Wohlstetter greatly admired some aspects of Paxson’s work—the elegant modeling, the manipulations of all those variables, how he made them interact in a single piece of quantitative analysis. But Wohlstetter also noted some peculiarities in some of Paxson’s major assumptions.
Most glaringly, there was a chart in Paxson’s study comparing turboprop and turbojet bombers in terms of cost and combat radius. The SAC operational plan in the early 1950s was to fly bombers from the United States to overseas bases and then to mobilize and launch the attack against the Soviet Union from there. In his study, Paxson had arbitrarily picked for his staging area a base in Newfoundland, about 3,600 miles from his proposed set of targets in the U.S.S.R. According to Paxson’s chart, a turbojet plane operating at a 3,600-mile combat radius would cost almost three times as much as a prop plane of equal range—$32 million, compared to about $12 million. Yet the chart also revealed that at 3,000 miles or less, a turboprop and a turbojet plane were about evenly priced. Upon further analysis, it appeared that for the state of the art of that period, an airplane traveling at high speeds or at very low or very high altitude—things that a jet-powered plane could do—hit their maximum range at about a 3,000-mile radius, beyond which a much bigger, heavier and, therefore, more expensive airframe would be needed. Indeed, according to Paxson’s chart, the cost of a jet bomber rose very gradually up to 3,000 miles and then shot up dramatically—in fact, doubling between 3,000 and 3,600 miles.
Wohlstetter had recently been assigned by Charlie Hitch to do an Air Force-commissioned study on the selection and use of overseas bases. It hadn’t struck Wohlstetter as being very interesting at all. But now, looking at this diagram in Paxson’s study, he saw that the location of a base—particularly its distance from the target—made a critical difference in determining what sort of bomber might be best for the Air Force. The turboprop looked good for longer-range missions; but had Paxson examined operations from bases much closer to the Soviet Union (and most bases were within 2,500 miles), he might have come up with an entirely different conclusion. From this, Wohlstetter realized that the issue of base selection was vital.
Wohlstetter’s first task was to find the right questions to ask; clearly, Paxson had missed a few. He started by doing essentially what Paxson had done—considering the bombing campaign as if it were a sort of transportation problem, getting the airplane from the U.S. to the target and then destroying as many targets as possible. But he centered the analysis on an issue that Paxson had not considered: where were the best places to put overseas bases? Then he broadened the problem to ask where the best places would be if the Soviets had air-defense weapons protecting the targets. How would that alter the flight path of a SAC bomber, and how might that affect the choice of bases?
Shortly after embroiling himself in the mathematics of the problem, Wohlstetter detected a major dilemma lying at the heart of the whole matter. On the one hand, as bases are moved farther away from the target, costs rise considerably: aircraft must be larger and heavier, so that they can travel great distances. That alone makes them more expensive, but there are also related rises in costs for longer runways, more fuel and fuel storage, increased stock and maintenance, and greater manpower requirements.
On the other hand, a close look at a map revealed a severe disadvantage to basing the bombers closer to the target, a disadvantage that the more traditional methods of bombing analysis might have detected but did not begin to analyze: when the base is close to the Soviet Union, the Soviet Union is also close to the base. In other words, SAC might more swiftly and easily strike the Soviets; but the Soviets might also more swiftly and easily strike SAC.
The significance of this dilemma struck Wohlstetter primarily because of two other streams of thought running through various RAND corridors, quite separate from the sorts of analyses done by Ed Paxson and his fellows in systems analysis.
The first was the spread of game theory throughout the mathematics and economics divisions of RAND in the early 1950s. The Fourth Annual Report of RAND, published in March 1950, exclaimed in its section on the mathematics division that in “the analysis of systems for strategic bombardment, air defense, air supply, or psychological warfare, pertinent information developed or adapted through survey, study or research by RAND is integrated into models, largely by means of mathematical methods and techniques…. In this general area of research… the guiding philosophy is supplied by the von Neumann-Morgenstern mathematical theory of games.”
There is no doubt that Wohlstetter was exposed to principles of game theory in his early days at RAND. His good friend J. C. C. McKinsey was heavily immersed in game theory, writing an introductory text on the subject and publishing more arcane articles in The Annals of Mathematics Studies, a highly technical journal published at Princeton by Johnny von Neumann. Ed Paxson was also intrigued, as were many in the systems-analysis field. Wohlstetter had several conversations with a RAND economist named Kenneth Arrow, who was writing a treatise that applied principles of game theory to questions of social choice. (The resulting book, Social Choice and Individual Values, published in 1951, became an instant classic and later won Arrow the Nobel Prize in economics.)