Calculating the “SIOP Degrade”
In 1991, Maj Gen Robert Linhard was the Director of Plans and Resources at SAC in Omaha. I had retired from the Air Force and was working at the RAND Corporation. There had been some discussion in Washington about deploying an active defense to counter any attack against the United States by a third country (that is, one other than the Soviet Union) with nuclear-armed ballistic missiles. Such a deployment would not be consistent with the ABM treaty of 1972. Rather than withdraw from the treaty, the United States was considering a concept that would allow the Soviets to deploy a similar defense along their southern borders to guard against an attack by their neighbors to the south.
General Linhard wanted to know how such a defense, if allowed, would affect the United States’ ability to execute the SIOP. In the terms he used, he sought to understand the “SIOP degrade.” To this end, he invited a group of analysts to convene in Omaha to address this question. The invitees included analysts from the Los Alamos, Livermore, and Sandia National Laboratories; two analysts from the RAND Corporation (Dean Wilkening and myself); one representative from the U.S. Arms Control and Disarmament Agency (ACDA); someone from the Department of Defense (DoD) Office of Research and Engineering (DDR&E); and others.
The meeting opened promptly at 0830. General Linhard stated his question and problem. The three analysts from the national labs set forth their approach to answering the question. After further questions and discussions, we finally disbanded for lunch. After lunch, General Linhard opened with a statement: “What I learned this morning is that, if I gave each of you a million dollars, after six months of ‘computer crunching,’ you could provide some tentative answers.” They all nodded affirmatively.
At two o’clock it was my turn. I opened by saying, “General Linhard, I am prepared to provide you considerable insight as to the implications of such a Soviet defense, this afternoon and for free. First, the bottom line: The degrade to the SIOP will be minimal (something like 10 percent), provided (1) that you employ decoys based on the latest decoy technology and (2) that you forbid the Soviets to deploy any forward engagement radar in the northern part of their country (a radar to control the engagement of a Soviet interceptor engaging U.S. RVs).”
To scope the problem,
1. Assume that each side is allowed no more than 200 interceptors.
2. Assume that each interceptor has a P_k (for a given engagement) of 0.7, for a total kill potential of 140.
3. Assume that the attack by Blue is 1,000 RVs against 1,000 targets, one RV per target.
4. Assume that 1,000 targets contain people and industrial facilities amounting to 1,000 units of “worth”—the proper choice of a scaling factor can make this true. Note that, for convenience, one unit of worth is an erdel (erdel is a fabricated word and means nothing).
5. Assume that the distribution of worth (erdels) among the 1,000 targets obeys the distribution according to the equation by the renowned economist Vilfredo Pareto, in which
V_cum = [ (n / N)^0.5 ] * w
where V_cum is the cumulative value, n is the stated number of targets, N is the total number of targets in the set, and w is the worth in the total set. The 1/2 is the exponent Pareto derived, which of course indicates the square root. It follows that one-half of the total value is in the first one-fourth of the targets.
Note that I was not breaking new ground with regard to the distribution according to Pareto. Many analysts have used this distribution, including the assignment of one-half as the value of the exponent.
6. Assume that the Soviets are not allowed to deploy an “engagement” radar to the north of the tier of provinces in the south of their empire.
7. Without an engagement radar to the north, they cannot engage in “threat-tube sorting.” That is, they cannot determine the intended target DGZ of each attacking RV and thus employ their 200 interceptors against the 200 RVs that are destined for the 200 most lucrative targets. Note that the defense has great leverage if it has a control system that provides this capability. Without it, the defender has to engage the incoming RVs without regard to the value of the target that each RV is intended to destroy.
8. Also, by not allowing the Soviets to deploy an engagement radar to the north, we assume that they cannot discriminate between decoys and RVs in the attack by Blue.
For the base case (no defense), the defense of course saves no worth (zero erdels), and there is no degrade to the SIOP.
Now take the case of a defense with a kill potential of 140 (200 * 0.7). There are 1,000 RVs versus 1,000 targets, and each target contains (on the average) one erdel of worth. Thus, the defense “saves” 140 * 1.0, or 140 erdels. This amounts to a 14-percent degrade.
For the next case, add 400 decoys to the attack. The decoys are, perhaps, Mylar balloons and very light. Assume that we must allocate 20 weapon spaces to employ the 400 decoys—a rate of 20 to one. The 980 remaining weapons attack 980 targets. These 980 targets contain 990 erdels:
1,000 * SQRT(980 / 1000) = 990.
Now, with 400 decoys (and 1,380 total objects), the expected erdels saved per object killed by the defense has been reduced from 1.0 to 0.717:
990 / 1,380 = 0.717,
assuming that the Soviet defense system is unable to distinguish between RVs and decoys.
Then, the erdels saved by killing 140 objects is equal to 100. To this number, we must add the erdels saved by replacing 20 weapons with decoys. This number is 10. So, the total erdels saved by the defense is 110, and the degrade is 11 percent.
If the technology of lightweight decoys permits 40 decoys per weapon space allocated rather than 20, the degrade will be a little less. The defense now “saves” less per object killed, 0.556 versus 0.717, as was the case for 400 decoys. Now, the defense saves 78 erdels (140 * 0.56)—plus the 10 erdels in the 20 targets not attacked—for a total of 88 erdels, a degrade of slightly under 9 percent for the case of 800 decoys.
On the other hand, if the Soviets can do threat-tube sorting, the problem takes on a different complexion. With threat-tube sorting (and no credible decoys), the Soviets would allocate their 200 interceptors to attack (selectively) the 200 RVs that are directed toward the 200 most lucrative targets. These 200 RVs put at risk nearly 45 percent of the total value of the system of 1,000 targets. The expected value saved by the defense per RV destroyed is now 2.25, and a kill potential of 140 saves 315 erdels. Now, the degrade is a whopping 32 percent.
We can see the powerful reasons for outlawing forward engagement radars:
(1) There is no threat-tube sorting, and
(2) there is no discrimination between RVs and decoys.
At this point, some of the other analysts could see their prospects for substantial future work slipping away and proclaimed that the problem could not reliably be reduced to such a simple calculus. Both General Linhard and the gentleman from ACDA thought otherwise, and they stated that they now had adequate insight to inform some key policy decisions:
1. Outlaw forward engagement radar (or radars).
2. Hold the number of interceptors the Soviets were allowed to a low number—a few hundred.
3. Pursue a vigorous program to develop lightweight decoys.
In the presence of these three provisos, the problem of SIOP degrade was minimal and presented no compelling argument against negotiating with the Soviets to allow both countries to deploy a limited defense to counter the threat of attack by third countries.
The key here is to scope the problem and address the key assumptions in a manner distinct from a focus on “computer crunching.” In other words, just sit back and think. Often, doing this can provide a basis for calculations that, while quite straightforward, yield new insights into the most important aspects of the problem.
For reasons external to those examined here, the whole concept of each side deploying a limited defense was lost in the turmoil surrounding the collapse of the Soviet Union and the United States’ decision, in 2001, to withdraw from the ABM treaty of 1972.
