Figuring out the effectiveness of a missile defense system is complicated business, and often the matter is oversimplified in order to make it understandable.
It is for example easy to confuse the maximum range of a missile with the size of an area that the missile could potentially protect. For a variety of reasons that is not the case because the effective range of an air defense missile is much smaller and depends on the relative movements between the incoming missile and the air defense missile. This misunderstanding of the effective coverage area can for example be found in the Danish debate about the need for SM2 missiles on the frigates of the Iver Huitfeldt class, where it has been widely claimed that a single frigate with these missiles would be able to protect most of the country. While a circle around the center of Denmark with the radius of the maximum range of an SM2 missile does cover most of the country on the map, that is unfortunately not even close to the actual effective protection that such a frigate would provide.
But even more importantly, the success of the missile defense system depends on probability calculations that are somewhat counterintuitive for most people. It is not just a simple matter of missiles one-on-one, but a question of figuring out an overall probability of success in a scenario with X number of incoming missiles against Y number of defensive missiles. And the uncomfortable truth is that it usually doesn’t take very many incoming missiles to saturate your defensive system.
A basic understanding of the mathematics of probability is therefore important when trying to determine the effectiveness of your missile defense system and the level of trust you can put on that system. If decision makers don’t understand the concept of probability, they may get overconfident about their defensive systems.
A few weeks ago, Donald Trump talked to Fox News about North Korea:
“We have missiles that can knock out a missile in the air 97 percent of the time, and if you send two of them it’s gonna get knocked out.”
So president Trump seems confident in his defense system against ballistic missiles from North Korea, and that may lead him to believe that a preemptive first strike could be a good idea. But as Ankit Panda and Vipin Narang show in War On The Rocks, the president is wrong:
Trump’s remarks, however, make it clear that he believes each interceptor has [a single-shot probability of kill] of 97 percent (rather than 57 percent). Hence “if you send two of them it’s gonna get knocked out.” This is a wildly inflated — almost delusional — sense of how accurate the system is, and how many North Korean ICBMs it could potentially successfully intercept. Trump’s claim is almost correct if four interceptors are assigned per incoming warhead, not one. To get to “gonna get knocked out” (with >99 percent assurance), we would need to assign six interceptors per incoming warhead if each has an SSPK of 57 percent. No doubt the president heard either 96 or 97 percent effectiveness for homeland missile defense during a briefing, without realizing that this did not refer to the accuracy of each interceptor but to four against a single incoming ICBM.
While this may seem like statistical nitpicking, the United States does not possess unlimited GBIs. This year, the GBI inventory will be expanded from 30 interceptors to 44. Assuming the four-per-ICBM concept, successive North Korean ICBMs begin to pose real problems. For instance, let’s imagine a scenario where North Korea fires at least 11 ICBMs, the number needed to exhaust all 44 planned U.S. GBIs. Assuming the empirical SSPK of 56 percent (meaning four interceptors gives you a 96 percent chance of destroying each ICBM warhead), we quickly arrive at an overall system effectiveness of just 66 percent. That’s a one in three chance of a U.S. city absorbing a devastating nuclear strike.
To that can be added the possibility that North Korea could apply deceptive measures to increase the possibility of penetration and further decrease the reliability of the defense system.
And if that isn’t enough to scare you, this should: Even if U.S. missile defense gets lucky and takes out North Korea’s missiles, the tyranny of geography means U.S. salvo launches of GBIs against North Korean Hwasong-14s might ignite a nuclear war with Russia. Simply because of where the U.S. GBIs are located in Alaska and the trajectory a Hwasong-14 would follow from North Korea to a West Coast city, U.S. interceptors may have to make midcourse contact over the Russian Far East.
Which is why it is a good thing that Russia has assigned a ship with ballistic missile radar detection to the Pacific Fleet. If it should come to an exchange of ballistic missiles between North Korea and the United States, we depend on Russia to keep a cool head.
But the fundamental problem is that the president of the United States may have such a wrong understanding of the mathematics of probability that he believes the dynamics of nuclear deterrence have changed in a way that makes it possible for America to attack a nuclear power without fear of retaliation. Even if it never comes to an actual exchange of missiles, it may lead to a whole range of terrible foreign policy choices and a declining interest in maintaining strong alliances, because the American leadership would be complacent about its own security situation.