American Nuclear Primacy: the End of MAD or a New START?

May 22, 2012
Peacekeeper Missile Test
By David J. Elkind
In 2006, Professors Keir A. Lieber and Daryl G. Press published “The End of MAD? The Nuclear Dimension of U.S. Primacy” a provocative article which argued that the United States had acquired the ability to launch a disarming first-strike against Russia’s nuclear weapons sites.The article derives its title from the doctrine of “mutually-assured destruction” (MAD), which expressed the strategic balance of arms between the United States and the Soviet Union during the Cold War. According to MAD, neither superpower would dare initiate war without fearing cataclysmic retaliation. The authors argue, however, that the gradual erosion of Russia’s strategic posture a decade-and-a-half after the end of the Cold War, combined with qualitative improvements in the American arsenal, relieved the United States of retaliatory concerns.
This article is composed of several parts. The first is a brief overview of Lieber and Press’s model of a counterforce nuclear strike on Russia and their assumptions. This includes an assessment of the key features of the US-Russian strategic balance that have shifted since their article’s publication in 2006, and the (sizeable) limitations of their analysis. Second, I adapt Lieber and Press’s model for the current force deployments as the two nations bring their arsenal into compliance with New START, as their original plan is no longer possible. Third, I assess the likelihood of a successful first strike under this modified version of Lieber and Press’s model. My analysis shows that reducing the number of weapons assigned to each target dramatically increases the likelihood of target survival and, in my view, confirms that the United States no longer possesses nuclear primacy (and perhaps never did, but that is a separate question). Sensitivity analysis amplifies these concerns. Even after making dramatic accuracy improvements, the odds of a target surviving remain far too high to claim that the United States has achieved nuclear primacy or that it will be within reach for the foreseeable future. Finally, I conclude with some remarks on the desirability of nuclear primacy.
This article is not intended to persuade policymakers to pursue an improved nuclear arsenal – quite the opposite. I share Gen. (ret.) James Cartwright’s view, expressed in the most recent Global Zero report, that “there is no conceivable situation in the contemporary world in which it would be in [the United States or Russia’s] national security interest to initiate a nuclear attack against the other side.” This is true for a multitude of political, ethical, and humanitarian reasons, but this article will leave those considerations to other analysts; my results demonstrate that current arsenal levels maintain the strategic balance, and therefore such an attack is ill-advised for purely military reasons. In this way, I hope that my quantitative analysis can make a modest contribution to those involved in contemporary arms control debates.
The Lieber and Press Model in 2012: “Oh dodgy, very dodgy.”2
Lieber and Press begin their scenario planning with a discussion of Russia’s deterrent posture, and base their proposal off of a few key judgments. On the Russian side, the authors identify several critical vulnerabilities that may have enabled the United States to conduct a first strike against Russia. First, because Russia’s most survivable forces, truck- and sub-based missiles, did not conduct continuous patrols, these forces were often left stationary, and therefore vulnerable, in their ports or garrisons. Ordinarily, these two capabilities would provide Russia with a very survivable nuclear arsenal since they are incredibly difficult for an adversary to locate and destroy. Conversely, the uncertainty associated with locating and destroying all of an opponent’s mobile forces left the attacker open to devastating retaliation, and was a critical component of the strategic balance.
Second, Lieber and Press argue that blind spots in Russia’s satellite and radar observation could make it unaware of the alerting of US ICBMs and the launch of SLBMs from the Pacific. Because of the time lag between launch and detonation of a ballistic missile, observation of launch could provide the leadership in Moscow with the time needed to ready its own arsenal and launch its own forces before the American missiles arrive. Blind spots in detection could create avenues of attack that would leave leaders unaware of an attack in progress until too late. For this reason, the authors propose stealthy means for the initial waves (B-2 strikes, cruise missiles, and SLBMs), with follow-on attacks to assure targets’ destruction (ICBMs supplemented by more SLBMs). This sequencing does not change how the attack is evaluated in quantitative terms; however, early detection could have devastating consequences if the Russian leadership is able to retaliate.
On the American side, the authors tout improvements in warhead yield and accuracy that promise even hardened targets, such as silos, have an exceptionally low likelihood of survival. In their analysis, updated navigation systems, reentry vehicles and warheads give American SLBMs and ICBMs levels of lethality on par with that of the decommissioned Peacekeeper.
Moreover, this notional strike ignores several of the qualitative developments in Russia’s arsenal. In 2006, Lieber and Press wrote off the most survivable elements of Russia’s arsenal – its mobile ICBMs and SSBNs – with the understanding that they spent the majority of their time in port or in garrison, respectively. There is reason to believe that both of these elements could be on periodic, if not continuous, patrol.
As of 2012, however, Russian Navy Commander-in-Chief Admiral Vladimir Vysotskiy has announced that Russia will soon resume continuous SSBN patrols as of June 1, 2012 (though the article also notes deficiencies in submarines’ serviceability).3 Moreover, Russia announced plans on April 19, 2012 to begin patrolling two Borei-class SSBNs. Analysts, such as Pavel Podvig, have expressed doubts that Russia will return to Cold War levels of submarine patrol, but the these announcements certainly indicate Russian intentions to restore patrols of its strategic submarines.
The patrols of mobile ICBMs are somewhat more difficult to determine. On the one hand, Podvig expressed doubt that Russian ICBMs patrolled much at all in 2008, echoing Lieber and Press’s 2006 assessment. On the other hand, the blog Russian Defense Policy provides translations of several articles in Russian newspapers that claim SS-25, SS-27 Mod. 1, and SS-27 Mod. 2 mobile ICBMs are patrolling more often, as of January 2012. I am unable to assess the validity of these papers’ claims, but if these forces are patrolling more often, it would make a counterforce strike against the Russian arsenal difficult to carry out with a high degree of confidence.
Even if we accept the premise of boastful Russian media and conclude that Russia’s SSBNs and truck-mounted ICBMs only sporadically patrol, significant questions remain about the feasibility of Lieber and Press’s counterforce attack. Even these forces remain largely “on the reservation,” that does not mean that they are both garrisoned or in port simultaneously. A prudent nuclear planner would time the patrols of each such that at least one mobile missile contingent is deployed on land or sea at all times to assure a survivable retaliatory force.
Moreover, in the event of a crisis that could escalate to war, we have every reason to believe that Russia would flush its submarines and scatter its mobile missiles to the four winds to assure that its nuclear deterrent is difficult to locate, available for use in a counterattack, and assure that no rival would dare to initiate a conflict. This reasoning is the explicit purpose for building SSBNs and truck-mounted ICBMs. In planning their scenario, then, Lieber and Press are contemplating a US president ordering a bolt-from-the-blue nuclear attack on Russia in the total absence of a crisis that could cause Russia to mobilize its forces.I find it very difficult to imagine this set of circumstances existing in reality, or, as Gen. (ret.) Cartwright’s Global Zero panel writes, “nuclear planning for Cold War-style nuclear conflict between our countries functions on the margins … using outdated scenarios that are implausible today.”
In assigning multiple warheads to each aimpoint, Lieber and Press risk nuclear “fratricide,” by which imprecise warheads would destroy each other or create disruptive debris clouds. The authors acknowledge this risk, but argue that the reliability problems that would risk fratricide are no longer present. To them, either the first wave will destroy the target, making fratricide irrelevant, or the weapon will fail in one of its early launch phases and fall a considerable distance away from the target. For my purposes, I will accept their assessment.
Lieber and Press also argue that Russia would not launch a retaliatory attack in the event the Russian early-warning system detected the US launches because the steps in confirming the launches, informing political leaders, releasing launch authority and launching the missiles would take longer to occur to complete than the time required for the US weapons to reach their target. Perhaps this is true, though I am not in a position to contribute insights on this topic; as Lieber and Press note, a large component of Russian retaliation hinges on the Kremlin’s decisionmaking speed and process. Rather than make an airtight case for counterforce strike against Russian facilities, this analysis is primarily concerned with feasibility of destroying Russian targets; I will suspend the question of retaliatory launch on warning, despite its obvious relevance to the strike decision.
Once the attack begins and nuclear detonation is detected, we can be certain that all remaining Russian military installations would begin preparing a retaliatory attack. Lieber and Press do not address this possibility directly in their analysis, likely because they expect the barrage of closely-timed warheads would make these preparations futile.
The conclusions that Lieber and Press reached in 2006 reflect nuclear deployments that do not exist today. Arms reductions mean that the number of warheads required exceeds the deployed US arsenal by nearly 20 percent, even after adjusting the number of targets to reflect Russia’s reduced deployment. Again, this observation is not intended to spur policymakers to build more weapons or otherwise augment the US arsenal. Given the previous caveats in about Russian force posture, hypothetical arsenal improvements would be easily defeated by simply patrolling its mobile weapons. 
However, despite these gargantuan caveats, I think that it is still valuable to apply their approach to a counterforce strike to current arms deployments, if only to point out that planning such an attack is an absurd proposition. In their analysis, Lieber and Press adopt a 95 percent confidence level to evaluate whether the United States has achieved nuclear primacy. That is, if their model predicts that nearly all of the Russian nuclear arsenal can be destroyed with 95 percent confidence, the attack is regarded as a success. The choice of a 95 percent threshold is consistent with conventional academic practice, though I believe it is ill-suited to our unconventional subject matter. In evaluating the results of the model, this analysis will assume that the United States has achieved nuclear primacy if it can execute an attack that has a 99 percent chance of destroying all targets (identical to a 1 percent chance of one or more targets surviving). At the same time, however, I recognize that any threshold, no matter how low, requires the analyst to accept a certain likelihood of a Russian missile surviving and the corresponding danger to American lives. It is my opinion that every scenario presented here has an unacceptable outcome; any parameter specification has a risk of a Russian weapon surviving and corresponds to the destruction an American city as part of a counterattack.
A Surprise Attack in 2012
Data on the US nuclear arsenal are drawn from Hans M. Kristensen and Robert S. Norris’ article, “US Nuclear Forces 2012” (see Table 1), save for accuracy numbers, which are drawn from Liber and Press (“The End of MAD?” 18). The only changes update the number of aimpoints for truck- and silo-mounted ICBMs; the remainder of the assessment remains unmodified due to limited access to information about the Russian nuclear arsenal. Note that for the purposes of this article, accuracy is defined as “circular error probable” (CEP), which is the probability that half of the shots made with a particular weapon will fall within a certain radius of the intended target. For example, this article assumes that the nuclear-armed ALGM-129 cruise missiles have a CEP of 30 m, indicating that half of them will fall within a circle with radius 30 m about the aimpoint.
 US Strategic Nuclear Arsenal, 2012
This article will use data pulled from a number of sources. Information about Russia’s nuclear arsenal is drawn from Pavel Podvig’s April 12, 2012 blog post “Parsing the New START data.” Though Podvig admits that his numbers are speculative, I have used them here because they are drawn from most recent data exchange under New START. (Since New START only reports aggregate numbers of arms, there is no definitive set of numbers publicly available.) Compiling a list of targets is somewhat more difficult, as the resource Lieber and Press draw on, The US Nuclear War Plan: A Time for Change, is more than a decade old today, and I was unable to locate any current material nearly as comprehensive. In light of this, the list of targets will be based on Lieber and Press’s original plan ("The End of MAD?" table 3), with modifications made to the circumstances of New START where possible.
In 2006, the Strategic Rocket Forces deployed 291 mobile ICBMs, for which Lieber and Press designated 40 aimpoints. If we assume that Russia chooses to collapse its forces to a smaller number of sites (rather than play a shell game that disperses its active shelters over a larger area), we can designate 26 aimpoints for Podvig’s estimate of 186 mobile ICBMs. (This assumes a proportional relationship between shelters and aimpoints: 291/40=186/25.567, rounded up to 26.) Since each ICBM silo is its own aimpoint, we simply adjust this figure to reflect the smaller number of active silo-based ICBMs.
To re-evaluate the effectiveness of the United States conducting a first-strike on Russia’s nuclear forces, I attempted to follow the methodology Lieber and Press outline: first, assigning fast-arriving warheads to each aimpoint and adding follow-on attacks to assure the target is destroyed. Highly accurate weapons, such as the AGM-129, and high-yield weapons, such as the B83-1, are assigned to silos, as they are the hardest targets. Table 2 presents the notional outline of a nuclear attack on Russia’s nuclear facilities. Note that Table 2 was constructed to assign the same “batch” of weapons to each type of target (e.g., all SS-18 silos are targeted with the same set of weapons). This is designed to simplify the probability computations, though it is possibly suboptimal. Concerns about range, flight paths, and detection may mean that this particular model is unfeasible, but I am not in a position to evaluate these considerations.
 Notional Outline of a Counterforce Strike
Carrying out this attack would require use of the entire SSBN fleet and large components of the US bomber wings. This outline calls for a surge of all 14 deployed SSBNs; this unusual deployment risks Russian detection and may even signal the impending strike to Moscow. The attack outlined in Table 3 leaves the United States with merely 96 deployed warheads (68 SLBNs, 19 ICBMs and 9 nuclear bombs), likely to be augmented with warheads stored in reserve. The implications of such a bare deployed arsenal are beyond the scope of this paper.
Table 3 presents the results of the attack plan outlined in Table 2, showing the probability of one or more targets surviving. The top row reflects the “baseline” specifications that that Lieber and Press assume in their analysis. In the base case, SS-18 silos are assumed to be hardened to withstand 3000 psi overpressure; SS-19 and SS-27 silos are assigned 5000 psi. Terminal reliability is assumed to be 80 percent. Yield and CEP figures are drawn from Table 1.
In evaluating these figures, keep in mind that for our purposes, “reliability” encompasses the likelihood that all systems function as intended – reentry vehicles, missile launch, warhead triggers, etc. – except those related to accuracy. Accuracy is governed by CEP, and varies independently of reliability in this model. Also, while reliability is treated as having a binary outcome – e.g. the trigger detonates or it’s a dud – accuracy computations evaluate the likelihood that the weapon falls near enough the target to destroy it. (Lieber and Press discuss the computational dimensions of this model in the first appendix to “The End of MAD?”)
Subsequent rows show the results of sensitivity analysis, in which one parameter is adjusted. The “Increased Accuracy” row adjusts the entire US to have CEP reduced by 25 percent, which Lieber and Press tout as one of the core reasons that the United States has obtained nuclear primacy. For the baseline scenario, we can see that this attack is just on edge of the 95 percent threshold for Russian nuclear silos, but enjoys a high degree of confidence in destroying Russia’s land- and sea-mobile missiles. (Even though this model allocates warheads to target Russian strategic aviation, the following analysis will not assess the likelihood of these targets surviving because I am uncertain how to replicate the procedures Lieber and Press used.)
 Probability of One or More Targets Surviving
When interpreting this table, it is important to keep in mind two considerations. First, the model does not target individual mobile ICBMs, but instead groups several together as a single aimpoint, on the assumption that the lethal radius will extend far enough to destroy multiple truck-mounted ICBM shelters at once (Lieber and Press, “The End of MAD,” 41-42). This means that a single surviving mobile ICBM aimpoint could leave several fully-functional missiles intact for use in a retaliatory strike. Regarding the primary naval aimpoints, the reverse is true. While this model identifies 30 aimpoints, Russia only owns a handful of operational SSBNs, meaning that in the event that an aimpoint survives the volley, it would not necessarily contain a strategic target. However, as Lieber and Press note, the survival of a single Russian SSBN could destroy the United States, a fact sure to weigh on the mind of any American decision maker contemplating nuclear use.
It may be tempting to fixate on the high likelihood of the attack destroying Russia’s entire arsenal, especially because the probability of a single aimpoint surviving is below six percent in the baseline scenario. This reasoning is breathtakingly reckless. A single surviving truck launching a MIRV-equipped SS-27 could destroy four American cities, a tragedy of unimaginable scope. Moreover, the sensitivity analysis should make the reader ever more cautious about the feasibility of this scenario, since the likelihood of target survival rapidly increases as one nudges the parameters upward.
Regarding mobile ICBMs, the foregoing analysis also makes the assumption that these mobile ICBMs are “tightly packed” into a condensed number of shelters compared to the 2006 figures. This is an important consideration, since the core assumption of the aimpoint/lethal radius method that Lieber and Press use is that several warheads targeted at the same location will be able to destroy a dozen or so truck-mounted missiles – hence scattering these missiles over a larger number of shelters will reduce the effectiveness of the attack. However, this model affords the United States a “balance” of 96 deployed warheads, making subsequent attacks on these additional facilities possible.
The sensitivity analysis evaluates the likelihood of target survival for a modified set of parameters. In
Table 3, only one parameter is modified in each row and all other parameters remain fixed at the baseline values. “Stronger Targets” increases silo and submarine hardness by 50 percent;4 “Reduced Accuracy” increased circular error probable (CEP) by 20 percent; “Reduced Reliability” changed the reliability of the weapons from 80 percent to 70 percent; “Increased Accuracy” decreased CEP by 25 percent for the entire US nuclear arsenal. This analysis makes clear that even if finds a 5 percent chance of target survival acceptable, accounting for these deviations from baseline expectations radically reduces confidence in carrying out a counterforce strike. Even impressive improvements in the accuracy of the American arsenal are unable to crest the 1 percent likelihood of survival.
Increased target hardness increases the likelihood of one or more targets surviving to well above the 99 percent threshold in every category except submarines. This is because the submarines’ hardness is assumed to be 315 psi in the base case and is only increased to 472.5 psi in the sensitivity analysis. Considering the sheer magnitude of the weapons’ yield, these hardness figures are not even remotely close to the level of hardness necessary to assure survival of surfaced submarines.5 Notably, even though SS-19 and SS-27 silos are assumed to have the same hardness, the sensitivity analysis reports a 2 point difference in the survival of these silos. This is due to the warheads I assigned to these targets. Four out of the five weapons assigned to the SS-19 and SS-27 silos are the same; the only difference is that the SS-27 silos were assigned the B83-1 bomb, which has a larger yield and higher accuracy than the B61-7 bombs assigned to SS-19 silos.
Reducing the accuracy of US nuclear weapons nearly doubles the odds of survival for all Russian nuclear silos over the baseline, but leaves the survival of mobile ICBM shelters and primary naval targets virtually unchanged. This reflects the importance of accuracy to destroying hardened targets. Because submarines and mobile ICBM garrisons are not explicitly designed to withstand nuclear blasts, their hardness (as measured in psi) pales in comparison to that of ICBM silos. Given the nonlinearities present in these calculations, even the marked improvement in hardness for these two targets translates to insignificant improvements in their survivability.
Even a cursory examination of Table 3 reveals that reliability is a central consideration in these computations. In this model, reliability essentially sets the “ceiling” for the probability of a given weapon destroying its target. The lower reliability is, the lower that ceiling, and hence target survival is more likely. For reliability of 70 percent, the survivability of the Russian nuclear arsenal becomes quite high. Even the survival of Russian submarines, slightly below one percent in each scenario, jumps to seven percent for reduced reliability, while the likelihood of one or more ICBM silos surviving increases to 20 percent or more in each category.
The increased accuracy case reduced CEP by 25 percent. The choice of a 25 percent improvement in accuracy is deliberate, and intended to help contextualize some of the claims that Lieber and Press make about the modernization programs underway in 2006. Lieber and Press advertise that these improvements would put give US ICBM and SLBM accuracy on par with the decommissioned Peacekeeper, estimated to have CEP of 90 m, corresponding to a 25 percent improvement over the 120 m accuracy estimates for the Minuteman III. My analysis, however, goes one step further and applies this 25 percent improvement in accuracy across the entire arsenal in order to dispel the notion that accuracy improvements will ensure nuclear primacy for the United States. Even these dramatic gains in accuracy do not push the probability of one or more targets surviving below the 1 percent threshold for any category except submarines. (Submarine survival was already below the 1 percent threshold in the baseline, so this change is hardly dramatic.) This analysis shows that even if the US were to undertake a remarkable program of arsenal modernization to improve warhead accuracy, there is still an unacceptable likelihood of one or more Russian targets surviving.
It’s important to note, however, that Lieber and Press’s claim that arsenal improvements circa 2006 were intended to improve accuracy is disputed. Following the publication of Lieber and Press’s article in Foreign Affairs, then-Assistant Secretary for Defense International Security Policy, Peter C. W. Flory, penned a rebuttal which stated that the upgrades to Minuteman III missiles enhanced safety features of the weapons and did not increase accuracy. Even if Lieber and Press are correct, and the Pentagon is increasing ICBM and SLBM accuracy despite its explicit statements to the contrary, my analysis will underestimate the likelihood of target survival because it applies accuracy improvements across the entire US arsenal. That is, if only ICBM and SLBM accuracy are improved while the rest of the arsenal retains baseline accuracy levels per Lieber and Press, the likelihood of each target surviving will be slightly higher that the figures in the improved accuracy case.
In keeping with this section’s epigram, Figures 1-3 each vary pairwise the values for weapon accuracy, weapon reliability and target hardness.6 Each figure displays the survivability of a particular Russian nuclear silo. The color of any particular point indicates the percent chance that one or more targets will survive for the pair of parameters at that (x.y) point. In each diagram, the black dot indicates the location of the pair of parameters used in the baseline case. The black contour lines indicate the location of the 1 percent survival threshold. This line does not appear in Figure 3 because it is not in the visible area of the graph. Note that due to software limitations (or, perhaps, my programming limitations), the color scales are not consistent across the three diagrams; rather, each diagram has its color scheme scaled to reflect the data in the diagram.
Taken as a whole, it is my hope that these three figures will demonstrate that nuclear primacy could not be obtained without a decisive departure from current policy. Increasing the number of warheads allocated to each target would obviously improve the chance of success (assuming Lieber and Press are correct in their assessment that fratricide is no longer a serious concern in nuclear planning), but this would mark the end of decades of arms control efforts to reduce nuclear stockpiles in the United States and Russia. Qualitative improvements would not necessarily deviate from limits on the number of deployed launchers or warheads established in New START, but would require incredible investment on the part of the United States. Despite Sen. Jon Kyl’s bellicose outlook, fiscal considerations make this unlikely. Furthermore, we can anticipate that announcing an expansion of the US nuclear arsenal would further deteriorate US-Russian relations, exacerbate Russian feelings of insecurity, and spur further improvements to their arsenal.
   SS-18 Survival
Figure 1 simultaneously varies accuracy and reliability figures for all the weapons used in a strike on Russia’s SS-18 silos. (Keep in mind that this analysis applies accuracy adjustments across the entire nuclear arsenal. Hence, this figure actually over-represents the consequences of accuracy improvements for the US arsenal that concern Lieber and Press, since they only mention improvements in ICBMs and SLBMs; see Lieber and Press, “The End of MAD?” 28) Notably, reliability appears to be the factor that limits the success of the attack, since we can see that decreasing CEP as much as 50 percent over the baseline does not move the likelihood of an SS-18 silo surviving to within the contour line denoting a 1 percent likelihood of survival. After even a 20 percent decrease in accuracy, the model predicts likelihood of survival will stop decreasing. This is due to how the model computes target survival. As CEP decreases, the likelihood of that particular warhead destroying the target, single-shot kill probability (SSKP), approaches unity. SSKP is then multiplied by reliability, r, to compute terminal kill probability (TKP) for that warhead. In a scenario where all warheads aimed at a target report SSKP of unity, the joint probability of target survival essentially becomes an exponential decay function of r, where each additional warhead reduces the likelihood of the target surviving by a factor of 1-r. Because this model is very near the “accuracy ceiling” – the boundary beyond which the returns for increased accuracy radically diminish – only increasing reliability or allocating a larger number of warheads to each target will decrease the likelihood of one or more targets surviving to below the 1 percent threshold. The first option is undesirable because nuclear primacy is assumed to be destabilizing. The second option is impractical because it would mean the reversal of decades of arms control agreements and require a tremendous investment in nuclear weapons procurement in an age of austerity (while also destabilizing the international system).
 SS-19 Silo Survival, Sensitivity Analysis
Figure 2 simultaneously varies reliability and silo hardness for the modeled attack on an SS-19 silo. Even if the SS-19 silos are considerably weaker than Lieber and Press anticipate, there is little appreciable gain in the likelihood of success. Even for baseline estimates, it is only feasible to move the likelihood of success to within the 99 percent window if there are dramatic improvements in warhead reliability. An improvement in reliability to 85 percent, however, is still tenuous and highly sensitive to variations in silo strength. That is, if SS-19 silos are considerably more hardened than Lieber and Press’s baseline values indicate, this model would require reliability figures above 90 percent to ensure the likelihood of one or more targets surviving is below 1 percent. In evaluating this diagram, analysts should note that an increase in hardness above 40 percent would require warhead reliability well above 90 percent to assure target destruction. The uncertainty associated with these computations should instill policymakers with a sense of caution and humility in evaluating this model’s predictions.
 SS-27 Silo Survival, Sensitivity Analysis
Figure 3 varies CEP and target hardness simultaneously for SS-27 silos. The contour line denoting the one percent threshold does not appear because it does not fall within the visible area of the graph. Expanding the graph’s area would not be analytically useful because it would evaluate exceptionally flimsy ICBM silos’ survival against weapons whose accuracy would be more appropriately measured in centimeters than meters. What is most striking about Figure 3 is that arsenal improvements over the baseline do not meaningfully change the likelihood of target survival. Even increasing target hardness 50 percent corresponds to a subtle change in hue and a modest rise in target survival. The uniform red of nearly the entire diagram shows just how insignificant any accuracy improvements or hardness adjustments are in the vast majority of circumstances. Only if the US weapons are dramatically less accurate and Russian silos much more hardened does either of those parameters meaningfully impact the results of the model.
Taken together, the three figures show that the most important consideration is reliability, with accuracy second and target hardness third. Certainly these hypothetical improvements in accuracy move the likelihood of target survival very close to zero, but pairing CEP with other parameters demonstrates that within the constraints of this model, improvements in accuracy do eventually “level off” and no longer contribute meaningfully to target destruction.
Concluding Remarks
These results show that the United States cannot reasonably claim to have obtained nuclear primacy. Reductions in the two nations’ respective arsenals, coupled with the large number of Russian targets collaborate to make it exceptionally difficult to destroy the Russian arsenal in a counterforce first strike. Even though my results demonstrate a modest level of confidence in the baseline scenario, I believe that mutually assured destruction remains in place. Because the costs of even a single Russian warhead surviving would have such devastating consequences for the United States, I do not believe that any President or military planner would care to wager America’s most populous cities in conducting a nuclear first strike. While these results speak to the purely military considerations of that choice, the political, ethical and humanitarian considerations likewise make such an action highly unlikely.
Even though this article concludes that the US could not carry out a counterforce strike on the Russian arsenal in 2012, and therefore does not possess nuclear primacy, this should not be interpreted as a call to restart the arms race or otherwise acquire primacy. Liber and Press write that “the shift in the nuclear balance could significantly damage relations among the great powers and increase the probability of nuclear war,” and outline a variety of possible mechanisms by which this could come to pass and present rebuttals to counterarguments (interested readers should refer to Lieber and Press, “The End of MAD?” 31-38). To bridge the gap in nuclear capabilities, Russia and China may undertake perilous activities to restore the nuclear balance, such as pre-delegated launch authority, a launch-on-warning posture, or larger nuclear arsenals. Pre-delegated launch authority increases the risk of unauthorized nuclear use; Cold War experience confirms that launch-on-warning postures are vulnerable to false alarms initiating a counter-attack to imaginary missiles; arms races carry the risk that one side will perceive that it has gained the upper hand and undertake a nuclear first use. Furthermore, nuclear primacy carries considerable risks in times of crisis. In the event of a political crisis or a conventional war between the US and a rival power, the threat of a disarming strike by the United States may predispose the rival to land the first blow while it still has the means to do so. In this way, having a reduced confidence in the ability of the US to carry out a first strike should be read as a stabilizing feature of international politics, as strategic stability (if it had ever departed) has been restored as a pillar of the international system.
External to these considerations, achieving nuclear primacy would be a pyrrhic victory. The preceding analysis assumes that the United States is in possession of perfect intelligence on the locations and attributes of Russian nuclear weapons facilities and is able to carry out such an attack unhindered by air- or missile-defenses (and concludes such an attack is ill-advised despite possessing perfect information). Even if mobile missiles do not continuously patrol, it would make sense for Russia to shuttle them from one garrison to another in order to decrease Russia’s opponents’ confidence in accounting for all of them. Furthermore, Russia’s decision to deploy its mobile forces in the event of a crisis (or continuously as a matter of policy) could spark concerns in Washington that either a Russian attack is immanent or simply that United States’ confidence in a first-strike option has evaporated, creating further perceptions of insecurity and upsetting the strategic environment which, in the mind of US policymakers, has assumed nuclear primacy. What’s more, mobile deployments are a cheap, easy countermeasure that would effectively negate the confidence gained (such as any is gained) from believing that the United States has nuclear primacy. Achieving, and then maintaining, a position of primacy introduces several significant strategic concerns of its own, and would hardly enhance the security of the United States or the international system.
I would like to advance this line of argumentation one step further. If this model accurately reflects reality and a Liber and Press-style counterforce strike on Russia’s nuclear arsenal is unlikely to succeed, then deep cuts to the nuclear arsenal and the decision to abandon counterforce targeting gains credibility. That is, deep cuts to the nuclear arsenal would not mean abandoning counterforce doctrine because that has already happened. Simply put, attempting the counterforce attack would include an inescapable risk to the United States – and we can rest easier knowing that this is the case.

David J. Elkind is a research intern for the Project on Nuclear Issues. The views expressed above are his own and do not necessarily reflect those of the Center for Strategic and International Studies or the Project on Nuclear Issues.

1Keir A. Lieber and Darryl G. Press, “The End of MAD? The Nuclear Dimension of U.S. Primacy,” International Security 30 no. 4 (Spring 2006): 7-44.
2Likeminded readers will recognize this quotation from Brigadier Pudding of Gravity’s Rainbow, in which the character attempts to construct an estimation of everything that could transpire in European politics after World War I, only to discover that the features of the strategic landscape are constantly shifting. Thomas Pynchon, Gravity’s Rainbow (Penguin: New York, 1995), 77.
3“Russian nuclear submarines to resume continuous patrols on 1 June - Navy C-in-C,” BBC Monitoring Former Soviet Union (Nezavisimaya Gazeta), February 7, 2012, LexisNexis
4A simple increase in hardness is not possible for mobile ICBM shelters because it is not known. Lieber and Press treat them as blast-resistant concrete structures and derive the lethal radius from Glasstone and Dolan, The Effects of Nuclear Weapons, Figure 5.140. To evaluate stronger shelters, I decreased the lethal radius of the weapons 15 percent, approximately the percent difference in lethal radius between a given weapon aimed at a target with hardness H and a target with hardness 1.5H, as per the lethal radius equation in Lieber & Press, "The End of MAD?" appendix 1.

5The Federation of American Scientists estimates the test depth of the American Ohio-class submarine to be “greater than 1000 ft,” implying that it can withstand water pressure of at least 448 psi. If Russian submarines have similar capabilities (test depths at or near 300 m), then this sensitivity analysis may be the more accurate reflection of Russian SSBN capabilities, rather than Lieber and Press’s baseline figures. These baseline and sensitivity figures of 315 psi and 472.5 psi are retained because they are the values used in Lieber and Press (“The End of MAD?” 43). For Ohio-class submarine specifications, see “SSBN-726 Ohio-Class FBM Submarines,” Federation of American Scientists website, no date (accessed May 7, 2012), 

 Graphics produced using R 2.15.0 software. R Development Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL