Missile.Exchange Calculator Tutorial

Missile Exchange has a lot of buttons and levers. All layers are created wherever the camera is focused. They can be dragged and dropped or locked and reordered using the layer management panel. An example has been posted here.

Since this site is fairly new, expect this page to change a lot as I figure out better ways to explain how it works. Feel free to contact me with reviews or questions.

Many of the values are probabilities written as P(x), with representing whatever event is being examined. The calculator ultimately puts out P(0), the probability of no warheads reaching a target, but also handles individual P values for each separate defensive and offensive layer so that the user can see what is the most effective offensive and defensive choices.

There is a box for managing all of the offensive and defensive layers, each of which can be renamed. Each layer can be moved up or down so that they can be moved around separately. Each can also be locked or unlocked to prevent accidental movement. The layer box is meant to mimic the management tools on Photoshop or GIMP and becomes increasingly useful as a user’s architecture becomes more and more complex.

In general, the final probabilities are listed in both the graph in the lower right corner and when you mouseover a given region.

Final probabilities are region based. Moving your mouse over different circles or intersections will show P(0) for that region, taking both offensive and defensive systems into account. Clicking on a region will generate the graph for that region.

  • Reading the Output
    1. P(0) Graph: The graph in the bottom right shows the probability of no warheads killing their targets ( P(0) ) within the clicked region, with the X axis representing the number of incoming warheads.

Definitions, Variables, and Quick References

Variables & Terms Definition Example Value Example Meaning Systems Involved
The Offense The actor who is firing offensive ballistic missiles Houthi Yemen (Bukhans, Qahirs, Tochkas) Offensive Ballistic Missiles
The Defense The defense who is operating ballistic missile defense (BMD) systems UAE & Saudi Arabia (PAC-2) Ballistic Missile Defenses
Range Range of System in Meters 300km System can kill a target 300km away. Holistic to system
SSPK Single Shot Probability of Kill, Probability of a Single Offensive or Defensive Missile Destroying Its Intended Target.


Represents combination of accuracy, precision, payload/blast yield, and hardness of target.

.95 System has a 95% chance of killing its target. For offense, this means a missile has a 95% chance of killing (or, talking about a city, just striking) a target.

For the defense, this is the percent chance of a missile interceptor striking and destroying its target.

Ballistic missiles, missile interceptors/anti-ballistic missiles
Reliability Probability of the System Working (and not failing due to technical fault) .75 System as a whole has a 75% chance of succeeding in its mission from a technical standpoint. Holistic to system
Tracking Probability Probability of a Defensive System Identifying, Processing, and Tracking an Incoming Target .85




BMD Radar and software has an 85% overall probability of initially detecting, tracking, and discriminating targets. Future versions of Missile.Exchange will disaggregate this number to account for decoys and different reentry vehicles Radars, battle management software, data & command structures, basically all C4ISR and data related functions
P(x) Probability of x event Variable
P(x, unopposed) Probability of x event if there is no defensive system to oppose it .85 85% chance of x event succeeding without BMD. Used for offensive systems only. Specifically used for offensive systems
P(0) Probability of Zero Offensive Warheads Killing Their Targets .90 90% chance of no warheads reaching a specific target within a selected region on the map All
Notional Notional Offensive system Offensive Systems
Ground Burst Ground Burst Nuclear Detonation Offensive Systems


Some variables get fairly confusing upon first read. For example, SSPK and Reliability can look similar, but are estimating the probabilities of success of different aspects of the system.

SSPK is an estimation of a system’s success, but is conditional upon a system’s reliability and (for BMD) a separate tracking probability. SSPK represents the combination of a missiles accuracy, precision, payload/blast yield, and the hardness of the target. For defensive systems, SSPK represents the same, effectively everything that effects whether or not a missile can kill its target assuming it finds that target to begin with. SSPK is about the missile itself, while things like tracking probability (Wilkening’s P(track)) are about the accuracy and precision of radar and other data/data-fusion oriented systems.

Below is a general walk-through, but is fairly redundant. I recommend users open up the calculator and just start throwing numbers in.


  • Making an Offensive Layer: This layer will represent all missiles of a given system at a given point. 
    1. Click the + sign next to “Offensive Layer”
    2. Select “Notional or Ground Burst” from the drop down menu
      1. Ground Burst will give you the variables necessary to simulate a ground burst nuclear blast. The SSPK of a ground burst offensive system is calculated from the yield of the weapon, the CEP of the system, and the hardness of the desired target.
      2. Notional allows for a more generalized offensive weapon where the specific blast yield and system precision are unknown, instead the SSPK is entered by the user.
        1. Notional:
          1. Enter the range of the system in meters.
          2. Enter the single shot probability of kill (SSPK) of the system. SSPK is the probability of a single missile killing its target.
          3. Enter the reliability (R) of the system. Reliability is the probability of a single missile not experiencing a critical system failure that prevents it from reaching its target. Reliability is exclusively internal and is not affected by defensive systems.
          4. Drag and drop the circle
        2. Ground Burst:
          1. Enter the range of the system in meters.
          2. Enter the yield of the blast in kilotons.
          3. Enter the reliability of the system.
          4. Enter the circular error probable (CEP) of the system. CEP represents the precision of the system. CEP is the radius of the circle that 50% of shots fired will land within. If one fires 10 missiles with a 60 meter CEP at the same point, one would expect 5 missiles to strike within 60 meters of the aim point.
  • Making a Defensive Layer
    1. Enter the range of the system in meters.
    2. Enter the SSPK of the individual interceptors. This represents the probability of a single interceptor killing its target.
    3. Enter the tracking probability of the entire defensive system. This repents the ability of the whole defensive system, including radars, command and control systems, etc. to pick up, identify, track, and transmit tracking data to the interceptors. In effect, this is a defensive system’s ability to see and follow incoming targets.