Definitions

# Probability of kill

Computer games, simulations, models, and operations research programs often require a mechanism to determine statistically whether the engagement between a weapon and a target resulted in a kill, or the probability of kill. Statistical decisions are required when all of the variables that must be considered are not incorporated into the model, similar to the actuarial methods used by insurance companies to deal with large numbers of customers and huge numbers of variables.

The Probability of Kill (or Pk) is usually based on a Uniform random number generator. This algorithm creates a number between 0 and 1 that is approximately uniformly distributed in that space. If the Pk of a weapon/target engagement is 30% (or 0.30), then every random number generated that is less that 0.3 is considered a kill. Every number greater than 0.3 is considered a "not kill". When used many times in a simulation, the average result will be that 30% of the weapon/target engagements will be a kill and 70% will not be a kill.

This measure may also be used to express the accuracy of a weapon system. For example, if a weapon is expected to hit and kill a target nine times out of ten with a representative set of ten engagements, one could say that this weapon has a “Pk” of 0.9. If the percentage of hits is nine out of ten, but the probability of a kill with a hit is .5, then the Pk becomes .45 or 45%. This reflects the fact that even modern warheads may not always destroy a target such as an aircraft, missile or main battle tank.

You can also specify a probability according to a class of targets, for example, it has been stated that the SA-10 surface-to-air missile system has a Pk of 0.9 against highly maneuvering targets.

## References

• A.M. Law and W.D. Kelton, Simulation Modeling and Analysis, McGraw Hill, 1991.
• J. Banks (editor), Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice, John Wiley & Sons, 1998.
• R. Smith and D. Stoner, "Fingers of Death: Algorithms for Combat Killing", Game Programming Gems 4, Charles River Media, 2004.

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