A Simple Probabilistic Combat Model
MIT Lincoln Laboratory Lexington United States
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The Lanchester combat model has been used extensively to model the results of combat between two sides with potentially different quantities and qualities of forces. The model is deterministic assuming that red attrition is proportional to blue force size and quality and similarly for blue attrition. In the model described here, all attrition is modeled probabilistically and it is possible although unlikely for the weaker side to be successful. The model consists of a number of discrete waves in which red and blue forces attack each other. Since each attack has a probabilistic outcome, after each wave there will be a probability distribution of red and blue survivors. This distribution serves as the input to the next wave. For each wave, the model determines the discrete output probability distribution for each possible input of red and blue weapons. This discrete output probability is then convolved with the input probability to get the resulting overall output probability of red and blue survivors. This process is repeated for as many waves as needed to determine the probability that red or blue will win the battle. Results are shown for a variety of cases.
- Statistics and Probability