A DATA FARMING ANALYSIS OF MULTIPLE SALVO EQUATIONS

Abstract

In 1995, retired U.S. Navy Captain Wayne Hughes formulated a salvo model for assessing the military worth of warship capabilities in the missile age. His model suggests that modern naval surface warfare can have regions of instability and that numerical superiority provides a consistent advantage. However, Hughes’s model is deterministic and provides no information about the distribution of outcomes that can result from an inherently stochastic salvo exchange. In 2005, Michael Armstrong added random variables to Hughes’s model and created a stochastic salvo model. By using mathematical approximations, Armstrong provides closed-form solutions for some stochastic outcomes. This thesis examines the two salvo models using data farming. That is, sophisticated designs of experiments are used to evaluate the models at thousands of input combinations. For each model, responses such as ship losses, proportional ship losses, and fractional exchange ratio (FER) are reformulated as readily interpretable regression and partition tree metamodels of the model’s inputs. For the stochastic salvo model, this is also done for the probability that one side wins. The metamodel fits are outstanding, generally explaining over 97 percent of the variance of the experimental results. The data farming results reinforce Hughes’s basic findings.