Aggregation, Disaggregation, and the 3:1 Rule in Ground Combat.
Abstract
Validity of Aggregation. In this report I illustrate some generic subtleties of aggregation and disaggregation in combat models by starting with an analytically tractable model at one level of detail and then attempting to derive an aggregate model. In particular, suppose that a Lanchester square law is valid for ground combat in each of a number of individual sectors. What equations then describe events at a higher, more aggregate, level? What factors determine whether a closed aggregate-level model exists (i.e., a reasonably accurate model dependent only on aggregate-level variables and with any coefficients being independent of time)? The answer is that what matters is "outside" the "detailed model" altogether, notably (1) higher-level strategy, (2) command and control, and (3) the relative durations of several time scales for battle and maneuver. These factors have major effects on whether a valid aggregate-level model exists and, if it does, what values its coefficients should have. The 3:1 Rule. A bonus of this analysis is a clarification of when the famous 3:1 rule applies. If it applies at the sector level, then it may or may not apply at a more aggregate level. Indeed, in a theater with multiple corps sectors (e.g., the old Central Region of Europe), the theater-level break-even ratio will typically be more like 1.5:1 than 3:1. By contrast, it is possible for the same 3:1 rule to apply at several lower levels (e.g., corps, division, brigade, and even battalion). In mobile combat in which there is no particular defense advantage, the theater-level break-even force ratio may be about 0.8 or 0.9.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1995
- Accession Number
- ADA302819
Entities
People
- Paul K. Davis
Organizations
- RAND Corporation