Calculating Battle Ratings and Costs in ACKS II

Merry Christmas, patrons! It's time for our December update. Since the ACKS II Kickstarter has ended, offering you the ACKS II Kickstarter playtest rules isn't enough! You demand more, and I provide more. Today I provide you with an update to the rules for calculating Battle Rating.

Why an update? Well, it's complex....

Lanchester's laws are mathematical formulae for calculating the relative strengths of military forces. When the weapons used by military forces can only attack one specific target per weapon, Lanchester calculated that the power of such a force as proportional to its number of troops. This is known as Lanchester’s linear law. However, when the weapons used by military forces can attack multiple targets and can be attacked from multiple directions, Lanchester calculated that the power of such a force is proportional not to the number of troops it has, but to the square of the number of troops. This is known as Lanchester's square law.

The battle rating (BR) formula in Domains at War: Battles Chapter 8 implemented Lanchester’s square law. (Specifically, battle rating was derived from unit hit points and unit attacks, both of which were derived from unit size, such that the square of unit size drove battle rating.) Unfortunately, Lanchester’s square law does not accurately reflect the relative strength of military forces in the ACKS battlefield. Nor, however, is the ACKS battlefield the strictly linear exchange of the linear law. The correct scaling actually lies in between Lanchester’s square and linear laws.

Another error in the original BR formula was that it treated armor class (AC) as a linear modifier to battle rating. However, given that most troops have attack throws of 9 to 11 in most circumstances, AC is not at all linear in its effects. When measured by a unit’s expected damage over time, the difference between AC 0 and AC 1 is very minor while the difference between AC 8 and 9 is huge!

Since the ACKS II Monstrous Manual presents battle ratings for every creature in ACKS II, I decided to develop a new equation for battle rating that would better match the underlying reality of the game world. As with the original rules found in Domains at War: Battles, this material is quite mathematically complex. Calculating BRs using this formula is not a process intended to be undertaken during play, and is best done using an appropriately-programmed Excel spreadsheet. We offer it primarily for Judges who like to see “how the sausage got made”.