User talk:Erdtirdmans
This is my talk page, where I will very rarely dump little bits of math that I am working on despite my inability to comprehend their significance. Also, I might just dump my strats here since I won't be posting my province and KD #s anywhere.
Weighted Average Cost of Army per Acre
A possibly useful formula for attackers, this seeks to demonstrate the economic viability of running a predetermined OPA and a predetermined DPA through the most population-efficient means. It does not take in to consideration variables beyond troop stats and cost. Because of this, its utility is limited, as other bonuses could have economic consequences that mitigate a race's higher WACAA. Obviously, Humans have an income bonus that mitigates this, but things such as Dwarvves' BE bonus or even Avians' Attack Time redux could mitigate the cost by enabling you to run more Banks, Libraries, or Schools. I will note such things where appropriate. Other bonuses such as Magic Effectiveness are economically impactful only in negligible ways (you could run lower WPAs or save on Channeling costs) and will not be noted, as they are primarily lures for the hybrids, and I am using the extreme case (Heavy Attacker) in my analysis.
Introduction to the Formula
In order to evaluate the economic viability of race's armies, we'll need a goal for them to reach. For attackers, this is obviously a goal Offense per Acre and Defense per Acre. They will be noted in our formula as gOPA and gDPA. Let's get specific so it is easier to discuss and go with 90 OPA and 70 DPA - fair raw numbers for a heavy attacker. Let's assume we're Avians too so that we can give concrete examples alongside the arcane symbols.
In the interest of population - the most important resource of all - we'll be using as many elites as possible. Since no race has a primarily defensive elite, we'll be getting all of our offense from elites and adding defensive specialists to bolster what's left. This means we can already get our first derived variable - Elites per acre (Epa)!
- Epa = gOPA / EO
- Epa = 90 / 8 = 11.25
- (EO refers to Elite Offense)
Now, we can do the same for our gDPA. However, we have to account for the defense provided by the number of elites we just determined we'll need.
The formula I'm using is as such:
- WACAA = FLOOR( Apa * WACT )
With Apa being Army per acre and WACT being Weighted Average Cost per Troop. By multiplying the number of troops per acre that we'll need in total by the weighted average cost of training one troop, we'll be able to find the actual cost per acre of maintaining our army.
