Gold Efficiency (again)

This is just a short note on gold efficiency again.

Here's a look at gold efficiency of units from last time

You don't have to read that post, its just for reference.

The short note I want to make here is that a relationship exists between total cost, gold efficiency, and total possible production for a fixed amount of gold.

Total_cost_A/Total_cost_B × Gold_efficiency_A/gold_efficiency_B = Gold_cost_A/gold_cost_B.

Why might this relationship be important? Because it provides an easy way to decompose the effects of a cheaper gold price on a unit.

For example take the steppe lancer. It has a 40 gold cost compared to a 75 gold cost for the knights. We're going to ignore villager time this time and focus on absolute costs to make things more clear. This is the same as assuming food and gold are gathered at the same rate.

Anyway using the knight and steppe lancer we have:

135/110 × 0.5556/0.3636 = 75/40.

So what does this tell us? The first term tells us how many more units we can produce for a set number of villagers. The second number tells us how much longer those villagers can continue production before exhausting gold.

So for the knight vs steppe lancer example you get ~23% more production, and it lasts ~53% longer. These multiply to the total number of extra units we can make (ratio of gold costs).

We can also do this for the polish cavalier:

135/90 × 0.5555/0.3333 = 75/30

Thus you can produce 50% more cavalier and continue doing so 66% longer. I would also like to point out archers are one of the most gold heavy units in the game. This has pretty obvious implications for how you should treat the unit when using it in combat.

You can also upgrade this relationship by multiplying both sides by a ratio of total gold available:

Total_cost_A/Total_cost_B × Gold_efficiency_A/gold_efficiency_B × Total_gold_B/Total_gold_A = Gold_cost_A/gold_cost_B × Total_gold_B/Total_gold_A

So if you spend 6000 gold on units normally and Poles have an extra 1500 to spend on units you get:

135/90 × 0.5555/0.3333 × 7500/6000= 75/30 × 7500/6000

The take away here is that extra gold scales the length of production available. So not only can Poles have 50% more production but can actually maintain that production more than 66% longer.

Anyway I hope this helps if you're thinking about different time horizons and using a more expensive unit vs a slightly weaker but more sustainable unit. It also helps for mapping intuition about one unit into intuition about another unit.