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Specialist Economic Equivalency - Merchants vs Scientists

In the wake of the Epic 12 report by pindicator, a discussion arose about the economic production of specialists. Like most players in the Epic, pindicator had Delhi as a huge commerce city with lots of science buildings. He noted that it seemed more efficient to run Merchant specialists in other cities, in order to keep the science slider percentage high to leverage Delhi's science productivity.

The questions are, is that intuition right? And how can we quantify it?

The short answer to the former is yes. Gold and beakers do not exist in a 1-to-1 equivalency in Civ 4. There most certainly is a difference between merchant and scientist specialists.

For purposes of this discussion, we make a few simplifying abstractions. Strictly speaking, the game economy does not directly convert between gold and beakers. We convert future commerce or specialist production to either gold or beakers, but I'll speak as if they are currently equivalent. Second, the in-game research slider only operates in 10% increments, while I assume a slider that can adjust in increments of arbitrary precision. This is correct if you consider the aggregate operation of the slider over time. For example, if you want to run 78% research, you can run 70% for two turns and 80% for eight turns.

For every empire, there exists a conversion factor between gold and research beakers. This conversion factor is essentially the ratio of the average empire-wide multiplier for each type of production. As a simple example, suppose you have a single city, with +0% gold and +100% science, producing 60 commerce per turn. You can convert that 60 commerce to 60/0 gold/beakers, or 59/2, or 40/40, or 1/118, or 0/120. For this empire, 1 gold = 2 beakers.

You can derive this ratio in-game. Look at the F2 economic advisor screen and click your slider one step. Disregarding roundoff artifacts, the change you see in each of your gold production and science production is your national ratio.

This ratio applies across your entire civ's production. Suppose we need 20 gold per turn to pay our civ's expenses, so that Delhi is producing 20/80 gold/beakers. Now suppose you have a second city that's producing nothing except for one specialist with no multipliers. If you make that specialist a scientist, that's +3 research, making the national production 20/83. But if we hire a merchant instead, we can bump our science slider so that Delhi is producing 17/86 gold/beakers with the merchant making up the rest of the cash shortfall. Our merchant is actually indirectly generating 6 beakers!