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"Behind the BANG!" is a new irregular blog series that looks behind the scenes of the mechanics of the game engine. I don't know yet how often I will write such blogs, but I'll see how it goes down.

Caravans are a great way to get gold quickly, especially when playing in co-op. However, many wonder how the yield is calculated. There have been many speculations, but today I want to reveal the secret.

Caravan Gold Yield Formula
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For those who do not know: AOEO is based on the same engine as AOE3 and AOM. Therefore it is also "purely coincidental" that the following calculations also apply to AOM. In other words, the logic in AOEO is nearly identical to that in AOM. Therefore, we can see what the AOM-wiki has to say about it:

The Town Center 'gives' gold to the Caravan, which is added to the player's stockpile when the Caravan returns to the Market. The amount of gold generated by a single run of a Caravan is (approximately) directly proportional to the square of euclidean distance between the Market and the Town Center. Therefore, the total gold production of a straight line trade route is directly proportional to its length.

Although it is possible for players to trade with their own Town Centers, trading with that of an ally will provide 50% more gold.​

In principle, the information is correct, but there are some factors that were not mentioned. The full formula is:

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I was surprised that there are more factors at play than I thought. Therefore, let's go through all the variables.

The most important variable here is "dist", which is the euclidean distance from the caravan unit to the marketplace. Heard correctly: from the caravan unit and not from the town center. This means that if the caravan unit theoretically hits the town center from another side, the yield can be higher. But of course this will not happen in practice. This distance value is multiplied by itself so that we have the square of this value. This means that the yield difference is much higher for long distances, or the possible yield increases quadratically with distance.

The second most important factor here is the so-called "work rate". Basically just a number that is used as a factor for different units. Wherever there is "work", so to speak, be it converting/healing units, mining resources or trading with the town center. So also the caravan unit has a work rate, which can be changed by gear and advisors. By default, caravans in AOEO have a work rate of 0.8 (for Egypt it is 0.72). In AOM, the value is much lower.

The town center factor is an unusual value, since it corresponds to the carry capacity of the town center. In my opinion, this value was misused to serve as a variable factor for trade, since it does not make sense that a building has a carry capacity. The town center has a factor (carry capacity) of 1.0 for gold and therefore this value can be ignored, but theoretically you could design a new building that has a higher carry capacity, which would lead to a higher income from the caravans.

The last value is the bonus factor. When trading with an ally, this factor is x1.5. It makes no difference if this is a real player in co-op or an ally AI. At the same distance, a caravan would yield 100 gold at its own TC, while an ally would yield 150 gold. The bonus factor for trading with an enemy town center would even be x2, although this is a relic from back in AOM. I guess that it was planned to be able to trade with enemy town centers, but then it was not really implemented.

Now the multiplied values are divided by the size of the map. This size corresponds to either the length or the width of the map, whichever is greater. For a size of 400x300, the value would be 400. This means for the full yield that caravans must travel for a longer distance if the map size is larger.

Gold/Distance Chart
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Let's consider an example: I want to get the maximum profit on a 400x400 map with the smallest possible distance (without gear and techs):

Own TC: (dist2 * 0.8 * 1.0 * 1.0) / 400 = 150 gold → dist = 273.86 tiles (68% of the map size)
Ally TC: (dist2 * 0.8 * 1.0 * 1.5) / 400 = 150 gold → dist = 223.60 tiles (56% of the map size)​

If we plot a graph on this:

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Of course, these are pessimistic values, since they do not include gears/techs/advisors. Roughly speaking, if you cover half the map length and have some techs and gears, that should get you to the full amount of 150 gold. The same formula can be applied to Docks, of course. The only difference is that the Merchant Transports can carry up to 300 gold (while taking 2 population slots, of course).

Display Trade Preview
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Finally, I would like to provide an update on the marketplace preview feature. More than two years ago I implemented a feature that displays the expected yield of caravans via the "Display Trade Preview" hotkey (default: Shift+Z). Unfortunately, the values were not always correct, because it didn't include the effects of gears/techs/advisors. This will change with the next patch.

Here you can see how the values of the preview now correspond to those of the caravan:

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There are certainly still cases where there will be deviations of +/-2g, especially at longer distances, but I believe it is negligible.

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