At what point is it more efficient to build ships than harbors?

Question

With the cargo ships upgrade, every ship gives a 2% bonus to harbor capacity. I've noticed that my harbors cost ~290 scaffold, ~2800 slab, and ~4000 plate, which with the 105 ships I have give an additional 1437 wood storage.

On the other hand, building 3.94 ships provides about 8k wood storage for 100 scaffold, 150 plate, and 25 starcharts.

Clearly, I've built too many harbors as it is far more efficient to build ships at this point.

What is the point at which building ships becomes more efficient than building harbors? Does this at some point get hit with diminishing returns (which would then complicate the equation) or is it once you've hit that point, its always better to build ships?

For ease of calculation, the efficiency should probably be restricted to scaffold to make the comparisons easier unless the other materials become a much more significant factor.

Answer 1

Ships are almost always the better idea; the limiting factor will usually be starcharts once you start building them a ton. Their effect doesn't diminish, and their cost never goes up. In fact, as you build workshops/factories, the cost per ship goes down, effectively, because you get more per craft.

At very low numbers of harbours, and very large numbers of ships, the numbers almost certainly do tip the other way. In practice, that's unlikely to happen, as starcharts don't become truly plentiful prior to SETI, by which point you'll have a bunch of harbours.

All the above being said, though, if you need storage, and you've run out of starcharts, then harbours certainly aren't a bad idea.

So, I've gotten home, looked at the code, and... the above wasn't entirely right.

Firstly, Cargo Ships (as of this writing) is only worth +1% to harbor capacity per ship. I've reported the bug, time will tell whether the upgrade description is wrong, or the code.

Secondly, the Cargo Ship boost is subject to diminishing returns; the cap is 225%, with the Reactor Vessel upgrade increasing it by 5% per reactor. This means that your first 168 ships are working at full power, and past that, the function described here applies.

Still, 168 is a decent number of ships, so I still sat down and did some math for their costs in plates and scaffolds, since those are the two resources they both cost.

If you have no ships yet:

• For Scaffolds, you need 30 harbours before buying ships is cheaper.
• For Plates, you need only about 18.

If you already have twenty ships:

• For Scaffolds, you need 32 harbours before buying ships is cheaper.
• For Plates, you need only about 19.

At a hundred ships:

• For Scaffolds, you need 35 harbours before buying ships is cheaper.
• For Plates, you need only about 21.

Thus, around 20-30 harbours, it suddenly becomes profitable to start buying ships en masse, at least until you hit the diminishing returns a fair bit.

Overall, though, I think my original answer's advice still stands; buy both. Star Charts will usually be the limit to your ship-buying anyway, and they do have other uses:

• Each ship increases the chance of titanium when trading with zebras. Chance is (15 + (0.35 * ships))% No diminishing returns here (I checked), though it stops being a benefit once you hit 100%, which is at 243 ships
• A ship is needed to unlock Zebras for trading in the first place. Unlocking zebras also unlocks the Caravanserai upgrade (though, the Navigation tech will generally unlock Caravanserai first).
• A hundred ships are needed to unlock trade with Spiders