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OK, that did take some time to deconstruct. I see what you're trying to do here, and math looks reasonable. You're underestimating planks size though as you refer to workshop pop requirements instead of actual planks. I haven't been validating the calcs, that's just one thing I noticed. It doesn't materially change the outcome.Right, missed that one
@MinMax Gamer re mountain halls.
I have a spreadsheet floating around showing how good it is somewhere, but the basic idea is that due to a factories TRUE SIZE being around 150-200 squares once you count workshops, residences culture and roads, the production from Mountain halls is better per square as long as it affects 6+ factories.
https://docs.google.com/spreadsheet..._aF9cnqUYN_6a1ksQDsbNNfZ8vI/edit?usp=drivesdk
That's not the best one, but all I can find atm
TL;DR: So let's say that calculations are correct. I do not necessarily agree with conclusions though, and as in most of modeling, it boils down to assumptions. So here we go.
You assume that we support factories with regular residences, workshops and culture. So let's look where effective calculated size requirements are coming from. Direct culture requirements are not material, so whatever. Direct manufactories size is a given, so that's fine. This leaves indirect requirements of space for pop and supplies, and these dwarf the other components. But does it make sense? I can agree on residences used for pop requirements (because *I* primarily use straight residences for pop ), but if someone relies on event buildings and AWs for pop to a significant degree, their effective space requirements for pop can be significantly lower.
Which brings us to supply requirements. 1/3rd of total effective space comes from that. Let's step back a bit, and see what your projections tell us. If I am not mistaken, according to your calcs you're saying that in order to support 2/2/2 manufacturing setup (one of the smallest that can be reasonably used), you need to have basically 5 fully upgraded workshops, dedicated just for running goods production. This means that supplies for troop productions, build/upgrades, research activation are on top of that. Let's just say that this is not very believable. This way, I'd need to have probably 20 fully upgraded workshops to support all supply needs. I don't know any cities that run with such setup.
The reason for that is not that the math is incorrect (even though that is always an option ), but the aggregate supply production for most cities - and certainly efficient ones - is a lot more, um, space-efficient than straight workshops. Whether you do PoPs, AWs, special buildings or (oh horror ) quest cycling, you gain a lot more supplies than your calculations would assume. Heck, I can run the whole city (not just production) with a dozen of L1 WS on quest cycling alone. I don't, but I can. And I never had more than 6 of reasonably upgraded workshops, and I am capped on supplies most of the time. And I don't even notice supply requirements for production in 3/2/2 setup - comparing to troop production and research/upgrades.
So there is that. Now there is another side to all this, and that's applicability of per-tile analysis to making actual decisions. Per-tile analysis works well in cases where your domain is infinitely divisible, or at least meaningfully so (e.g. residences). It gets a lot less clear cut where your units are discrete and chunky, like 1 or 2 manufactories. Ultimately, our decisions need to operate in terms of whole buildings and space constraints of the cities.
Basically, we have hard space constraints. Ultimately, the primary reason to get more efficiency from different setups is to reduce space needed to achieve your target rate that you need to support your objectives. There is no reason to absolutely maximize production as you will get bottlenecks elsewhere. There is no downside in using higher efficiency setups when you operate in infinitely divisible units. You can get higher production in the same space, you can get same production in smaller space, or anything in between, but you can get in a place that is strictly better than your less efficient per tile setup. E.g. if I get a 3% pop improvement on my residences, and I have 30 of them, then I can drop 1 of them and get the same pop in less space. Or just keep all of them, and get 3% more pop in the same space.
Now, this is not necessarily true for more discrete cases. So let's look at decisions that you can make in the manufactories cases. Let's start with 1 manufactory setup (for each boost) - somewhat extreme, but not unrealistic. You obviously cannot reduce your space requirements of this setup with MH, even at L100 - you can't drop any of your manufactories as MH will have nothing to boost. You can in theory reduce your collection frequency to reduce supply requirements, but similar logic would apply there as well. Also, collection cycles generally are not driven by those considerations.
So building MH in this case strictly increases utilized space (by the size of MH) because you're not dropping anything else (unless you're dropping residences as you get pop boost). For that, you're getting a rather lackluster increase in production - even though it might be efficient at some point.
Bottom line is, until MH is leveled enough so that it can save you a whole manufactory (which is unlikely to ever happen in lean setups like 2/2/2) you're not saving space (compare with EE or PT which do, as you can drop a whole WS there). Your production efficiency may go up a bit, but in a larger footprint. L1 gives you 3% total production increase; and it doesn't get much better until much later (and that's tons of KPs). Low-level MH just doesn't move the needle. If you had sufficient goods before MH you still have sufficient goods, just a tad more (but with less space). If you did not have sufficient goods, low-level MH is not going to change that.
So for me, with 3/2/2 setup, MH turned out to be pretty disappointing. I have more than enough goods with or without MH. MH is not significant enough to drop any of the manufactories. Extra pop is nice, but again, at lower levels is nothing to write home about.
YMMV.