That’s really a lot of questions. I could answer them all with detailed description but I will keep it as short as possible as it would go way too far into detail.
The calc consists of two parts, one build I did for FC into 4 TC boom with Magyars. This I use as Reference for all the other calculations. When I calc a different civ, I will approximate all the eco bonusses the other civ got at a given timestamp (18 Minutes). This is basically a sum of all the advantages and (possibly compensations for the advantages like for the tatars sheep I calc them as the food they provide but substract the time needed to collect in form of wood).
Then I have developed a tool that estimates that having Ressources Earlier is better than later. Assuming that when you full boom your eco will double in a certain amount of time. This means after each of this time delta called HalfWorthPeriod (HWP) ressources available at that point are basically only worth half of their current worth. WIth this assumption I can calculate how much economical prowess a vill, farm and tc has and how much investment is needed to make them. This allows to reciprokely calculate the HWP and ressource worth of each civ by setting the investment/gain of farms and tcs + vill production each to 1.
This values then can be used to calc the economic power of each civ at the 18:00 Timestamp and a timespan they need to double that power. Then I just chose a Economic Power to reach to be “fully boomed” and calculated for each civ when it would reach it. I chose this because there are several civs which have very different economies and therefore just looking eg on vill numbers would be inaccurate. Instead I just set a specific economic power I found reasonable. I think it approximately corresponds to a 120 vill economy, but I never actually compared this. As it is also basically impossible to compare, as you never have a “hard” stop in booming u usually just decide to not add more tcs but add military buildings instead.
That’s the basic concept how it is calculated, the most easy explanation I can come with.
Answers to your questions:
Yes.
The build was optimised to get them asap for best result.
Yes.
Yes and ofc all civ bonusses that reduce that kind of investment.
As I used a build for the first 18:00 minutes, this is included naturally for that time period, but I also regard this in two ways later: Civ bonusses that have influence in that are regarded. Also walking time (towards ressources) is inherent element of the worker efficiency calculations.
I will now try to get into some of your civ specific mentions as I think this is way more interesting to discuss here:
Here I calculated how much impact it has to send the 5 vills that made the TC directly to the spawned sheep. This way tatars benefit way more from the extra sheep as if they would get like 2 farms for free, as the food gathering from the sheep would be much faster and allow them to place extra tcs earlier than other civs. This is ofc a theoretical opimized use of that bonus, as we all know how hard it is to find the right eco balance for tatars with that bonus. But I made the deicision to not account for poor buildorders. just assuming that you have found the “perfect” balance, even if you have no idea how to achieve it.
Yes, this is an interesting point. The key is that the teutons bonus comes in later than the franks one. So the franks initially start with an eco already better than the Teutons, but the Teutons can alrady catch up until the end of their boom. From that on the Teuton eco is just better than the franks one.
But yes, it’s an interesting result that shows how strong franks are actually.
But I must admit, I think it is the franks before the foraging nerf, I think I forgot to adapt for it, goes on my todo list.
Food is way more worth than wood at this stage of the game. For most of the civs I get a 1:1.887 proportionalty factor between them. Interestingly Teutons, because of the Farm bonus have one of the best ratios with 1:1.695 (Only Poles have 1:1.55). That means while Booming the wood savings don’t have that big of an Impact. Also as I told before, Franks just have the better initial start to the boom, it takes time for the teuton player to compensate for having to invest into the farm upgrades and the berry bonus. The better initial start of the boom gives the Franks player a nice advantage to snowball.
The super fast TCs are the main factor there. Note that because of this building time advantage the sicilian player does economically best by building the extra tcs with 2 vills only. NOt only are they faster to build this than other civs. 3 Vills can be left on wood to gather ressources while the others would need move and build - a nice eco advantage worth about 140-150 wood in total. The better farms don’t have such big of an impact - and probably sic are indeed even better if you would skip heavy plow. But in my calc I didn’t. The main benefit comes from the TC bonus.
Well it’s “only” place 3 for the civ that comes to mind first when talking about booming… I’m quite dissappointed they aren’t strictly number one. The vill discount is such an insanely strong eco bonus, I expected them to be number one actually. And they were before Cumans and Poles mixed things up.