Played my first game with NFP for an hour over lunch... Ended up having a ridiculous start with first meets on Nazca, Armagh and the Vatican while going for an Ethiopia RV.
Not a remotely representative game, but getting those updated envoys early added up to a lot of extra yields... Especially when going religious as you tend to get some districts online a lot earlier than most victory types. I am just swimming in faith at the moment.
You have to distinguish faith coming from civilization unique bonuses from faith coming from city-state bonuses, but yes I believe that the Holy Site district and its buildings ares the ones that benefits the most from the changes to the city-state envoy bonuses.
Here I further complete my analysis that I started in the OP:
A proper analysis of the overall impact (buff or nerf) of the new tiered bonus system for city-states envoys is a complex one as you first need to make two different sets of assumptions, namely about
A) When you reach the 1/3/6 envoy thresholds
B) When you complete the T1, T2 & T3 district building
A) When do you reach the 1/3/6 envoy thresholds?
Reaching the 1 envoy threshold for 1 city-state comes much earlier than reaching the same threshold for all 12 city-states on a standard sized map. So which one should be considered? (possibilities of 1 to 12) I arbitrarily choose 4 city-states, because it is the max number on a single type of city-state that you can get on a standard sized map and also because if all city-state types (6) are evenly distributed (2*6) it allows you to focus your strategy on 2 different city-state types (2*2).
As previously mentioned in my other post, there is a number of sources for bonus envoys that you do not get every single games (such as the Apadana, specific civilization bonuses, great persons). I do not take these into account in my analysis.
Furthermore, there is also the RNG factor of quests that is difficult to quantify. How easy are the quests? Do the quests deviate from your planned strategy? Are the city-states you focusing on the ones giving you the easy quests? If you find a city-state late, you have less opportunity to get more quest. If you go a war with a civilization that is suzerain of city-states, your quests will get canceled, etc.
So, my conservative guestimate is the following:
First meeting: Early ancient era (bonus envoy that may or may not happen for any nb of city-states)
Threshold reached for 4 city-states:
1 Envoy: Early Classical era
3 envoys: Late Classical era / Early Medieval era
6 envoys: Late Renaissance / Early Industrial era
B) When do you complete the T1, T2 & T3 district building?
First, similarly to the above point, I have to make an arbitrary choice. How many copies of the same building should I consider in my analysis? Getting your first library built comes at a different timing than completing your 3rd or your 10th… Here, I arbitrarily chose the number of 3 copies so that the bonus from city-states envoys “starts to become more relevant”. Variability in terrain, production/chopping, ability to rush buy, etc. can all affect build times. Here, I consider an ‘average start’. I am not making any assumptions about what the current meta is or what it should be or what strategy a player should focus on. I’m only considering what it is possible to build at what time during the game.
Second, the answer is unique for each type of districts that benefit from city-state bonuses (7), because their respective buildings are unlocked at different places in the tech or civic trees.
So, my conservative guestimate for 3 building copies is the following:
Holy Site: 3 Shrines in Late Classical era / 3 Temples in Late Medieval era / 3 T3 religious buildings in Late Renaissance era
Campus: 3 Libraries in Late Classical era / 3 Universities in Early Renaissance era / 3 Research Labs in Late Atomic era
Encampment: 3 Barracks in Late Classical era / 3 Armories in Early Renaissance era / 3 Military Academies in Early Modern era
Commercial Hub: 3 Markets in Late Medieval era / 3 Banks in Late Industrial era / 3 Stock Exchanges in Late Modern Era
Harbor: 3 Lighthouses in Late Medieval era / 3 Shipyards in Late Industrial era / 3 Seaports in Early Atomic era
Theater Square: 3 Amphitheaters in Late Medieval era / 3 Museums in in Late Industrial era / 3 Broadcast Towers in in Late Atomic era
Industrial Zone: 3 Workshops in the Industrial era / 3 Factories in Early Modern era / 3 Power Plants in Early Modern Era
C) Nerf or buff?
So is the change a nerf or a buff? I believe there are 22 different answers to that question! One for each level of building (3) for each district type (7) plus the early meeting consideration. For this, you need to consider the intersection of the timings I outlined in A and in B.
Evaluations:
First meeting/Capital bonus: Nerf++
Holy Site: T1: Nerf- / T2: Buff / T3: Buff++
Campus: T1: Nerf- / T2: Buff- / T3: Buff-
Encampment: T1: Nerf- / T2: Buff- / T3: Buff+
Commercial Hub: T1: Nerf+ / T2: Neutral / T3: Buff
Harbor: T1: Nerf+ / T2: Neutral / T3: Buff
Theater Square: T1: Nerf+ / T2: Neutral / T3: Buff-
Industrial Zone: T1: Nerf++ / T2: Neutral / T3: Buff+
Scale : Nerf++, Nerf+, Nerf, Nerf-, Neutral, Buff-, Buff, Buff+, Buff++
D) Discussion
First meeting envoy bonuses are effectively halved and reduce the early game luck / variability.
This nerf is doubled in the specific case of trade city-states (from +4 to +1).
T1 buildings:
Even for the early T1 buildings (Shrine, Library, Barracks), the gain of at max 20 turns of +1 yield does not compensate for the -1 yield for the rest of the game (50+ turns) even when you consider that earlier yields are more valuable than later ones. The main reason is that you can unlock the 3 envoy threshold relatively early which reduces their timing window.
For the Industrial zone, you won’t even have a workshop completed when you would reach 3 envoys to an Industrial city-state. Thus the early compensation factor is null and the long term reduction is in full effect.
T2 buildings:
The first set of T2 building does benefit from the threshold reduction of 6 envoys to 3 since you are expected to be able to complete a sufficient number of them before you are reasonably expected to get 6 envoys to their corresponding city-state types. These are the Temples, Universities and Armories.
The second set of T2 buildings does not benefit from the threshold reduction of 6 envoys to 3 since you are expected to be able to get 6 envoys to their corresponding city-state type by the time you complete them (if you had chosen to focus on them). They are the Banks, Shipyards, Museums and Factories.
T3 buildings:
You get the T3 religious buildings right about the same time you would unlock the 6 envoy threshold to religious city-states if you had focused on them. They are the earliest T3 buildings you can unlock in the game; thus they also are the buildings that benefit the most for the new 6 envoy bonus.
On the other end, the Research Labs and Broadcast Towers are the T3 buildings that are unlocked the latest. They still do get a buff, but you benefit from it for less turns since they are built much later.
*Note: I am considering the era the player is in, not the world era.