TLDR: The bonus farming speed from English Mills is NOT stacking additively with other gathering speed techs (e.g HRE, Abassids. the English’s supposed to be 75% total gathering speed for farms in Imperial is giving them a higher income than the Abbasids’ 80%) in contrast to the way other Civs’ unique gathering speed bonuses stack with the generic gathering speed techs. A plausible explanation is that there is a multiplicative stacking for English’ influence.
I am not sure if this is a bug or intended. I am reporting in case it is unintended as I spotted some inconsistencies in the way gathering speed buffs work, but found no mention of it on the web and I believe this should be transparent information (although it is more for nerds) to allow players to accurately compare the economy of the different civilizations in the late game. I did some testing with English, Abbasids and HRE (I haven’t checked the Chinese and their unique tech and Granaries yet). Based on my in-game tests:
1- HRE inspiration buffs stacks additively with gathering speed technologies
2- Abassid’s House of Wisdom tech for farms (Agriculture) as well as the Golden Age gathering speed buff both stack additively with mill farming upgrades. Therefore combined they give 45%(mill) + 15% (HoW) +20% (golden age III)=80% gathering speed bonus to farmers
3- English on the other hand, have an influence of 30% gather speed near their mills, while the typical gathering speed tech at the mill gives 45%. If these stacked additively we would get 75% in total (which would be less than the Abassids’) but (see below) they have a higher value than intended which I inferred through Income estimates and comparisons, and I made the hypothesis that the influence bonus is stacking multiplicatively with gathering speed techs and it seems to be plausible.
So the English seem to be the exception.
When I check the English’s actual income and compare it to the Abassids’ for example, I realize that the English influence is not stacking additively with gathering speed techs at the mill. The income is significantly (statistical significance) higher than for Abassids: For instance, for Abassids with all techs except the drop off bonus tech called Improved Processing (so 80% farming speed) I get an estimate of 0.9726 food/second/villager while for the English who are supposed to have less I got 1.0042/s/villager (btw I did this test many times).
My assessment is that we have a multiplicative stacking (i.e 1.45 x 1.3=1.885 or 88.5% gathering speed in total which is equivalent to having 43.5% gathering bonus with an additive stacking). This is based on both the magnitude and the comparison to HRE’s inspired villagers (which I won’t focus on in this post since HRE villagers have different carrying capacity which complicates things a bit. The English values are very close to the HRE’s with 40% from non upgraded inspiration, they are very slightly lower due to lower carrying capacity which means the English are probably having more than 40%).
Even if we compare the English to the Abassids we can have a similar hypothesis. In general in the area around 50% bonus gathering speed an increase of 10% translates into 5% extra income, the higher we currently are at the lower the increase in income as a percentage will be. So if English is having a multiplicative stacking aka 88.5% bonus compared to the 80% of the Abassids i.e 8.5% extra, then one would except them to have say somewhere between 3% and 4% more income than the Abassid’s assuming they don’t have the 8% extra drop off (the 3 and 4 percent are rough values just for a quick estimate based on my mathematical instinct and my experimentation in the game). If I multiply the estimate for the Abassid’s by 1.03 and 1.04 I get 1.0018/s/villager and 1.0115/s/villager. The English value is between these two indeed, so it seems plausible the English are getting multiplicative stacking (I believe from a programmer point of view this would be a very easy mistake to make when coding).
- Notice that the numbers above are actual estimates of Income not gathering speed.
- All tests I did were with 8 farmers around a mill.
- The estimation windows have long durations to minimize estimation errors and noise from how many villagers return to drop their holdings at the end of the estimation period etc e.g I run 8 farmers for 30 minutes or even 1 hour then estimate the income.
If really needed I could provide videos of the tests (I actually deleted the ones I had which are very large video files but could redo them and get new estimates as well).