This topic is something which often confuses the average player. As such I decided to make a small guide explanation how Workshop Efficiency correlates with Research Speed and give some examples with additional efficiency boosts from Order and Faith.

Workshop efficiency does not correlate with research speed but I think the bellow clarify more how efficiency vs research rate work.

What we need to take into consideration is calculate the efficiency of a workshop as an actual physical workshop. Do not confuse this with research rate. So taking this into consideration we have:
1st workshop = 100%
2nd workshop = +100% Total 200%
3rd workshop = +100% Total 300%

Considering the above values
100% Efficiency = 100% research rate
200% Efficiency = 130% research rate
300% Efficiency = 150% research rate
Then for any additional workshop is +10% research rate

The reason I mention this as a calculation is because it actually simplifies the way efficiency boosts work in terms of understanding how your research rate is affected.

A workshop with an efficiency of 120% is basically like having 1.2 Workshops
30% x 0.2 = 6% Increase in Research with a single workshop

The 0.2 is the 20% efficiency boost we gain from either Shrines or Agitator.

Talking from an Order path agitator gives a flat 20% boost (like shrines) and foreman gives another 40% boost for the time is active.

So for a single workshop with an 160% efficiency means our research rate is 100% + (30% x 0.60). 30% x 0.6 = 18% Research Rate Increase so we have a total of 6% research rate increase from Agitators and an additional 12% Research Rate Increase from Foreman which brings our total research rate at 118% Increase.

Basically what one needs to consider regarding research is 300% work efficiency = 150% research rate. To reach 200% research rate you need 700% work efficiency in total with your workshops.

If you have 2 Workshops working with Agitators or Shrines then their combined work efficiency is 240% which is 2.4 workshops.

From 200-300% efficiency the research rate is increased only 20% so 20% x 0.4 = 8% Research Rate Increase. If we add Foreman as well then is 20% x 0.8 = 16% Research Rate Increase (8% from Shrines/Agitator and 8% from Foreman).

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The whole research rate then needs to correlate to actual research hour per technology. Depending on difficulty, lets take for example Medium for Drawing Boards.

Medium Difficulty requires a total of 8 hours of research. The more Research Rate you have the lower the research hours get. So if we consider 2 Workshops with all the efficiency boosts for Order (Agitators + Foreman) they work as 2.8 Workshops (280% work efficiency total) with a combined Research Rate of 100% + 30% + 16% total research rate 146% per hour.

8 hours / 1.46 = 5.47
.47 x 60 (which is minutes) = 28.2 minutes

Total research for Drawing Boards will therefore be with 2 workshops and full efficiency boosts is 5 hours 28 minutes with Order

If we take just the flat 20+20% boost from Shrine for example with faith then we have 130% + 8% total 138% research rate

8 hours / 1.38 = 5.88
.88 x 60 (which is minutes) = 52.8 minutes

Total Research for Drawings boards will therefore be with 2 workshops and just shines or agitators 5 hours and 53 minutes.

For Extreme Difficulty with Order Agitators and Foreman the Research time from 14 hours drops to 9 hours 35 minutes

For Extreme Difficulty with just Shines or Agitators the Research time from 14 hours drops to 10 hours 17 minutes

Personally I don't recommend running Foreman on Workshops unless you don't pass the Agitators. But Foreman is insanely strong on resource facilities. For example a Steam Coal Mine produces 600 coal within 10 hours which is a normal working day without extended shifts etc.

600 x .4 = 240 Coal Extra

With Shrines which is 20%

600 x .2 = 120 Coal Extra

Agitator + Foreman total 160%

600 x .6 = 360 Coal Extra

So for resource facilities you get 3 times more with Order what you would get with Faith and Foreman only has 18hours of cooldown so you can run it every other day.

I hope this gives a bit better understanding how research rate with workshop efficiency work.