Tomoyo said:
Commercial, when you hit the OCN, gives you 25% more production and gold, assuming you have improved your entire empire. That's 25% more.
Commercial doesn't need half-priced markets and banks. It's great like it is. Any more would be overpowered.
Really. Is this really how it works?
lets actually go through the formula, (doing this for myself as well as others), and see how much it helps.
Distance Corruption first:
Distance Corruption = 0.5^Ni * min(Gd * t * d, MaxD) / Max
MaxD is a distance of 1/4 the size of the map.
Ni is corruption reducing buildings. Gd is 1.5 for despot, .75 for democracy, else 1. t is 1, unless not connected by a road, where its 1.25. d is distance.
Say I am on a standard size map, and have a fair number of cities (we're in the midgame). Those close to my capital will have distance corrutpion of around 5-10%, those farther will be in the 20-40% range. I'll probably have courthouses in many distant cities, cutting that to 10-20%.
Commercial doesnt effect this.
Now there is rank corruption.
Rank Corruption = R / (2 * Nopt), if R < Nopt
(2 * R – Nopt) / (2 * Nopt) otherwise
For close cities, rank corruption is R/2*Nopt. For cities of rank over Nopt, the increase doubles for every rank above Nopt.
What is Nopt?
Nopt = (OCN * (L/100 + c + Gr + Gp*Nwe + 0.25*Ni) (but max of 100%)
OCN is optimal number of cities, by map size.
L depends on difficulty level
c is .25 if commercial
Gr is .1 for lower corruption governments, Gp*Nwe is 3/8 times number of corruption reducing wonders (say we have 1, the Forbidden Palace). Ni is number of corruption reducing buildings, say 1 for significant farhter cities, 0 for very close cities.
Say we're on a map size with OCN = 12.
Say we're on a high difficulty level, and not getting a bonus from the L/100 term. We're just geting the base of 1.
With commercial, c is .25, we're in an ok government, so Gr is .1 (not communal government here).
Gp * Nwe is .375 * 1, or .375. (We see that having a forbidden palace gives the 150% of the same bonus to fighting corruption that commercial does!!). Ni is going to be .25 for further cities, with a courthouse.
Total is (for farther away cities): 1.975 with courthouse and commercial, 1.725 without commercial or without courthouse. 1.475 without both.
This makex Nopt be either 24 or 21 depending on courthouse for commercial, 21 or 18 without commercial.
Lets say we have 20 cities.
For closer cities, changing Nopt from 21 to 18 reduces rank corruption from N/42 to N/36. For N=4 for example, this goes from 9.5% to 11%, an increase of 1.5%. These cities had 5-10% distance corruption. Say 7%. Overall we thus reduce corruption in these cities from about 18% to 16.5%. Thats from .82 uncorrupted to .835 uncorrupted.
.835 / .82 = 1.5% gain in commerce and production in close cities.
For middle cities, say N=10, the change means we go from 24% to 28%, a change of 4%. Thats .76 uncorrupted to .72
.76/.72 = 5.5% gain in commerce and production in middle distance cities (a bit less %age gain if a courthouse is there).
For the most distant cities, we're getting over Nopt, so the increase in corruption is doubled for each extra city over Nopt.
Say for city 18, we have a courthouse, so Nopt is 24 or 21. We reduce corruption from 18/42 to 18/48 via commercial, or from 43% to 37.5% 5.5% reduction.
Add to that 10-20% distance corruption with courthouse (say 15%), and we're at 58% or 52.5%. Thats .42 uncorrupt or .475 uncorrupt.
.475 / .42 = 13% increase in commerce and production.
When our number of cities grows to well over Nopt, then commercial will have a significant boost (approaching 25% perhaps, boost to net commerce and production), for a few of these cities, but as it gets too high we just hit the corruption cap anyway, even with commercial.
So in summary, you get a boost to commerce of a couple percent (~2%) near the capital (mid single digit city rank, first ring), of 5 or 6% in middle cities (like city 10 or so), low double digit bonus in far away cities (which are less developed and less productive in total).
Lets say that our closest 6 cities are producing at a value of 20, middle 8 cities 15, farthest 6 cities 10. (Again, we're talking about %age bonuses after corruption taken into effect).
2% * 6 cities * 20 = .02 * 120 = 2.4 bonus.
6% * 8 cities * 15 = .06 * 120 = 7.2 bonus.
13% * 6 cities * 10 = .13 * 60 = 7.8 bonus.
Total bonus is 17.4.
total production before the bonus from commercial was 6*20 + 8*15 + 6*10 = 300. 17.4 / 300 = 5.8%.
We're getting around 5-6% net gain to commerce and production, empire wid,e in my example (similar to the average effect on middle distance cities). I think this is a pretty reasonable estimate of the bonus from commercial's reduction in corruption.
This is a far cry from a 25% total bonus.
Its something, but I'd take a number of other things over it.
Still, it IS true that commercial gives you MAPMAKING as a starting tech. If you arent seafaring, this is very cool, (on continents and especially archipelago). It helps you find the AIs early, thus trading tech, and not falling behind. Plus, you can research writing.
I'd think that this good starting tech is probably as important a bonus as the corruption reduction...
So I guess, I'd say commerical was 2nd tier on more watery maps, when your other trait is not seafaring. Because it gives a good first tech, plus some moderate boost to commerce and production.
