Multiplier´s math

[Unimatrix11]

So here is a thing a have always wondered about, was always too lazy to check and think many people would like to have it set clear once and for all:

How do multipliers work exactly ?

This is the way i THINK it works:

1. All the fixed numbers are added up. ´All´ means: From worked tiles, specialits, super specialits, corparations, shrines, city improvements, wonders.

2. To that sum all multipliers (e.g. universities, catherdrals and the likes, civic boni - everything with +X%) are applied SEPERATELY and then added to the total.

Example: A city (A) has:

8 production from tiles
1 smith (well that thing you can build with metal casting)

The civilization is running organazied religion and the city has the state religion

So it would be:

8
+2 (25% of 8 = 2 from the smith)
+2 (25 % of 8 (still!) = 2 from civic)
----
12 total

Now if i add mining inc, giving, say another 4 it would be:
8
+4 from mininc inc.
---
12 sum of fixed numbers
+3 (25% of 12 = 3 from the smith)
+3 (25% of 12 = 2 from civic)
---
18 total

If it IS this way, that would mean, that for example there would be no reason to prefer the capital for the wall street under bureaucracy, as both boni would be calculated seperately (X+(50%*2)=2X) instead of sequencialy ((X+50%)+50%)=2.25X). Shrines, providing ´fixed numbers´, would still go well with wall street tho. And what about corps ? They also provide fixed numbers - so do they count towards the ´raw´ and then become multiplied ? You see: A lot of confusion...

I know i could make a series of experiments to figure all this out and check the detailed info in the city-screen tooltips, but yet i´d rather have the exact correct description on how it really works from someone who knows (so no more guesses, like mine above, please, as to avoid further confusion).

[snoopy369]

Preferring the capital for wall street is because of the two part nature of commerce.

Commerce = (raw commerce)*(sum of multipliers on commerce)

Gold = (commerce)*(% to gold)*(sum of multipliers on gold)

So the commerce multiplier and the gold multiplier do multiply together (not add). Some things work this way, most don't outside of commerce multipliers (most hammer bonuses apply additively, so apply based on the raw hammer amount).

[Unimatrix11]

oh yeah - the gold/commerce thingie escaped my attention in this example - seems compatible with the logic described above, since commerce is calculated before it splits into its ´usable parts´, giving their raw numbers to be multiplied repectively.

You say some work this way - if you have any other examples in mind, i´d like to ask you to mention them, cause they might have as well espaced my attention.

You say most hammer boni get appied additively - is that true for ´fixed numbers´, namely corporations and specialits, as well ? Is there even a point really to distinct between ´fixed numbers´ and ´multipliers´ in terms of the sequence they add up ? Is it over simplified to say, as a rule of thumb, ´add everything then multiply with sum of multiplier boni ´ ?

[snoopy369]

I don't know very well which are multiplicative and which are additive.

I think that specialists and corporations (fixed bonuses) are pre-multiplier; so if you have 10 hammers, and 5 hammers from specialists, and a forge, you will get 15+25%(15) or 18 hammers (plus .75 that is dropped). Hammers from chopping or whipping are multiplied as well (so if you can, chop when you have a bonus to get the most of your chop).

I'm not sure all specialist things are multiplied though - I think I remember hearing that sometimes scientist specialist beakers aren't multiplied, but I don't recall the circurmstance.

[Unimatrix11]

Thanks for the advice on choping - i didnt know that !
Isnt that crazy ? I mean i thought my question was a bit stupid and everybody would just be like "look it up, dude !" (thx for your quick answers btw), but it turns out even quite reputated forum-members dont know all about it for sure...

[Quillan]

Add the modifiers together before applying them. Example, a city that has a forge, factory, power plant, Iron Works, and has access to both Iron and Coal.

+25% for forge
+25% for factory
+50% for power
+100% for Iron Works
+50% for Iron
+50% for Coal

I might be mistaken as to the amount of bonuses, as this is from memory, but that adds up to a +300% to hammers. So you take the base hammers produced by the city, add any hammers from specialists or overflow/chopping, then multiply it by 4. If the city produced 25 hammers per turn, 4 hammers per turn from a pair of engineer specialists, and had a 15 hammer overflow from the previous build, you put 176 hammers into the new item in the coming turn (25+15+4=44, 44*4=176).

[Quillan]

Arggg, I hate getting interrupted by customers! Sorry about the double post. Cant' seem to delete it.

[couerdelion]

Originally posted by Quillan
Add the modifiers together before applying them. Example, a city that has a forge, factory, power plant, Iron Works, and has access to both Iron and Coal.

+25% for forge
+25% for factory
+50% for power
+100% for Iron Works
+50% for Iron
+50% for Coal

I thought that the +100% for Iron Works was the same as the +50% for Iron and +50% for Coal

[darrelljs]

Originally posted by couerdelion I thought that the +100% for Iron Works was the same as the +50% for Iron and +50% for Coal

Yeah...me too.

Bureaucracy is the only thing that gives a percentage boost to commerce, and hence is the only instance in all of CIV where bonuses are multiplicative. Its really what made the early CS slingshot so powerful, if you can get an Academy up and running (and hence a Library) you are at 1.5 * 1.75 = 2.625 bonus over your capital's raw commerce. Heck, that is 13 extra commerce just from the Palace.

Darrell

[Unimatrix11]

okay - so what i assumed seems to be correct (in general) - now only corps remain somewhat of a riddle... Do their boni also get multiplied (e.g. the hammers from mining inc.) ?

[snoopy369]

Yep, they're raw also.