SoggyShorts
Mathematician par Excellence
I see. Then how many premium expansions could you place to maintain the same CAL if you had no GA?
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Your Elvenar Team
Best Ancient Wonders?
- Thread starter Tehya1
- Start date
iamthouth
Tetris Master
@SoggyShorts another 10 it seems, noting the model only went to chapter 17 at the time, so may be inaccurate for Ch20. But alas, I don't have the diamonds for that. 10 expansions would cost 68,400 diamonds at normal price, 61,650 at 10% discount, and 54,720 at 20% discount (offered Cyber Monday only).
MaidenFair
Chef - Head Philologist
I’ve been adjusting the regular expansion numbers for this type of calculation.
MaidenFair
Chef - Head Philologist
@iamthouth, thanks for looking at it again! I appreciate the time you put into it. 
Obviously, in your city, the answer is that the AW levels are worth that space to you, for multiple reasons. I was just trying to emphasize the importance of being aware that, because of the formula, it’s not quite accurate to count the AWs as only having their base footprint when doing calculations on their efficiency compared to other buildings. I’m a firm believer in taking into account the population and culture required when calculating efficiency for manufactories or armories…this feels like the same approach to me with AWs. Most people recommend the GA solely as being an immense space-saver on population, and I’m just offering a small caution on that reason for recommendation.
In your case, not having those 32 wonder levels would reduce your catering costs by almost 5%…by the time you calculate all the space saved on 5% of your orcs and mana and standard and sentient goods production, would it balance out? Maybe, maybe not, in a pure math comparison of squares, but as your analysis shows, it wouldn’t actually be space-saving on the ground in your city, not least because you have no more regular expansions to place. I’m on the other end of that spectrum, with 22 unplaced expansions in inventory and many more to come in the tree yet, so the approach to efficiency calculations is rather different in my city.
Obviously, in your city, the answer is that the AW levels are worth that space to you, for multiple reasons. I was just trying to emphasize the importance of being aware that, because of the formula, it’s not quite accurate to count the AWs as only having their base footprint when doing calculations on their efficiency compared to other buildings. I’m a firm believer in taking into account the population and culture required when calculating efficiency for manufactories or armories…this feels like the same approach to me with AWs. Most people recommend the GA solely as being an immense space-saver on population, and I’m just offering a small caution on that reason for recommendation.
In your case, not having those 32 wonder levels would reduce your catering costs by almost 5%…by the time you calculate all the space saved on 5% of your orcs and mana and standard and sentient goods production, would it balance out? Maybe, maybe not, in a pure math comparison of squares, but as your analysis shows, it wouldn’t actually be space-saving on the ground in your city, not least because you have no more regular expansions to place. I’m on the other end of that spectrum, with 22 unplaced expansions in inventory and many more to come in the tree yet, so the approach to efficiency calculations is rather different in my city.
Pheryll
Set Designer
1. I do not think that the Mountain Halls bonus (added to the relic bonus for boost) is part of the CAL; if it is, then the wonder is doing you a significant disservice (not that this affects the comparison).
2. The province calculation and the AW level calculation are different multipliers. If the ratio between these changes significantly as you progress (especially since you are getting to the later chapters) then the number of expansions worth 32 wonder levels will also change.
maeter75
Well-Known Member
Loving this thread, all good thoughts and thinking and what to ponder especially as ones works on more AW's, it got me thinking.
To me unless all things where a lot tougher, the 121 extra squares of space more then makes up for the penalty of AW levels.
Now IF it was 20% harder I would worry more but looking at peoples stats in this thread, it look more like 5% tougher
- My level 30 Golden Abyss, currently provides 182,000 people
- My current housing is ~34K a house in 24 squares or 1400 people a square, these are all Magical Residences (regular houses would require more)
To me unless all things where a lot tougher, the 121 extra squares of space more then makes up for the penalty of AW levels.
Now IF it was 20% harder I would worry more but looking at peoples stats in this thread, it look more like 5% tougher
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Grishnak
Active Member
First, apologies for resurrecting a two year old thread....MinMax’s calculator doesn’t go past chapter 17 so these values aren’t quite right, but I plugged your numbers (as best I could) in and found that 1 expansion would give approximately the same increase at your chapter as 5 wonder levels. (Apologies for the fuzzy picture…
That means your level 32 GA increases your costs approximately as much as adding another 6 expansions.
Second, could someone walk me through the math here?
Looking at MinMax's formulas (here) there are two variations (which MinMax says are equivalent...):
If I'm just interested in the difference between two options (I'll call it RELATIVE_CAL just so its clear it is not CAL, and since I haven't thought long enough about a name):
1. adding non-premium expansions
2. adding AW levels
then I should be able to ignore everything before the AW term. For simplicity, I'll also assume zero premium expansions, so it looks like this:
RELATIVE_CAL = (0.003A + 1) * (V - 4.5)
or
RELATIVE_CAL = (0.003A + 1) * (0.8942V - 4)
(depending which version of the formula you pick).
So depending on which formula, it seems like it takes 298-333 AW levels to have roughly the same impact as one expansion.
But @MaidenFair says that CAL would increase (in a particular situation) the same from one expansion as much as 5 wonder levels.
So, I'm just confused. I guess my math is failing me?
(And I'm aware that the formula is very likely more out of date now especially after the AW changes last year and the upcoming Spire changes, but hopefully its still a worthwhile discussion.)
Pheryll
Set Designer
Just use @iamthouth 's numbers. 350 AW Levels and 143 expansions for the first one. 1 + 350 * .003 = 2.05 and 143- 4.5 = 138.5. Now compare .003 to 2.05 and 1 to 138.5 and you will find that .003/2.05 is approximately one fifth of 1/138.5