[Guide] Comparison of break-even time for all FP-producing GBs

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DeletedUser27525

Introduction
This guide is similar to my earlier one on the analysis of Cape. Here we use the same method to compare the time needed to reach break-even in terms of FPs for all FP-producing GBs. I make no recommendations for or against any of the GBs considered here - all but Cape have a second effect, and thus a slow return in FPs does not necessarily mean the GB is not worth building. This guide simply gives you an idea of how quickly you can expect a profit in FPs after power leveling these GBs.

FP-Producing GBs
GBs can produce FPs directly or indirectly. In the former case, the player is able to collect FPs directly from the GB. There are 6 direct FP-producing GBs:
  • Hagia Sophia
  • Castel del Monte
  • Cape Canaveral
  • Innovation Tower
  • Arctic Orangery
  • Kraken
The analysis for these GBs is exactly the same as that of Cape. Please refer to my earlier guide for details. Here we assume all spots are filled at 1.9x.

There are 2 GBs that may lead to FP rewards with some probability:
  • Temple of Relics
  • Blue Galaxy
To compare them with the rest, a simple model is presented as follows.

ToR
We make the assumption that the player completes 64 GE encounters on a weekly basis. The expected FP per encounter is given by
20 x P(20 FP reward) + 100 x P(100 FP reward)
= 20 x P(relic) x P(common) x 1/7 + 100 x P(relic) x P(uncommon) x 1/6​
The 1/7 and 1/6 factors are estimates since the exact probability is unknown. The equivalent daily FP reward is then
64 / 7 x [20 x P(relic) x P(common) x 1/7 + 100 x P(relic) x P(uncommon) x 1/6]​

BG
To maximize FPs through BG, the player must collect from Indian Palace or Terrace Farm, each giving 5 FPs. We assume the player has enough of these for double-collection attempts. The expected FP is then
5 x P(double collection) x N_attempt​

All data is obtained from wikia.

Results
The figure below shows the time needed to reach break-even as a function of target level for all 8 GBs. A local minimum, representing the level of fastest return in FPs after power leveling, is observed for most of the GBs. This level (L) is tabulated with the corresponding time (D in days) and net investment in FPs to reach it at 1.9x. In ascending order of break-even time:
  1. Cape is the fastest at 236 days at target level 60. It is indeed the best GB for FP production!
  2. Inno Tower: 303 days at target level 65.
  3. HS: 332 days at target level 55.
  4. AO reaches break-even in a little bit over a year: 383 days at target level 57.
  5. CdM: 411 days at target level 55.
  6. Kraken: 515 days at target level 55.
  7. BG is the second worst in this list: 582 days at target level 54. However, this is derived from the maximum of 5 FP per double-collection attempt. If 10 FP buildings are offered in the future, the time to reach break-even would be halved, and BG would become the second best in the list.
  8. The level of fastest return for ToR does not exist, since the curve is monotonically increasing through level 70! This is very different from the 7 other GBs that all have a local maximum at around level 20. Power leveling ToR for the sake of FP profit may not be a good idea.
FP_GB_all.png

GBLDNet FP investment
ToR---
HS5533210953
CdM5541113545
Cape6023614135
IT6530311801
AO5738321820
BG5458222309
Kraken5551522617
 
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DeletedUser32824

I like you and these math posts. Would you care to put in the cost of leveling each GB to that level? (assuming all 1.9 rewards)
 

DeletedUser29726

In the case of ToR, it's best viewed through breaking it down into frequency of various relics :

upload_2018-11-6_20-8-36.png

5* gold + silver is an approximation for utility as a source of FP (more or less converting golds into "equivalent silvers").

One thing to notice to start here is that even a level 1 temple already creates an equivalent of 15 silver relics a week (a bit over 5 silvers + a bit less than 2 golds). It requires getting to level 30 (!) to double this. This is unlike any other building you'd consider for FP purposes.

The primary reason to level a ToR is for jade relics - if you don't want those, just do what's cheap and leave it sit.
 

Claire the Divergent

Active Member
Outstanding post. FYI, I collected data on over 580 relics (so far) and the percentages are not the same within each category of relics - but they are really close and I think your assumptions are fine to use. A couple other thoughts:
  • Players leveling GBs this high will eventually go past the optimum level on all of them. I would recommend changing the name to "cheapest" level, because optimum might make people think they should stop there, and the next level might be a lot better than the next level on any other GB
  • In defense of the ToR and BG, neither are just FP GBs, and their value is greatly affected by the value of goods created for players at higher levels.
 

DeletedUser27525

I like you and these math posts. Would you care to put in the cost of leveling each GB to that level? (assuming all 1.9 rewards)
Good suggestion! I've included those numbers now.

The primary reason to level a ToR is for jade relics - if you don't want those, just do what's cheap and leave it sit.
Thank you for sharing your insight!
 

DeletedUser27525

Outstanding post. FYI, I collected data on over 580 relics (so far) and the percentages are not the same within each category of relics - but they are really close and I think your assumptions are fine to use. A couple other thoughts:
  • Players leveling GBs this high will eventually go past the optimum level on all of them. I would recommend changing the name to "cheapest" level, because optimum might make people think they should stop there, and the next level might be a lot better than the next level on any other GB
  • In defense of the ToR and BG, neither are just FP GBs, and their value is greatly affected by the value of goods created for players at higher levels.
Thank you for your suggestion. I agree that the word "optimum" may lead to misinterpretation. I have changed "optimum level" into "level of fastest return after power leveling."

Yes, I understand the usefulness of ToR and BG. Indeed, the value of goods is not considered in this guide. A complete assessment of BG would require a list of the top N event buildings and the price of goods. It would be interesting to look at when I have time. As an aside, AM can also be considered as an indirect FP-producing GB. I didn't include AM in this guide because there are too many parameters (number of neighbors, percentage of successful attacks, percentage of plundering valuable buildings, etc.) that can vary a lot for different players.

As for myself, I have ToR but not BG. If we can get multiple buildings that produce more than 5 FPs (preferably 10) I will build BG and power level it. :) As a non-diamond player I don't have enough valuable buildings right now to power level BG.
 
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DeletedUser36624

64 in GE every week? That accounts for about 5% of all players.
I think that fits well the sort of players who would dig into an analysis of FP producing buildings. If they can't do GE64, they will go, "Why not?", dig in, figure it out, and fix it. The only difficulty is finding a guild that opens GE4 on a regular basis.
 

Stephen Longshanks

I think that fits well the sort of players who would dig into an analysis of FP producing buildings. If they can't do GE64, they will go, "Why not?", dig in, figure it out, and fix it. The only difficulty is finding a guild that opens GE4 on a regular basis.
I know one on Vingrid. :)
 

Emberguard

Senior Ingame Moderator
The level of fastest return for ToR does not exist, since the curve is monotonically increasing through level 70! This is very different from the 7 other GBs that all have a local maximum at around level 20. Power leveling ToR for the sake of FP profit may not be a good idea.
Not necessarily correct. Consider this post from the (en) International forum

Thread Link
I levelled my TOR to level 100 and found that the relic appearance % is stuck at 33.75

Is this the highest it can go? If so, it's kinda unfair that Arc spammers can get an increase with every level and yet TOR is capped

(Yes, I know that I am more likely to get a jade relic with each subsequent level: I couldn't care less about that because I already have in my inventory dozens of the buildings that it gives).
Based purely on the info given in the post above,

While it would require lvl'ing higher then that to determine whether or not there is an absolute maximum for relic appearances, it is enough to suggest the rate of growth slows down considerably some time between lvls 70-100. Which would effect the level of fastest return if the spawn rate of any relic in general appearing slows to a standstill. Of course without lvling it well above lvl 100 it's impossible to know whether it will ever get to a point of only FP relics. But hypothetically once the spawnrate stops increasing that's the maximum return you could expect with the only possible changing factor being when each type of relic spawns - assuming that wouldn't get stuck at some point too

(and yes, being from the International forum that could mean slight changes in mechanics between there and here - but it does show there may be a level of fastest return, just you haven't gone high enough to find it)
 

amokka

New Member
Excellent post. Persuaded me to get that CC and raise it to level 70.

Inspired by Laozi, I did a similar analysis for the Himeji Castle and Space Carrier. With the same assumptions. For comparison I included CC, Inno and BG with a 5-fp return. Also added BG with an average of 10-fp return on double collection, which should now be feasible with all the newer special buildings.

HC
HC and SC on average gives 18.5 FP as spoils_of_war when paying out. (10*0.25 + 50*0.12 + 200*0.05 = 18.5).
The expected average payout is thus 18.5 x P(spoils_of_war) x N_attempt.

Data for HC and SC grabbed at wikia.

Results
The figure below shows the time needed to reach break-even as a function of GB level. Legend: Himeji Castle (HC), Cape Canaveral (CC), Innovation Tower (Inno), Space Carrier (SC), Blue Galaxy with a 5fp average double reward (BG-5), Blue Galaxy with a 10fp average double reward (BG-10)

The overall conclusion is that
- CC is still the GB with fastest break-even on invested FP.
- BG with an average of 10 fp payout on each double collection is (as predicted) the second best.
- BG with an average payout of 11.6 fp or more will become the best FP with regards to break even on FP investment (not shown in figure).
- HC at level 41 is almost as good as Inno at level 65.
- The curve for HC is "flat" from level 20 to level 58. So why not take it to 58, and optimise other benefits from it?
- SC has same payout as HC only its a little more expensive, so it takes roughly 25 days more to reach break even.

Days to break-even.png
 

DeletedUser41025

In reality, unless you are in an era above VF, you cannot negotiate every day with the SC. I don't know the exact number but depending on how GE falls, how competitive your guild is and the guilds you are competing against, and when GBG starts/ends, you are probably missing 1-5 days a month. Any chance you can make some sort of calculation to factor that in?
 

UBERhelp1

Well-Known Member
In reality, unless you are in an era above VF, you cannot negotiate every day with the SC. I don't know the exact number but depending on how GE falls, how competitive your guild is and the guilds you are competing against, and when GBG starts/ends, you are probably missing 1-5 days a month. Any chance you can make some sort of calculation to factor that in?
In theory you miss one out of every 14 days. But that is not the case. You can collect from the SC and on Monday, wait until Tuesday until GE begins, negotiate, and then collect from the SC again. In other words, it doesn't really matter that much.