[Guide] Analysis of Cape: number of days to reach break-even

Discussion in 'Guides' started by Laozi, Jun 15, 2018.

  1. Laozi

    Laozi Member

    Joined:
    Nov 2, 2016
    Introduction
    Cape is a GB that produces FPs only. There has been much debate over whether one should build Cape (e.g. see the comments on the Cape wikia page), since it seems to cost more FPs than it generates. The problem is actually straight-forward: given the amount of FPs needed to level Cape, can a player reach break-even within a reasonable time frame? However, there has been no quantitative analysis to date, which is the purpose of this guide.

    Method
    Consider the following scenario that allows us to obtain a rough estimate on the shortest time required to reach break-even. Assume that all reward spots are taken by free donors with 1.8 - 1.9x Arc boost and that the owner contributes the remaining FPs. The total investment on each level can thus be obtained. By ansatz, assume that the owner flips Cape to a target level using the said FP allocation within 1 day, reinvests all the FPs generated upon leveling, and collects every day afterwards, waiting for the day of break-even. (The reason for adopting this strategy will become apparent after seeing the complete results.)

    Results
    Before presenting the complete results let us examine 2 cases which will illustrate how the algorithm works.

    Case study: Target level 1
    A target level of 1 simply means bringing Cape out of mud and letting it sit at level 1. At level 0, there are 2 free donors, contributing 19 FP for 1st place and 10 FP for 2nd. The owner contributes the remaining 60 - 19 - 10 = 31 FP. The total investment is 31 FP. Remaining at level 1 gives the owner 2 FP per day without further investment. Therefore, this will require 31 / 2 = 15.5 days to reach break-even. In other words, Cape becomes profitable beyond day 16.

    Case study: Break-even with respect to Shrine of Knowledge
    Cape is often benchmarked against SoK. Cape occupies 20 tiles, equivalent to 5 SoKs. Therefore, in terms of space efficiency, Cape should generate 5 FPs per day just to be on par with SoK. This is accomplished with a target level of 5, where the net total investment by the owner is 618 FPs. This will require 618 / 5 = 123.6 days, or about 4 months, to reach break-even.

    Complete results
    The following figure shows the number of days to reach break-even (denoted as D hereafter) for target levels 1-79 and free donors with 1.8x, 1.85x, and 1.9x Arc boost. The black point at level 5 is the benchmark with respect to SoK as discussed above.

    Cape.png

    We make the following important observations:
    1. D increases dramatically at the lower levels.
    2. The dent at level 10 is caused by an increase of 2 FP from level 9, reducing the rate of increase in D.
    3. The rate of increase in D slows down beyond level 10. This is due to the increased ratio of rewards, which reduces the portion of investment by self-leveling.
    4. D obtains a local maximum (blue points) at a target level of 21 (1.9x) or 22 (1.8x, 1.85x). The owner needs to wait for almost a year before s/he gets a return on FPs.
    5. D decreases to a local minimum (red points) at level 57-60 for 1.8-1.9x donors, corresponding to 302 days (10 months) down to 236 days (8 months).
    6. Going to higher levels, the drop in reward ratio causes D to increase again. Currently there is no evidence that D will ever drop again.
    The net profit in FP (generated minus investment) over a period of 550 days is shown in the next figure, where the cross-over points at break-even are marked by black dots. For clarity, only the case of 1.9x donors is considered. It is obvious how level 60 outperforms other levels within a time frame of 1.5 years. A close-up around the 0 line is provided as well.
    Cape2.png

    Close-up around 0 line:
    Cape2b.png

    Strategies on target levels
    Best strategy: target level 60
    Fastest for break-even (8 months); profits are better than even level 80 within a time frame of 1.5 years.

    Worst strategy: target level 21
    Slowest for break-even (1 year); profits are very poor, even worse than level 10 within a time frame of around 450 days.

    Practical strategy
    In practice, I believe few players would wait to amass 50 sets of blueprints and the required 14135 FPs before building Cape. A practical way is to rush level in 2 stages. In stage 1, build Cape and end at level 10. In stage 2, upgrade to level 60 as fast as possible.

    Concluding Remarks
    While the presented model ignores (i) other sources of donors (e.g. goods buyers, competitive bidders, altruistic friends), (ii) alternative modes of leveling (e.g. swap-based leveling instead of self-leveling), and (iii) possible setbacks (e.g. owner bought goods with FPs to build Cape, denial of 1.9x donors due to snipers or mistakes), it provides a controlled and well-defined estimate for D.

    So, "Is Cape worth building?" If you plan to play longer than the corresponding D of your target level, the answer is yes. Moreover, if you go beyond level 10, it is important not to sit at around level 20 (worst) but to reach level 60 (optimal) as soon as possible, where D is about 8 months with 1.9x free donors and the net total investment is 14135 FPs; otherwise, the day of profitability could be significantly delayed.

    As a final note, this analysis only provides a working strategy of getting a return on FPs from Cape within the least amount of time. It does not mean that one should never level Cape beyond 60.
     
    Last edited: Jun 18, 2018
  2. xivarmy

    xivarmy Well-Known Member

    Joined:
    Jul 14, 2017
    Your analysis is in some ways much more rigorous than my own on the subject, but the conclusion reached is roughly the same - that once you can level a cape with arc assistance, it makes good sense to take it to 60, but not necessarily further. As for your 2 stage strategy, i'm not sure level 10 is the right point to pause while you wait to start getting the stream of blueprints - in general the levels up to 10 do get progressively worse, and level 7 specifically doesn't even give an additional FP (in order to make level 10 a big deal i guess so it can give two). As such my suggestion would be level 6 until you're ready to really run the thing (or lack better places to spend the FP).
     
  3. Laozi

    Laozi Member

    Joined:
    Nov 2, 2016
    I agree with you that level 10 may not be an ideal rest area and level 6 may be better. In the big picture (Fig. 2) though, the difference between the two cases may be almost negligible. What I had in mind was to make a compromise by taking out a chunk of the total investment as much as possible without being too close to the worst-case scenario (local maximum). For me, I expect on average I would get 1.85x donors. Drawing a horizontal line at the corresponding local minimum in Fig. 1 would intersect level 10. That's how I came up with the 2-stage strategy. Of course it could vary a lot depending on other factors too.

    Thanks for your input and giving me the opportunity to explain this a bit further!
     
  4. jobu523

    jobu523 Active Member

    Joined:
    Oct 14, 2016
    Very clear and to the point guide. Thank you.
     
  5. Ozyman Tremble Weaklings

    Ozyman Tremble Weaklings Well-Known Member

    Joined:
    Sep 10, 2017
    I've been looking at some numbers for leveling a Cape up to 80. I might be thinking along the wrong lines here, but the general strategy I'm showing is below:

    Level 0-1: Guild Stix to Brix thread, no fp cost to owner. (0 fp cost)
    Levels 1-19: More efficient to use swap threads than self leveling with Arcs taking reward spots. (13,233 fp cost)
    Level 20-80: Self Level with Arcs taking reward spots at 1.8 or higher if you can find anyone willing. (28,173 fp cost)
    Not counting double dips but counting a collection at each level gives 3,238 fp's.

    Puts the total fp's (less any rewards from swap threads) at 38,168 fp's.

    Pays off cost on the 478th day.

    Edited for correct tense and grammar.
     
    Last edited: Jul 3, 2018
  6. Claire the Divergent

    Claire the Divergent Active Member

    Joined:
    Jan 1, 2018
    Outstanding guide. You could get even more in the weeds comparing SoKs and the Cape based on how many roads touch the Cape vs. how many roads would be required to fit the SoKs. But, this guide does a great job of painting the big picture on how long the payoff time is on the Cape (and other FP-generating GBs although the curves are obviously different).


    I have 2 Recommendations:
    #1 - don't place the Cape (assuming you haven't built it yet) until you can power level it.
    #2 - If you have the FPs to level it to 60, do it ASAP to start the payoff clock running
     
  7. Ozyman Tremble Weaklings

    Ozyman Tremble Weaklings Well-Known Member

    Joined:
    Sep 10, 2017
    Played with some numbers and came up with a different strategy.

    Use swap threads to level up to 15
    Self Level with Arcs taking reward spots at x 1.8 up to level 80*

    *It's cheaper to get the first 3 reward spots locked at 1.8 and use swap threads for the remainder, but it also is more time intensive and in my mind not worth the savings.

    Total Cost to Level 80 = 31,305 fp's
    Days to Payoff after 80 = 392 days

    For everyone else to make their own choice for leveling technique please see below:
    Total FP's to Level (FPL)
    Owner's FP's Spent on Level (FPO)
    Owner's FP's Spent on Swaps (FPS)
    Arc Lock FP's Spent on Level (FPA)
    Approximate Reward FP's from Swaps* (FPR)
    * FPR assumes a 50% return, i.e. for every 100 fp's spent in swap threads, owner receives 50 fp's back from rewards

    7 Different Leveling Strategies:

    A - Self Leveling w/ Arcs: 32,309 fp's - 404 Days to Payoff
    FPL = FPO + FPA (FPO = cost of each level)

    B - Swap Groups w/ no Arcs: 82,487 fp's - 1032 Days to Payoff
    FPL = FPS (FPS - FPR = cost of each level)

    C - Swap Groups w/ 1st Arc Locked: 50,321 fp's - 630 Days to Payoff
    FPL = FPO + FPA + FPS (FPO + FPS - FPR = cost of each level)

    D - Swap Groups w/ 1st & 2nd Arc Locked: 30,376 fp's - 380 Days to Payoff
    FPL = FPO + FPA + FPS (FPO + FPS - FPR = cost of each level)

    E - Swap Groups w/ 1st - 3rd Arc Locked: 29,765 fp's - 373 Days to Payoff
    FPL = FPO + FPA + FPS (FPO + FPS - FPR = cost of each level)

    F - Swap Groups w/ 1st - 4th Arc Locked: 31,286 fp's - 392 Days to Payoff
    FPL = FPO + FPA + FPS (FPO + FPS - FPR = cost of each level)

    G - Swap Groups w/ 1st - 5th Arc Locked: 31,858 fp's - 399 Days to Payoff
    FPL = FPO + FPA + FPS (FPO + FPS - FPR = cost of each level)

    Best - Lowest fp cost by level - 28,775 fp's - 360 Days to Payoff

    Cape 30.PNG
    Cape 60.PNG
    Cape 80.PNG

    3rd Arc is shaded Orange instead of Green because I am on the fence about whether I would consider the GB eligible for swap threads with 3 reward spots already taken.
     
  8. amiar

    amiar Active Member

    Joined:
    Jan 7, 2018
    Me and one of the guys in my arc swap group were talking about doing cape after our arcs are done. Both of ours are at lvl 10. Since we will both have lvl 80 arcs I was thinking we just take 1st + our donation to maximize BPs and medals (still have like 9 expansions left). And the rest we could get from Arc80s. I think that might be the best way to ensure we each have all the BPs. Right now I have enough sets to get to lvl 45, but beyond that I wouldn't have enough.

    The only issue is that I'm pretty sure he makes more daily FPs than me :(
     
  9. jobu523

    jobu523 Active Member

    Joined:
    Oct 14, 2016
    Cape is best after you finish the Arc leveling. No need to plant it before. Once you finish the Arc, you can power level the Cape from zero to 80 in 2-3 months very easly.
     
  10. filthyhorse

    filthyhorse Member

    Joined:
    Jan 7, 2017
    I like this comment a lot. (ilikeitalot). The pause at level 6 advice is very good. Thanks.
     
  11. filthyhorse

    filthyhorse Member

    Joined:
    Jan 7, 2017
    Wow, fantastic post, Laozi. Thank you for doing this work. I am no mathematician, merely a little Rainman-ish when it comes to numbers, and I came up with similar time frames as well. This OP was exceptionally well done. I would only add, or maybe just stress, that in the real world the time frame will most certainly take longer than the minimum. Unless one is exceptionally disciplined, has a massive daily fp supply when they begin construction and has the support of a disciplined, max level arc guild/friend network, the minimum amount of time one can expect to see a return is closer to 1 year. For most people it's going to be even longer, of course.

    Again great information and thanks for posting it.
     

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