PDA

View Full Version : my thoughts on the CC economy



johnny boy phd
05-23-2013, 11:33 AM
Introduction

I have seen a recent discussion started by Glycogen regarding the CC economy - his question was when should he consider start building his NCs. There has also been the recent discussion regarding the effectiveness of current LTB, the 75 million Dockside Mills, together with the Pagoda analysis.

Since I have been here, CC economy has popped out as a topic everyonce in a while. There has been a significant amount of work done on it, dating back to the initial analysis by tramp stamp and duder's in-depth analysis (both on the best of the best guide), MXZ upgrade NC order guide, and very interesting thoughts shared here and there by murf, BigMoney and others I am not listing. My idea is not to conduct an extensive review of what is out there, but instead, to share the method I employ. This information might be quite uninteresting for most, but I am rather positive that a few people will find it engaging and discussion will certainly follow.

I am positive that what you are going to read below is nothing new, and most likely, it has been exposed already, but at least so far I have not been able to find a sythetic guide for economy maximization. At this point, I dare say that I am not a very big fan of the ROI analysis: I understand its validity, and most likely, yields similar results, but I think that economy planning should be about maximizing the rate of increase of IPH and not about paying back buildings and upgrades - much more could certainly be discussed about this "criticism", but that is not my goal here.


Preliminaries
I start by clearly stating the goal - maximize the rate of increase of IPH. Henceforth I will be using my numbers here, which are affected solely by a +10% tycoon bonus and +25% syndicate building output and I do not own any cost or upgrade time reduction bonus. Still, my analysis is still applicable to cases that benefit from these because they affect all buildings in the same fashion. As I am not a gold spender, I will not include into my analysis the gold buildings, but the same strategy should also apply, just with a different resource to build.

It is important to note that there is more to the IPH figure than one can initially think of. Not all buildings are the same, and most of their IPH production goes to waste if not collected on time. Note that a lvl 6 Laundromat contributes with 1,815 towards the total IPH. It pays off 151 each five minutes, but if I collect it only e.g. 10 times per day, its effective IPH is only 63. I define a concept which I will refer to as collectable IPH, which is the portion of your IPH that you actually are able to collect. At this point it is important to refer that because of different payout time of buildings, it is a common strategy to focus on buildings with payout cycles which one will be able to collect - not only in this way your IPH will tend towards the collectable IPH, but also it is extremely useful to defend robberies (where the best strategy is to collect on time). Thus, for this analysis (and for my particular case, pretty much like many others), I focus on the 12, 24, and 48 hr buildings, with the exception made to the 6hr NCs (and maybe with other 6hr buildings if time and money allows), and consequently, IPH increase will always be an increase of collectable IPH.

All benefits come with an associated cost. In the CC economy, the finite resources are: (1) money, and (2) upgrade time. There are also certain constrains, e.g. only 2 buildings of each type, but logically I will not dwell on those. It is not obvious to me how to choose which upgrade to do, with its associated cost and upgrade time, that will maximize the rate of increase of my collectable IPH. Note that if my collectable IPH increases faster, I am investing the money in the building that gives the most benefit and I will be able to afford more expensive upgrades earlier - thus penalty function #1, the money, and penalty function #2, the time, are both related to the rate of increase of IPH, the former directly and the latter inversely.

It is know that as upgrade lvl increases, its cost and upgrade time increases dramatically - it will be impossible to reach the point of having all buildings at lvl 10 (unless you are a time hacker). It is often implicitly understood that sometimes the most expensive upgrade is not the most effective upgrade to take. A similar argument applies for the cheapest, longest, or quickest upgrades, particularly when one has to make choices among different buildings with several orders of magnitude of payout difference, upgrade costs, and upgrade times. So, to state it clearly once again, the goal is: to maximize the rate of increase of collectable IPH taking into consideration the finite money (for upgrade costs) and time (for upgrade completion).


Methods
I will define two types of measures: absolute and relative. Relative measures are taken with respect to the current IPH and will distinguish properly the difference in impact between upgrading e.g. a MT or a loft. I am unable to incorporate symbols here, thus I will consider letter "d" as a capital detla; and I will consider a underscore "_" to denote relative measures. I will try to be explicitly explanatory at start to ease the readers. Let us define the absolute difference in IPH an upgrade accomplishes by

dIPH = IPH (lvl i+1) - IPH (lvl i)

For example, the dIPH of a NC lvl 2 upgrade is dIPH = 80,208 (note that this figures are respective to my particular case as mentioned above).

Now, let us define the relative difference in IPH an upgrade accomplishes by

dIPH_=dIPH / IPH

where IPH is my current IPH, which if one follows this strategy should equal the previously mentioned collectable IPH. In fact, my current IPH is 257,225, and my collectable IPH is 245,911. I have been following this strategy closely since almost the beginning of my game, thus the difference corresponds to, among others, laundromats lvl 6 and 5, 2 lvl 5 souvenir stores and italian restaurants, diners lvl 5 and lvl 2, etc. In the beginning, I was doing upgrades rather randomly and pretty much without a clue, and looking back, I lost a lot of time efficiently - still, as it is common knowledge, it doesn't matter much once the MT and lofts start to kick in, and those were obvious upgrades even before I laid up this strategy. If one employs my numbers, the relative difference in IPH of the NC upgrade to lvl 2 is dIPH_=31.18%

Now, I will define four ratios of increase IPH, two absolute and two relative, two with respect to investment (finite resource #1), and two with respect to upgrade time (finite resource #2). They are defined as

dIPH/$ = dIPH / (upgrade cost)
dIPH_/$ = dIPH_ / (upgrade cost)

dIPH/t = dIPH / (upgrade time)
dIPH_/t = dIPH_ / (upgrade time)

I find it useful to scale these. I scale the dIPH/$ per thousand bucks (i.e. dIPH/k), dIPH/t per upgrade hr (i.e. dIPH/k), and the relative ratios per million and upgrade day (i.e. dIPH_/m, and dIPH_/d). Just to make numbers more trackable and close to order of magnitude zero.


Results & Discussion
I have compiled these four ratios into an excel spreasheet. As results, I show first my current case in the Figure 1 below

http://farm3.staticflickr.com/2871/8804710404_126f46b403.jpg (http://farm3.staticflickr.com/2871/8804710404_126f46b403.jpg)
Figure 1 - No-brainer. Upgrade NC to lvl 2

The direct comparison of these numbers, taking into consideration the ability to cover the upgrade cost, will determine what is the best upgrade to chose from such that the rate of increase of collectable IPH increases the fastest possible. Ratios per cost quantify what is the best investment of money, whereas ratios per time quantify what is the best investment of upgrade time. Relative ratios measure the impact of each upgrade in respect to the current size of the economy whereas absolute rations measure precisely the improvement of IPH with respect to penalty functions money and time.

As can be seen from Figure 1, my best current upgrade is the NC to lvl2. The change in IPH will be 31.18%, better than to go for a lvl 4 pagoda. At the same time, it represents a much better investment as its dIPH/k and dIPH_/m are way better than the pagoda. In respect to increase in IPH with regard to upgrade time, they are pretty much comparable, but much better than all others. Note that to go for lvl 7 lofts is way worse with respect to money and time, approximately 0.69 for the former and 97.9 for the latter. Similarly, the relative impact of loft upgrades is comparatively less (around 5% and 1%). Now, it is worth to remark that a direct comparison between times of both nightclubs is not correct, as one is upgrade time and the other is build time (a limitation of my spreadsheet, I didn't want to go over too much trouble in distinguishing those and I left it as a task for the human behind the method).

http://farm3.staticflickr.com/2815/8794129883_3ccc672314.jpg (http://farm3.staticflickr.com/2815/8794129883_3ccc672314.jpg)
Figure 2 - Upgrade NC to lvl 3

Figure 2 shows the economy state after the NC upgrade. As opposed to previous knowledge, it is better a better investement for the money to upgrade the NC to lvl 3 rather than to build the second one. Just slightly, but better.

Figures 3 through 6 demonstrate the application of the current methodology to the near future of my game.

http://farm6.staticflickr.com/5461/8804710336_c07de13913.jpg (http://farm6.staticflickr.com/5461/8804710336_c07de13913.jpg)
Figure 3 - Build 2nd NC (perfect if still upgrading the previous one)

http://farm4.staticflickr.com/3759/8804710316_fa79615795.jpg (http://farm4.staticflickr.com/3759/8804710316_fa79615795.jpg)
Figure 4 - Upgrade 2nd NC to lvl 2

http://farm6.staticflickr.com/5343/8804710304_15f39c2b45.jpg (http://farm6.staticflickr.com/5343/8804710304_15f39c2b45.jpg)
Figure 5 - Upgrade 2nd NC to lvl 3

http://farm3.staticflickr.com/2858/8794129769_90973056f5.jpg (http://farm3.staticflickr.com/2858/8794129769_90973056f5.jpg)
Figure 6 - Maybe consider the 1st Pagoda to lvl 4 now

After lvl 3 upgrade, the next best investement of money is to build the 2nd NC (Figure 3), and upgrade it to lvl 3 (Figure 4 and 5). Lastly, the upgrade to lvl 5 of a NC will finally make it worse than the lvl 4 pagoda in respect to money invested, but still beats it in respect to upgrade time (although the upgrade time of the NC is longer, its more effective).

It is worth to remark that the necessary money to pay for the best upgrade might not be available. In such situation, one needs to compromise and go for a cheaper one while saving for the best one (another common piece of common knowledge I have read here and there in the forum). The question that remains is, what would be the best money saving upgrade? From the figures above, one can see that to upgrade the pagoda might be a good choice (as it costs only 25 million and has a absolute return of cash investment of 1.10 and return of time investment of 916.7, still way better than current lofts or MTs). This particular question is easily answered by this method when considering all the previous collectable buildings (Figure 7 below).

http://farm4.staticflickr.com/3691/8794129757_c6eafdc2bd.jpg (http://farm4.staticflickr.com/3691/8794129757_c6eafdc2bd.jpg)
Figure 7 - Complete different orders of magnitude and impact, but still the best way to pick which money-saving upgrades

When comparing older and weaker buildings, we must totally understand that we are dealing with one or two orders of magnitude lower - not only in benefits, but also in costs. Still, it was possible for me to determine that it would be a good idea to upgrade my 2nd meat factory to lvl 3 (with a dIPH/k=1.96) while waiting for my NC to finish building. Another recent decision I made was to upgrade the MT to lvl 7 (the numbers are shown in the 2nd one currently at lvl 6, dIPH/k=1.05, better than lofts to lvl 7 with 0.69, but 2 times worse with respect to time). Another example, if in the near future I end up having extra 8 hours of upgrade time somehow, I will be doing my bagel shop for lvl 4 (with a dIPH/k=1.78).

Lastly, I have decided to analyze the progression of the new LTB, the Dockside Mills. Most likely I will not build it because right now those 75 million are much more effective pumping up my NCs. As it can be seen from the previous figures, it has a dIPH/k of 0.45 (e.g. when compared with the 1.20 of the lvl 2 NC upgrade). Figure 8 below shows the progression of the building if I had infinite cash to upgrade it right away starting from now.

http://farm6.staticflickr.com/5346/8805149562_0e919f3fb9.jpg (http://farm6.staticflickr.com/5346/8805149562_0e919f3fb9.jpg)
Figure 8 - Dockside Mills, a money pit

As it can be easily seen, this building is clearly a money sink, and it increases in depth as upgrades proceed. Upgrade to lvl 6 costs at most 1 billion and results in a dIPH=100,000. Consequently, the dIPH/k is one of the lowest to be seen, more 3 times worse than to upgrade my beachside inn to lvl 7 (dIPH/k=0.36, the worst I have right now). And note that with all this money spent, my IPH has only doubled. In regard to upgrade time, it is rather quick all around, thus I might conclude that end game players with plenty of cash around might not have other and better investments available anymore. At least myself, I am clearly considering skipping it, unless if I am able to rob 40 million to build my second NC right away and then 75 million on top of that to build the mills.


Final Remarks
I proposed a different analysis on the economy of CC based solely on the maximization of the rate of increase of collectable IPH with respect to cash cost of upgrades (and thus maximizing return of investment) and with respect to time cost of upgrades (and thus maximizing rate of increase of IPH). I hope this analysis is helpful for the economy planner out there and shed light into novel ways of chosing one's path among different building upgrades.

Lastly, this analysis certainly suffers from certain limitations. To list a few:
(1) I have not considered a distinction between build time and upgrade time to make things easier, it most be noted that it is possible to upgrade one building while building another at the same time, thus the time cost to get to lvl 1 should be considered taking that into consideration;
(2) I have not considered penalties in IPH during upgrade times, that would make the analysis much more cumbersome, but it must be remarked that while a building is upgraded, its output is not collected;
and (3) I have considered the 4th daily payout of the NC (6 hours) as collectable IPH - although difficult, it is still possible on some days or to some players. This penalty could be considered in a straightforward manner simply by multiplying the NC payout by 0.75.

reras
05-23-2013, 11:41 AM
Nice work. Sticky

wa7sh
05-23-2013, 11:46 AM
Nice work. Sticky

i bet you didn't even read the whole thing ;)

GucciMane
05-23-2013, 12:23 PM
Final Remarks
I proposed a different analysis on the economy of CC based solely on the maximization of the rate of increase of collectable IPH with respect to cash cost of upgrades (and thus maximizing return of investment) and with respect to time cost of upgrades (and thus maximizing rate of increase of IPH). I hope this analysis is helpful for the economy planner out there and shed light into novel ways of chosing one's path among different building upgrades.

Lastly, this analysis certainly suffers from certain limitations. To list a few:
(1) I have not considered a distinction between build time and upgrade time to make things easier, it most be noted that it is possible to upgrade one building while building another at the same time, thus the time cost to get to lvl 1 should be considered taking that into consideration;
(2) I have not considered penalties in IPH during upgrade times, that would make the analysis much more cumbersome, but it must be remarked that while a building is upgraded, its output is not collected;
and (3) I have considered the 4th daily payout of the NC (6 hours) as collectable IPH - although difficult, it is still possible on some days or to some players. This penalty could be considered in a straightforward manner simply by multiplying the NC payout by 0.75.



As an Econ guy, I have to say your guide and TrampStamp's have been the most accurate to what I've seen and done with my own hood economy.


I might catch some flak with this, but The flaw with ROI tracking, however, is that "Return on Investment" implies that you are passively letting your income grow, much like you would with mid-long term investing in the real world (not counting the day and algorithmic traders here).


This is why I buy your approach much more - I originally tracked both ROI and IPH and quickly found that ROI didn't matter when I would travel to a camper's hood and pull enough money to make any early "returns" negligible.......while I felt like I was "maximizing" my income it really didn't matter when I bought BOTH 2 movie theaters AND 2 lofts through ACTIVE income attained through robbery.


To that extent, I've NEVER been sold on laundromats. Tramp has a convincing argument otherwise but as far as the growth of my own hood, even on days where i made plenty of collects the laundromat income was negligible compared to my ICS/IR income and robbery income.

GucciMane
05-23-2013, 12:37 PM
One thing of note that I've discovered NO ONE really brings up is this:


People truly maximizing INCOME PER HOUR will have a completely different hood than people who follow ANY helpful guide on this website, when you take "INCOME" out of just the scope of getting cash from money buildings

Dipstik
05-23-2013, 12:39 PM
I just build whatever's prettiest and upgrade whatever I can afford at the time. Wall of text is probably really useful though. Thanks for that.

My2cents
05-23-2013, 01:27 PM
I think I'll show this to my kids when they ask when will they ever use math. I will incorporate this to my econ planning.

scott(ST6)
05-23-2013, 01:29 PM
can you post a few charts and pictures...i don't read so good

(CCK) Cam
05-23-2013, 01:31 PM
Sticky this thread!!

zwiswoo
05-23-2013, 01:32 PM
Very nice guide! One "issue" in all this is how to deal appropriately with the fact that there are *two* scarce commodities for each upgrade: upgrade time and upgrade cost. You have a dIPH/$ and dIPH/t, and I'm not quite clear on what your rule of thumb is for relative priority between them.

My approach currently is to convert upgrade cost into a time - the time at current (collected) income per day it would take to save for the upgrade. So then I rank upgrades by IPH gain/(days to save + days to upgrade). It's not clear what the right relative weight should be, but treating save-days and upgrade-days on an equal footing is plausible: each day upgrading (saving for) X is a day not upgrading (saving for) Y.

It also seems sensible when you look at the results, say when you're low level deciding to build an NC. Or (appropriate right now) when considering a building like the dockside mill whose upgrade times are really good, but costs are awful. Obviously you lose info any time you smush two variables into one, but on the bright side there's a simple rank order that's not crazy.

M.C.
05-23-2013, 02:12 PM
I know I spend to much time on CC but now I feel better...awesome in-depth Analysis!

Carmine74
05-23-2013, 02:13 PM
Thanks for all the work. Good info here.

murf
05-23-2013, 03:18 PM
I might catch some flak with this, but The flaw with ROI tracking, however, is that "Return on Investment" implies that you are passively letting your income grow, much like you would with mid-long term investing in the real world (not counting the day and algorithmic traders here).


This is why I buy your approach much more - I originally tracked both ROI and IPH and quickly found that ROI didn't matter when I would travel to a camper's hood and pull enough money to make any early "returns" negligible

Just so you are aware dIPH/k is just the inverse of ROI. And I believe this along with dIPH/hr drives his analysis.

ROI = upgrade cost / dIPH / 24
dIPH/k = dIPH / upgrade cost

murf
05-23-2013, 03:26 PM
If I follow you correctly, I agree with everything you have done there. You have done a much better job of explaining it then I have. My ranking is also a combination of Addt'l IPH (dIPH), ROI (dIPH/k) and $$/Hr/Hr (dIPH/t).

One things I can add, is for cost of upgrade (k), I also include lost earnings. So, if your next NC upgrade takes 96 hours, it now only costs you $xxxm to upgrade, you also lose 16 collections, This of course favor the shorter upgrade times.

Well done

mxz
05-23-2013, 04:55 PM
Looking at things in a vacuum isn't going to maximize economic growth. You appear to be focused on ROI type measures without taking into account the net present value of investments over time.

Check out my thread on NC (or really, any Type A) build order (in the sig) - which goes through the reasons why you'd want to go 0>1, 1>2, 0>1, etc.. Besides the math it also includes a sim that proves economic growth faster. I think the one hole someone poked in it was at an IPH under $80k or so it broke down. There's probably a good way to calculate that point for each building but no ones bothered with the analysis.

Another good thread to look into is Ramshutu's GFI guide. By modifying his equation I think you get one of the simplest ways to maximize the increase in income per day. http://www.funzio.com/forum/showthread.php?33363-ROI-is-dead.-Long-live-GFI It takes into account cost, income, time, and IPH so its quite comprehensive.

murf
05-23-2013, 05:47 PM
Don't listen to MXZ, he doesn't know what he is talking about. :)

GucciMane
05-23-2013, 06:14 PM
Just so you are aware dIPH/k is just the inverse of ROI. And I believe this along with dIPH/hr drives his analysis.

ROI = upgrade cost / dIPH / 24
dIPH/k = dIPH / upgrade cost


uwotm8, his methods are tracking the relative difference in income/hour a particular upgrade yields. ROI tracking is maximizing the same variable, while w.r.t k.

In terms of Utility Maximizing (aka: getting the most bang for your time spent on this game and time), you come up with different utility had you been max ROI over t vs. max IPH over t, in a strict all-or-nothing sense.




I am positive that what you are going to read below is nothing new, and most likely, it has been exposed already, but at least so far I have not been able to find a sythetic guide for economy maximization. At this point, I dare say that I am not a very big fan of the ROI analysis: I understand its validity, and most likely, yields similar results, but I think that economy planning should be about maximizing the rate of increase of IPH and not about paying back buildings and upgrades - much more could certainly be discussed about this "criticism", but that is not my goal here.




What I'm arguing is that there's a third variable, active income a true utility-maximizing Econ can't overlook.





When posed with "What should you do, build a second NC or upgrade your only NC to level 2" what if maximizing this third variable I say "****, upgrade the only one and build second at the same time, rob and kill people this game is called crime city for a reason"

mxz
05-23-2013, 07:19 PM
When posed with "What should you do, build a second NC or upgrade your only NC to level 2" what if maximizing this third variable I say "****, upgrade the only one and build second at the same time, rob and kill people this game is called crime city for a reason"If you can raise $100M in a couple days without a NC - you're absolutely right. I'd be shocked to see a player without very heavy PVP activity in the shark tank be able to do such. But, those handful of players already have a robust economy or don't want an internal economy.

GucciMane
05-23-2013, 07:28 PM
If you can raise $100M in a couple days without a NC - you're absolutely right. I'd be shocked to see a player without very heavy PVP activity in the shark tank be able to do such. But, those handful of players already have a robust economy or don't want an internal economy.


Very true but We're talking in different tiers here my friend :rolleyes:


But it's completely viable to pull $1-2M/day across a crazy level range (20-80), which just blows incomes between $3K/hour - $100K/hour out of the water when it comes to making these calculations. Let's just say you can get very far "ahead of schedule" through PVPing. We're talking half of the beginning of Tramp's step-by-step guide gets glossed over because you can afford some heavy-hitters much earlier than expected

For people who are asking the question "Should I drop 66M on the upgrade or buy my second" - PVP, even light/moderate PVP plays a huge factor in this decision. At least it has for me across MT and loft, and has already influenced my savings toward Night Club.

mxz
05-23-2013, 11:12 PM
Very true but We're talking in different tiers here my friend :rolleyes:


But it's completely viable to pull $1-2M/day across a crazy level range (20-80), which just blows incomes between $3K/hour - $100K/hour out of the water when it comes to making these calculations. Let's just say you can get very far "ahead of schedule" through PVPing. We're talking half of the beginning of Tramp's step-by-step guide gets glossed over because you can afford some heavy-hitters much earlier than expected

For people who are asking the question "Should I drop 66M on the upgrade or buy my second" - PVP, even light/moderate PVP plays a huge factor in this decision. At least it has for me across MT and loft, and has already influenced my savings toward Night Club.The math doesn't change, just the timetable.

johnny boy phd
05-24-2013, 09:17 AM
I thank you for the compliments and insightful comments. I am positive they will certainly improve my approach. I provide some vis-a-vis responses bellow


Very nice guide! One "issue" in all this is how to deal appropriately with the fact that there are *two* scarce commodities for each upgrade: upgrade time and upgrade cost. You have a dIPH/$ and dIPH/t, and I'm not quite clear on what your rule of thumb is for relative priority between them.

My approach currently is to convert upgrade cost into a time - the time at current (collected) income per day it would take to save for the upgrade. So then I rank upgrades by IPH gain/(days to save + days to upgrade). It's not clear what the right relative weight should be, but treating save-days and upgrade-days on an equal footing is plausible: each day upgrading (saving for) X is a day not upgrading (saving for) Y.

It also seems sensible when you look at the results, say when you're low level deciding to build an NC. Or (appropriate right now) when considering a building like the dockside mill whose upgrade times are really good, but costs are awful. Obviously you lose info any time you smush two variables into one, but on the bright side there's a simple rank order that's not crazy.

The initial goal of my approach was not to provide a definite number that will rank upgrades in order from best to worst. Instead, my objective was to develop some optimal measures to guide the decision process. I considered two distinct classes of measures: (1) dIPH/$ results in the best upgrade with respect to upgrade cost; (2) dIPH/t results in the best upgrade with respect to upgrade time.

Most often, one is constrained by the upgrade cost - as one gets to the higher levels, it gets quite expensive and comparable with the output of your total economy during several days. One might not be able to afford the upgrade that will return the best investment of cash. In such a situation, one could for example choose a cheaper upgrade with still a good dIPH/$ (thus investing cash in an almost-optimal fashion), or alternatively, a really cheap and quick upgrade with a good upgrade time return (thus getting the most of that period of time.

Alternatively, one could develop a third measure which would be a compound of both, i.e.

dIPH/ ($ x t) = dIPH / (upgrade cost x upgrade time)

resulting in the upgrade that will return the best improvement of IPH with respect to cash invested and upgrade time. In such setting, one is giving the same "cost weight" to time and cash. By experiencing a little with this measure, I find it may in fact give me a definite optimal path - still, I might extrapolate that upgrades that are extremely expensive will be deemed worse while upgrades that are extremely quick will be over-rated. Alternatively, one could for example devise different combinations of weights for each of the scarce resources, e.g. 0.75 for cash and 0.25 for time, appearing as exponents of powers in the denominator in the formula above and resulting in strange units like square root of dollar or hour to (1/3). Experimentation with different possible combinations is certainly necessary, but the argument goes back precisely to your comment on "how to combine both finite resources into one".

One extremely important fact to remark is that CC economy is indeed open (please see my response to others below) and most (or at least a significant portion) of cash to cover upgrades comes from the outside through robbery. In this way, it seems to me difficult to convert cost of upgrade to "days to save".

To conclude, I usually find the critical analysis of both measures enough to guide my upgrade decisions, e.g. should I go for a cheaper one but still a good money and time investment while I save just a little bit more for my big time NC upgrade, or it seems that to go for a lvl 2 pagoda isn't such a bad thing right now. Briefly, I tend to implicitly give more weight to the dIPH/$ and I try to invest the most cash possible in an efficient upgrade (cash in hand is not cash invested). If dIPH/$ is close in between two upgrades, then dIPH/t clearly gives me a measure of how well I will be using my upgrade time.



If I follow you correctly, I agree with everything you have done there. You have done a much better job of explaining it then I have. My ranking is also a combination of Addt'l IPH (dIPH), ROI (dIPH/k) and $$/Hr/Hr (dIPH/t).

One things I can add, is for cost of upgrade (k), I also include lost earnings. So, if your next NC upgrade takes 96 hours, it now only costs you $xxxm to upgrade, you also lose 16 collections, This of course favor the shorter upgrade times.

Well done

Thanks. I completely understand that your ROI based strategy is pretty much similar to the one I follow. My "slight" critique to it is more on the conceptual side: I think the driving force for the improvement of the economy should be given in terms of maximizing the rate of increase of IPH (particularly, of collected IPH) and not in terms of minimizing the time to cover the last investment made.

Also, I really appreciate your comment in regard to include the loss of income while upgrading is taking place, and bringing my attention to this small detail. In fact, it is way simpler to compute that than what I have originally thought. In my particularly setting, it is just a matter of computing the total amount of income that building would produce if it were not upgraded, and add that on top of the upgrade cost, i.e.

dIPH/$ = dIPH / (upgrade cost + current building IPH x upgrade time)

This measure certainly describes in a better sense the effective cost of upgrade, which should not only be seen as an investment of cash, but also as some income that is forgone.

With this particular setting, it is clear that mxz strategy of upgrade order of NCs shows up. I am able to rob a lot of money and yesterday I went to build my second NC right after starting the upgrade to lvl 2 of my just built #1. My table with the update dIPH/$ shows up like this

http://farm9.staticflickr.com/8134/8814835318_4f1207b683.jpg (http://farm9.staticflickr.com/8134/8814835318_4f1207b683.jpg)

where it can be seen that the upgrade to lvl 2 of NC#2 is better in respect to cash investment that the upgrade of NC#1, but worst in respect to time investment. Here, the measure I have previously described above, dIPH/ ($ x t) seems to be able to weight these differences and return a definite result that is better to go for the upgrade to lvl 2 of NC#2 (with 0.021) in comparison to upgrade to lvl 3 NC#1 (with 0.016). The difference from yesterday is that I am now accounting for the increased cost of the upgrade to lvl3 of NC#1 associated with the loss of income occurring during that upgrade time period (building is shut down).



If you can raise $100M in a couple days without a NC - you're absolutely right. I'd be shocked to see a player without very heavy PVP activity in the shark tank be able to do such. But, those handful of players already have a robust economy or don't want an internal economy.

When posed with "What should you do, build a second NC or upgrade your only NC to level 2" what if maximizing this third variable I say "****, upgrade the only one and build second at the same time, rob and kill people this game is called crime city for a reason"

This is in my opinion the problem associated with considering the CC economy a closed economy. In fact, most of my upgrades are paid with money I rob from heavier campers than mysel - thanks, dreno33, invisigoth (both forum posters) and others - and a few suspect time hackers with lvl 8-9-10 NCs. Sometimes I walk away with 14 million plus. Yesterday, I was able to upgrade NC#1 to lvl2 right after building was complete and at the same time build NC#2. I am positive that as NC lvls increase I will not be able to generate such a robbery volume to cope with upgrade cost increase, no need to let me know about that, and I will have to employ the saving strategy like everybody else.

Anyway, my point is if one is following blindly a guide (e.g. upgrade laudromats to lvl 5 even, followed by dominican to lvl 3, then loft #1 1-2-3 and loft #2 1-2-3,...), one is not truly maximizing anything. To maximize, one must be able to understand where should the resources be allocated the most effectively taking into consideration the current situation, and this is where, in my opinion, the quantitative measures of rate of increase of IPH with respect to upgrade cost, upgrade time, and a combination of those play a big role.

murf
05-24-2013, 10:54 AM
Thanks. I completely understand that your ROI based strategy is pretty much similar to the one I follow. My "slight" critique to it is more on the conceptual side: I think the driving force for the improvement of the economy should be given in terms of maximizing the rate of increase of IPH (particularly, of collected IPH) and not in terms of minimizing the time to cover the last investment made.

Also, I really appreciate your comment in regard to include the loss of income while upgrading is taking place, and bringing my attention to this small detail. In fact, it is way simpler to compute that than what I have originally thought. In my particularly setting, it is just a matter of computing the total amount of income that building would produce if it were not upgraded, and add that on top of the upgrade cost, i.e.

dIPH/$ = dIPH / (upgrade cost + current building IPH x upgrade time)

This measure certainly describes in a better sense the effective cost of upgrade, which should not only be seen as an investment of cash, but also as some income that is forgone.



I find that it is a balancing act between dIPH/k and dIPH/t. Ramshutu tried to quantify it with his GFI index. I like the idea in general, but didn't have a strong opinion on the basis of the weighting. So I use a much simpler approach, which includes 3 steps.

1) Rank all potential upgrades by dIPH.
- Highest increase in income is ranked first
- This always causes NCs to be ranked highest
2) Consider all lower dIPH upgrades that have better dIPH/k then all upgrades with greater dIPH.
- So, for the upgrade to be considered it has to have a better dIPH/k then all higher dIPH upgrades, if not it's thrown out.
3) Rank the remaining upgrades according to dIPH/t.
- This causes Lofts, MTs and Crematorium to be ranked low because of their long upgrade times.

Then choose the highest ranked upgrade I can afford at the time.



There are times when this differs, such as if I'm 90% to saving for my next NC upgrade, I might do a very cheap upgrade to start the NC, or to make sure my upgrade doesn't end overnight, I'll choose a different one. But this is my basic process.

In practice, what happens is that after I upgrade my NCs, all the other top building have better dIPH/k, so then they become my priorities. Then as I move down the list and start with medium building upgrades, they are cheap enough to start saving. Eventually, I've saved enough to upgrade my NC and the cycle starts again.

The one flaw I see in my system is what Bald Zeemer pointed out. When I'm doing my medium upgrades and going from 50% saved for NC to 20%, then 70% to 40%, then 90% to 60%, then finally enough saved to upgrade my NC, I don't account for the cost of the uninvested portion of cash. The way I deal with it, as I stated above, is if I'm ~75% of the way towards a NC upgrade, I'll usually opt for very cheap upgrades, so I can get the NC upgrade started quicker.

wa7sh
05-24-2013, 11:08 AM
that moment when you read this thread and realise your not the only one who is an addict on CC.

Dipstik
05-24-2013, 11:16 AM
You read this? My finger gets tired scrolling past it...

#smug

johnny boy phd
05-24-2013, 11:20 AM
I completely agree with what you have posted, my strategy kind of follows pretty much the same reasoning.

At least so far I have been able to purchase all the best buildings and upgrades at all times when I wanted to, with an exception made to the NC because I ended up being right below lvl 51 for a long time and I wanted to shove in as many bosses as possible before advancing tier. I didn't have 300 mafia for the NCs, and I was afraid that the multiple goals (mafia, attack, defense) could give me sufficient experience to skip a boss - maybe I should have gone for it earlier instead of doing the lofts to lvl 6, then MT to lvl 6, even beachside inns to lvl 6 (I had yet another goal which was level a building up to lvl7), but it also proved to be the best when the pagoda showed up. Right now I am full blown on the NCs.

Still, I point out that from the perspective of ROI of cash at hand, you'll always get better in the short term (i.e. by the end of the upgrades and forgetting about any upgrade time considerations) if you pick an upgrade with a higher dIPH/$ at a sufficiently high volume of your current bank - the more you put in, the more you get out - rather than wait for the one that has a higher absolute value of dIPH.

The only consideration that must be made with respect to this point was already discussed previously somewhere and regards the difference in the payout algorithm in between buildings - I am not able to quantify it precisely, but if one ends up upgrading a type B building (with a higher dIPH/$) than the current lvl of the NC (type A), one is getting a better investment of the cash right now. At the same time, one is delaying later upgrades of the type A building that could eventually be better than the one that was chosen. Still, I find this very difficult to happen as dIPH/$ decreases significantly as lvls increase.

Nevertheless, it is important to note here my preference for the relative measures. Economy growth is exponential (and here is where the upgrade time and the saving time comes into play). Therefore, it might also be better to improve the availability of those super large upgrades that have significant impact in your overall economy.

Droop1972
05-24-2013, 12:51 PM
nice work.... I think. I left college many years ago and that was entirely too long to read. Can someone younger summarize this for an old man?

I should buy what and upgrade what and in what order? I'll take your word on the econ and math.

Thanks,


An old man with not a lot of time left who doesn't want to read all that.

MediumRawr
05-24-2013, 12:55 PM
An old man with not a lot of time left who doesn't want to read all that.

LMFAO...... OMG the most priceless comment ever. I'm sorry to Hijack to quote this, but one of the very few times reading the forum I've truly spit my coffee out laughing.

Way to throw the not much time left in there....amazing, thanks Droop

Droop1972
05-24-2013, 12:55 PM
one thing to consider also...

the game has a limited number of income buildings. if you don't build the mill at all, you will be two income buildings short of maximum. so I think that building a mill or two should be done even if you save them until the very end to upgrade.

good post

MediumRawr
05-24-2013, 01:02 PM
Personally, based on the cost to procure and upgrade the Mill, and it seems to be a Type B building. I built 1 and I will upgrade it a few times for the items associated. But I won't be building 2 and maxing them like the Pagoda's.

~MR

Droop1972
05-24-2013, 01:16 PM
LMFAO...... OMG the most priceless comment ever. I'm sorry to Hijack to quote this, but one of the very few times reading the forum I've truly spit my coffee out laughing.

Way to throw the not much time left in there....amazing, thanks Droop

thanks!...sadly there was more truth to that comment than I care to admit...lol

montecore
05-24-2013, 01:24 PM
That's a fantastic post and analysis, but I will reiterate two points in favor of the mill:

1) It's a limited time option. Building two of them will pay for themselves and then generate a profit over time, and if you have the hood space they may be worth upgrading once everything better is at level 10.

2) The weapons that come with each level of upgrade are useful and far better than anything you can buy with in game cash. Yes, if you focus on your night clubs and casinos and palms you will have a much stronger economy quicker, but at the end of the day I'm doing the upgrades for the weapons. The 13 million a level 5 will pay out every two days is merely icing on the cake.

I will probably buy a second one once I'm confident a level 6 upgrade is out of the question, but I don't plan on upgrading it for quite a while.

Droop1972
05-24-2013, 08:50 PM
bump

would like to see others input...and I still need the cliff notes version

bald zeemer
05-24-2013, 09:36 PM
I think your general approach is fairly solid, but that you are somewhat blinkered (due to the fact that you are still early-game) in respect to the relative scarcity of time and money.

The most obvious point, as many have pointed out throughout this thread, is that the supply of cash can be increased through methods unrelated to ones economy - ie, robberies (and to much, much lesser extent rewards for quest completion and jobs). The only way to increase the supply of time is to use gold to finish upgrades faster, an option that is realistically only worthwhile, to most players, for LTB completion. In these instances it's a question of utilising gold and in-game cash for weapons, and should properly be considered outside of ones normal upgrade routine.

As such, dIPH/t should be the primary deciding factor on which upgrade to choose.

It is only after the build order has been established according to dIPH/t that the scarcity of cash should be considered. The easiest way to account for the scarcity of cash is to simply perform the best dIPH/t upgrade that one can afford when it becomes time to upgrade. The real conundrum is basically when to consistently make the most affordable dIPH/t upgrade, and when to perform a save upgade in order to make the best possible dIPH/t upgrade.

The issues to consider when making this choice are less simple to directly quantify, but relatively easy to make a judgment call on once someone has a strong conceptual grasp of how their upgrade plan will look for the next 5-10+ upgrades.

Firstly, if the best dIPH/t upgrade is significantly better than the next-best (or best affordable) then it is likely that performing save upgrades will be the correct decision. This is the basis of the near-universal acceptance of the need to save for NC upgrades. Your method of analysis is extremely useful in quantifying the relative efficacy of these upgrades -and is especially timely, as the introduction of the Pagoda (which is more or less a 'mini-NC') has reduced the gap between NC upgrades and all other upgrades.

Secondly, the issue of how much a player actually needs to save is relevant. If someone with an IPH of $1m was ~$20m short of an NC upgrade then clearly it is in their interest to perform an upgrade that will result in $20m of savings by the time it completes. There are two broad categories of upgrade one could make to achieve this - a very cheap (ie, effectively free) upgrade that takes around 20 hours or a more effective upgrade that takes a longer period of time (a $20m upgrade that takes 40 hours, for example). The dIPH of the NC upgrade relative to the $20m upgrade needs to be compared to the $20m upgrade relative to the essentially free upgrade. If NC_$20m is not better than $20m_free, then it would be worthwhile making the $20m upgrade.

In this approach, the idea of a separate "save list" is somewhat discarded. Rather, the original list of dIPH/t upgrades are simply classified as either saving or non-saving upgrades based upon whether the cost of the upgrades exceeds IPH*upgrade time, and non-saving upgrades are discarded from consideration during this process. An interesting outcome of this is that once the NCs start really performing (say, L3 or thereabouts) almost every upgrade becomes a save upgrade.

The final point, and the only instance where departure from the dIPH/t approach should occur, is where path dependency risks a player reducing their ideal options later down the track. Again, the introduction of the Pagoda is the fly in the ointment here, as making a mistake here can only occur when a type-B upgrade is picked over a type-A upgrade. Previously this would mean overlooking an NC, Loft or MT upgrade. The NC upgrades are universally more powerful than any other, so are not unfairly discarded. The Loft and MT upgrades quickly fall off the list, so are generally not close enough to be unfairly ignored. Not having done the analysis I can't say precisely where the Pagoda upgrades should fall, but a good rule of thumb would be to choose Pagoda upgrades over type-B if and when they are close to comparable.

DPB
05-24-2013, 10:09 PM
Excellent post and method! I generally follow a very similar strategy, but I do the math slightly differently to get to the same final result. I started by making a column for Real Daily Income which is $ per collection * collections per day, where collections per day will depend on the individual and time it takes that building to produce. For me, I figure on 3x per day for 6 hour buildings, 2x for 8 hours, 1.5x for 12 hours, etc., but these numbers depend on how frequently you collect your buildings and how often you get robbed. Then, as you do, I run all of my math on these actual income numbers rather than the perfect collection rate numbers the game uses. I assume that after completing an upgrade, it will take a little time to resync that building with it's same-time building collections, so if the upgrade time on a 24 hour building is 18 hours, that's 18 hours upgrade time used, but 24 hours of lost income for me for that upgrade. I add that lost income to the actual upgrade cost to get what I call the Real Upgrade Cost. So now with Real Daily Income and Real Upgrade Cost, I calculate two metrics I call Real ROI and Real $ per Day per Upgrade Hour. I prioritize my upgrades in much the same was you do, with a sort of floating priority that moves between maximizing the Real Daily Income Increase, the Real ROI, and the Real $/Day/Upgrade Hour depending on the availability of cash and immediate savings goals for attractive upgrades that I can't immediately afford. Regardless, I always set some threshold for each metric that ensures that when I'm focusing on one metric, I'm at least making upgrades that aren't way out of line when considering the other metric. For example, my threshold Real ROI when focusing on time might be something like 15 days more than the ROI that I can get when I'm focusing on efficient use of limited cash. That gives me flexibility as I move between metrics, but still puts bounds on what upgrades are acceptable to me.

So I'm essentially doing the same type of process, but I like your layout better. My Real ROI is proportional to the inverse of your dIPH/k, so we're really maximizing the same thing there, and my Real $/Day/Upgrade Hour is just a longwinded way of saying dIPH/hr * 24. I've been thinking of cleaning up my spreadsheet for a while, so thanks for the tips. Yours is much simpler to interpret than mine for sure, and your post was well articulated, IMO.

My only critique (not with your method, really) has already been mentioned in this thread. This is coming from a player who already has all non-gold money buildings. You will eventually get to a point where you have no more buildings to build. I think if you skip the limited time buildings now, you'll regret that later. For me, my buildings are at a point where the ROI on buying the Dockside Mill is a bit weak, but not terrible, and it is a way to add to my IPH without using any upgrade time at all. I won't have the money to upgrade even to level 2 during the event unfortunately, but at least I can get both of them bought so I'll have them available to upgrade later whenever it makes more sense.

Mr T Perfect
05-25-2013, 06:12 AM
I could be totally wrong and i probably am. but from reading the tables and analysis - unless you are online 24/7 the best thing to do from starting out is get to the point you can build a movie theatre - then get both up to level 5. then get your loft and get both to level 5 and then get your nightclubs - do first one to level 3 then build the second?

any other building is a waste of space in your hood? unless you can get a couple of level 10 houses to keep the cash ticking over.

about right as a simple plan for a twice a day player?

murf
05-25-2013, 08:58 AM
I could be totally wrong and i probably am. but from reading the tables and analysis - unless you are online 24/7 the best thing to do from starting out is get to the point you can build a movie theatre - then get both up to level 5. then get your loft and get both to level 5 and then get your nightclubs - do first one to level 3 then build the second?

any other building is a waste of space in your hood? unless you can get a couple of level 10 houses to keep the cash ticking over.

about right as a simple plan for a twice a day player?

Whatever econ analysis you do to determine your next best upgrade, the one thing you must do first is adjust the daily income to meet your collection cycle. If you can collect your NC 4x's, great, use it's full value. If you only collect 3 x's and one of them is robbed, then use 2.4 x's it's value. The rest of your analysis stays the same.

mxz
05-25-2013, 02:43 PM
Whatever econ analysis you do to determine your next best upgrade, the one thing you must do first is adjust the daily income to meet your collection cycle. If you can collect your NC 4x's, great, use it's full value. If you only collect 3 x's and one of them is robbed, then use 2.4 x's it's value. The rest of your analysis stays the same.Itzkarkarot's spreadsheet is good at this as he comes up with a daily income/day based on the expected number of clicks per day for each hour-type building.

bald zeemer
05-25-2013, 06:43 PM
This thread spurred me on to finally update my own building spreadsheet. And the most interesting result of that is that despite all the hatred for the Mill, it clearly came out as one of the most powerful buildings in the game. Of the top 20 upgrades available to me (ie, excluding ones I've already completed) there are 5 NC upgrades, 5 Pagoda upgrades, 7 Mill upgrades, 2 Casino upgrades and one Palm upgrade. The worst Mill upgrade comes in above any upgrade on any building not mentioned here.

Seany527
05-25-2013, 07:14 PM
I have a much simpler approach. Buy every money building you can and upgrade when you have the money to support it. Easy enough.

murf
05-26-2013, 08:43 AM
This thread spurred me on to finally update my own building spreadsheet. And the most interesting result of that is that despite all the hatred for the Mill, it clearly came out as one of the most powerful buildings in the game. Of the top 20 upgrades available to me (ie, excluding ones I've already completed) there are 5 NC upgrades, 5 Pagoda upgrades, 7 Mill upgrades, 2 Casino upgrades and one Palm upgrade. The worst Mill upgrade comes in above any upgrade on any building not mentioned here.

I agree with this as well. The only things I have ranked above it, are my NC upgrade to L8 and getting my 2 Pagodas to L8 (currently 3 &7). Then for me the Mill to L2 is the next best. I see it as about 3 levels behind OB (and other similar buildings), but it has much better $$/upgrade time.

OneHoop
05-26-2013, 02:05 PM
I recommend adding a column for upgrade cost normalized per upgrade day. I use conditional formatting to indicate red or green based upon my collected/day (less robs&equipment budget). This helps immediately identify save-for versus savings upgrades.

ccmike
05-28-2013, 04:55 AM
Johnny boy this thread is awesome, thx for sharing your wisdom with us it helps me a lot in understanding the basics

Droop1972
05-28-2013, 07:23 AM
I'm still waiting for the Crime City Economy for Dummies version or the Cliff Notes for the Elderly version with BIG LETTERS

bald zeemer
05-28-2013, 07:26 AM
The best way to boost your econ is to maximise IPH (obviously), the best way to do this is to pick the upgrades that provides the best boosts to IPH for upgrade time.

In order to afford these, you need to differentiate between upgrades that save you more money over the upgrade time than they cost to initiate and those you need to save for. Perform the best of the former until you can do the best of the latter.
[/cliff notes]

Dipstik
05-28-2013, 07:26 AM
Introduction

I have seen a recent discussion started by Glycogen regarding the CC economy - his question was when should he consider start building his NCs. There has also been the recent discussion regarding the effectiveness of current LTB, the 75 million Dockside Mills, together with the Pagoda analysis.

Since I have been here, CC economy has popped out as a topic everyonce in a while. There has been a significant amount of work done on it, dating back to the initial analysis by tramp stamp and duder's in-depth analysis (both on the best of the best guide), MXZ upgrade NC order guide, and very interesting thoughts shared here and there by murf, BigMoney and others I am not listing. My idea is not to conduct an extensive review of what is out there, but instead, to share the method I employ. This information might be quite uninteresting for most, but I am rather positive that a few people will find it engaging and discussion will certainly follow.

I am positive that what you are going to read below is nothing new, and most likely, it has been exposed already, but at least so far I have not been able to find a sythetic guide for economy maximization. At this point, I dare say that I am not a very big fan of the ROI analysis: I understand its validity, and most likely, yields similar results, but I think that economy planning should be about maximizing the rate of increase of IPH and not about paying back buildings and upgrades - much more could certainly be discussed about this "criticism", but that is not my goal here.


Preliminaries
I start by clearly stating the goal - maximize the rate of increase of IPH. Henceforth I will be using my numbers here, which are affected solely by a +10% tycoon bonus and +25% syndicate building output and I do not own any cost or upgrade time reduction bonus. Still, my analysis is still applicable to cases that benefit from these because they affect all buildings in the same fashion. As I am not a gold spender, I will not include into my analysis the gold buildings, but the same strategy should also apply, just with a different resource to build.

It is important to note that there is more to the IPH figure than one can initially think of. Not all buildings are the same, and most of their IPH production goes to waste if not collected on time. Note that a lvl 6 Laundromat contributes with 1,815 towards the total IPH. It pays off 151 each five minutes, but if I collect it only e.g. 10 times per day, its effective IPH is only 63. I define a concept which I will refer to as collectable IPH, which is the portion of your IPH that you actually are able to collect. At this point it is important to refer that because of different payout time of buildings, it is a common strategy to focus on buildings with payout cycles which one will be able to collect - not only in this way your IPH will tend towards the collectable IPH, but also it is extremely useful to defend robberies (where the best strategy is to collect on time). Thus, for this analysis (and for my particular case, pretty much like many others), I focus on the 12, 24, and 48 hr buildings, with the exception made to the 6hr NCs (and maybe with other 6hr buildings if time and money allows), and consequently, IPH increase will always be an increase of collectable IPH.

All benefits come with an associated cost. In the CC economy, the finite resources are: (1) money, and (2) upgrade time. There are also certain constrains, e.g. only 2 buildings of each type, but logically I will not dwell on those. It is not obvious to me how to choose which upgrade to do, with its associated cost and upgrade time, that will maximize the rate of increase of my collectable IPH. Note that if my collectable IPH increases faster, I am investing the money in the building that gives the most benefit and I will be able to afford more expensive upgrades earlier - thus penalty function #1, the money, and penalty function #2, the time, are both related to the rate of increase of IPH, the former directly and the latter inversely.

It is know that as upgrade lvl increases, its cost and upgrade time increases dramatically - it will be impossible to reach the point of having all buildings at lvl 10 (unless you are a time hacker). It is often implicitly understood that sometimes the most expensive upgrade is not the most effective upgrade to take. A similar argument applies for the cheapest, longest, or quickest upgrades, particularly when one has to make choices among different buildings with several orders of magnitude of payout difference, upgrade costs, and upgrade times. So, to state it clearly once again, the goal is: to maximize the rate of increase of collectable IPH taking into consideration the finite money (for upgrade costs) and time (for upgrade completion).


Methods
I will define two types of measures: absolute and relative. Relative measures are taken with respect to the current IPH and will distinguish properly the difference in impact between upgrading e.g. a MT or a loft. I am unable to incorporate symbols here, thus I will consider letter "d" as a capital detla; and I will consider a underscore "_" to denote relative measures. I will try to be explicitly explanatory at start to ease the readers. Let us define the absolute difference in IPH an upgrade accomplishes by

dIPH = IPH (lvl i+1) - IPH (lvl i)

For example, the dIPH of a NC lvl 2 upgrade is dIPH = 80,208 (note that this figures are respective to my particular case as mentioned above).

Now, let us define the relative difference in IPH an upgrade accomplishes by

dIPH_=dIPH / IPH

where IPH is my current IPH, which if one follows this strategy should equal the previously mentioned collectable IPH. In fact, my current IPH is 257,225, and my collectable IPH is 245,911. I have been following this strategy closely since almost the beginning of my game, thus the difference corresponds to, among others, laundromats lvl 6 and 5, 2 lvl 5 souvenir stores and italian restaurants, diners lvl 5 and lvl 2, etc. In the beginning, I was doing upgrades rather randomly and pretty much without a clue, and looking back, I lost a lot of time efficiently - still, as it is common knowledge, it doesn't matter much once the MT and lofts start to kick in, and those were obvious upgrades even before I laid up this strategy. If one employs my numbers, the relative difference in IPH of the NC upgrade to lvl 2 is dIPH_=31.18%

Now, I will define four ratios of increase IPH, two absolute and two relative, two with respect to investment (finite resource #1), and two with respect to upgrade time (finite resource #2). They are defined as

dIPH/$ = dIPH / (upgrade cost)
dIPH_/$ = dIPH_ / (upgrade cost)

dIPH/t = dIPH / (upgrade time)
dIPH_/t = dIPH_ / (upgrade time)

I find it useful to scale these. I scale the dIPH/$ per thousand bucks (i.e. dIPH/k), dIPH/t per upgrade hr (i.e. dIPH/k), and the relative ratios per million and upgrade day (i.e. dIPH_/m, and dIPH_/d). Just to make numbers more trackable and close to order of magnitude zero.


Results & Discussion
I have compiled these four ratios into an excel spreasheet. As results, I show first my current case in the Figure 1 below

http://farm3.staticflickr.com/2871/8804710404_126f46b403.jpg (http://farm3.staticflickr.com/2871/8804710404_126f46b403.jpg)
Figure 1 - No-brainer. Upgrade NC to lvl 2

The direct comparison of these numbers, taking into consideration the ability to cover the upgrade cost, will determine what is the best upgrade to chose from such that the rate of increase of collectable IPH increases the fastest possible. Ratios per cost quantify what is the best investment of money, whereas ratios per time quantify what is the best investment of upgrade time. Relative ratios measure the impact of each upgrade in respect to the current size of the economy whereas absolute rations measure precisely the improvement of IPH with respect to penalty functions money and time.

As can be seen from Figure 1, my best current upgrade is the NC to lvl2. The change in IPH will be 31.18%, better than to go for a lvl 4 pagoda. At the same time, it represents a much better investment as its dIPH/k and dIPH_/m are way better than the pagoda. In respect to increase in IPH with regard to upgrade time, they are pretty much comparable, but much better than all others. Note that to go for lvl 7 lofts is way worse with respect to money and time, approximately 0.69 for the former and 97.9 for the latter. Similarly, the relative impact of loft upgrades is comparatively less (around 5% and 1%). Now, it is worth to remark that a direct comparison between times of both nightclubs is not correct, as one is upgrade time and the other is build time (a limitation of my spreadsheet, I didn't want to go over too much trouble in distinguishing those and I left it as a task for the human behind the method).

http://farm3.staticflickr.com/2815/8794129883_3ccc672314.jpg (http://farm3.staticflickr.com/2815/8794129883_3ccc672314.jpg)
Figure 2 - Upgrade NC to lvl 3

Figure 2 shows the economy state after the NC upgrade. As opposed to previous knowledge, it is better a better investement for the money to upgrade the NC to lvl 3 rather than to build the second one. Just slightly, but better.

Figures 3 through 6 demonstrate the application of the current methodology to the near future of my game.

http://farm6.staticflickr.com/5461/8804710336_c07de13913.jpg (http://farm6.staticflickr.com/5461/8804710336_c07de13913.jpg)
Figure 3 - Build 2nd NC (perfect if still upgrading the previous one)

http://farm4.staticflickr.com/3759/8804710316_fa79615795.jpg (http://farm4.staticflickr.com/3759/8804710316_fa79615795.jpg)
Figure 4 - Upgrade 2nd NC to lvl 2

http://farm6.staticflickr.com/5343/8804710304_15f39c2b45.jpg (http://farm6.staticflickr.com/5343/8804710304_15f39c2b45.jpg)
Figure 5 - Upgrade 2nd NC to lvl 3

http://farm3.staticflickr.com/2858/8794129769_90973056f5.jpg (http://farm3.staticflickr.com/2858/8794129769_90973056f5.jpg)
Figure 6 - Maybe consider the 1st Pagoda to lvl 4 now

After lvl 3 upgrade, the next best investement of money is to build the 2nd NC (Figure 3), and upgrade it to lvl 3 (Figure 4 and 5). Lastly, the upgrade to lvl 5 of a NC will finally make it worse than the lvl 4 pagoda in respect to money invested, but still beats it in respect to upgrade time (although the upgrade time of the NC is longer, its more effective).

It is worth to remark that the necessary money to pay for the best upgrade might not be available. In such situation, one needs to compromise and go for a cheaper one while saving for the best one (another common piece of common knowledge I have read here and there in the forum). The question that remains is, what would be the best money saving upgrade? From the figures above, one can see that to upgrade the pagoda might be a good choice (as it costs only 25 million and has a absolute return of cash investment of 1.10 and return of time investment of 916.7, still way better than current lofts or MTs). This particular question is easily answered by this method when considering all the previous collectable buildings (Figure 7 below).

http://farm4.staticflickr.com/3691/8794129757_c6eafdc2bd.jpg (http://farm4.staticflickr.com/3691/8794129757_c6eafdc2bd.jpg)
Figure 7 - Complete different orders of magnitude and impact, but still the best way to pick which money-saving upgrades

When comparing older and weaker buildings, we must totally understand that we are dealing with one or two orders of magnitude lower - not only in benefits, but also in costs. Still, it was possible for me to determine that it would be a good idea to upgrade my 2nd meat factory to lvl 3 (with a dIPH/k=1.96) while waiting for my NC to finish building. Another recent decision I made was to upgrade the MT to lvl 7 (the numbers are shown in the 2nd one currently at lvl 6, dIPH/k=1.05, better than lofts to lvl 7 with 0.69, but 2 times worse with respect to time). Another example, if in the near future I end up having extra 8 hours of upgrade time somehow, I will be doing my bagel shop for lvl 4 (with a dIPH/k=1.78).

Lastly, I have decided to analyze the progression of the new LTB, the Dockside Mills. Most likely I will not build it because right now those 75 million are much more effective pumping up my NCs. As it can be seen from the previous figures, it has a dIPH/k of 0.45 (e.g. when compared with the 1.20 of the lvl 2 NC upgrade). Figure 8 below shows the progression of the building if I had infinite cash to upgrade it right away starting from now.

http://farm6.staticflickr.com/5346/8805149562_0e919f3fb9.jpg (http://farm6.staticflickr.com/5346/8805149562_0e919f3fb9.jpg)
Figure 8 - Dockside Mills, a money pit

As it can be easily seen, this building is clearly a money sink, and it increases in depth as upgrades proceed. Upgrade to lvl 6 costs at most 1 billion and results in a dIPH=100,000. Consequently, the dIPH/k is one of the lowest to be seen, more 3 times worse than to upgrade my beachside inn to lvl 7 (dIPH/k=0.36, the worst I have right now). And note that with all this money spent, my IPH has only doubled. In regard to upgrade time, it is rather quick all around, thus I might conclude that end game players with plenty of cash around might not have other and better investments available anymore. At least myself, I am clearly considering skipping it, unless if I am able to rob 40 million to build my second NC right away and then 75 million on top of that to build the mills.


Final Remarks
I proposed a different analysis on the economy of CC based solely on the maximization of the rate of increase of collectable IPH with respect to cash cost of upgrades (and thus maximizing return of investment) and with respect to time cost of upgrades (and thus maximizing rate of increase of IPH). I hope this analysis is helpful for the economy planner out there and shed light into novel ways of chosing one's path among different building upgrades.

Lastly, this analysis certainly suffers from certain limitations. To list a few:
(1) I have not considered a distinction between build time and upgrade time to make things easier, it most be noted that it is possible to upgrade one building while building another at the same time, thus the time cost to get to lvl 1 should be considered taking that into consideration;
(2) I have not considered penalties in IPH during upgrade times, that would make the analysis much more cumbersome, but it must be remarked that while a building is upgraded, its output is not collected;
and (3) I have considered the 4th daily payout of the NC (6 hours) as collectable IPH - although difficult, it is still possible on some days or to some players. This penalty could be considered in a straightforward manner simply by multiplying the NC payout by 0.75.

There you go. Hope it helps.