ROI is dead. Long live GFI

[Ramshutu]

The problem

There are currently two metric in use to work out what to build next. ROI and $/hr/hr. These both have their own positives and negatives, but like quantumn theory and relativity, it has been very difficult to put them together, one works at low levels, one works at higher levels, but not both together.

This has made it difficult to answer questions such as 'when should I start saving for a nightclub' to a high degree of confidence as you will get different answers depending on which metric you use.

ROI

This, as we know, is a measure of how long it will take an upgrade to pay for itself. I have never liked it, as ROI minimises time required to save money, rather than maximise income per hour gain.

The big problem with it, is that buildings in CC tend to be cheap at first, getting exponentially more expensive, but also with much better income. This means it priorities lower quality upgrades over upgrades that you maybe able to afford, but would net you more of an increase in income.

$/hr/hr

This is a measure of how much income gain you will get for every hour of the upgrade time of a building. This is a good metric, one i have preferred, because it allows you to compare upgrades for their actual impact on your economy.

Unlike ROI, it prioritises high level upgrades that net big increases in your economy, over cheaper and quicker upgrades of lower level buildings.

The big issue with it, however, is that doesn't take into the fact that you have to save up for the upgrade or build. This saving time is a big deal as it is time where your economy is not expanding at its optimum rate. This has led me to try and be sensible when choosing upgrades.

The question.

Today, after a pigeon pooped on me (this has no relevance, but thought I had to tell someone), I asked myself this:

Can I come up with an equation that accurately includes saving time, and works in the real world, for all levels? One that appropriately scales depending on where you sit in the game, and fetches you beer.

The answer is yes. (well aside from the last bit)

GFI Gain for investment. * The Ramshutu Conjecture.

So, let's say you start saving for a night club and it takes you 10 days, plus the build time. Neither of the previous metrics take into account this 10 days of saving.

GFI takes into account the time to save, AND build time. Calculating the overall increase to your economy per hour spread over the entire investment period.




($/hr increase ) / ( Bc / Ec + Bt)



Bc. - Build cost.
Ec. - Current Economic output ($/hr)
Bt. - Build time.

The latter half of the equation calculates the total investment in time for the build. the former is the amount of increase the building provides.

Overall, it incorporates your economy stats to work out the overall time you will have to be 'economically inactive' and uses this to work out how much you will be gaining for each hour of inactivity.

So, let's take two upgrades of two buildings with the same collection time

1. Costs: 1m, $/hr increase: 5k, Time 24hr
2. Costs: 1k, $/hr increase: 200, time 12hr.

ROI would prioritise 2. $/hr/hr would prioritise 1.

What about GFI? Well, it depends!

Let's say your economy is 1k.

The overall GFI for 1 is 4.88. Total time taken 1024 hrs
The overall GFI for 2 is 13.38 Total time taken 13hrs

This number means that if you save and build these buildings, it works out as increasing you $/hr each hour by the amount given from the moment you start saving till you complete.

However, with an income of 100k the story changes.

In this case, the GFI is as follows:
1. 147
2. 16.7

What is this telling you? Well, it's saying that at higher levels, you get a better boost from higher level buildings. This isn't special news on its own, but as the equation gives you different answers as your economy grows, you can properly predict the most efficient path to take.

Why is this awesome?

This equation is fantastic for fringe cases where you want to work out whether you should save, or spend. You can PROOVE exactly which building will give you the biggest overall boost including the time you spend saving, and allows you to plan accordingly.

It's really a best of both worlds for ROI and $/hr/hr as at lower levels, the cheap buildings provides the quickest boost over a shorter time. With a bigger economy, the save time comes down and means the overall cash boost of the higher level building wins out.

Using this, has shown me an exact path that will maximise my economic increase, even including spending.

The typical thought that comes to you: 'can i increase my economy by more by upgrading lower level buildings instead of saving for a few days for that big upgrade' is primarily the aim of this equation.

What needs tweaking?

These equations may need some minor tweaking, as it doesn't take into account the typical 'upgrade crappy building while saving' that everyone uses. There are a couple of changes you can make to the equation to take this into account.

[mnju_03]

Are you Neo?

[sexkitteh]

To the comments!


Are you Neo?

( ._.) well that din't clarify much...

[femaiden]

just gonna say....thats alot of effort to put into a game...you should be on wall street....

[Ramshutu]

just gonna say....thats alot of effort to put into a game...you should be on wall street....

I have a conscience and a soul. No wall street for me.

[white frog]

That's the exact equation that I used to develop my "Goal Calculator" in the spreadsheet. It will actually use the real income and income growth based on your collection schedule!

[Ramshutu]

Damnit. I hate you :(

[Murda]

Mr shutu......love the concept. but I am not getting the GFI numbers you indicated using your example information. Can you double check and confirm that I am an idiot.....

[mnju_03]

Did you get the TPS reports?

[Murda]

Yeah. The coversheet. I know, I know.

[Ramshutu]

Mr shutu......love the concept. but I am not getting the GFI numbers you indicated using your example information. Can you double check and confirm that I am an idiot.....

I double checked with a calculator, your right. I did it in my head, but I'm not as smart as I thought :)

[Swearengen]

That's the exact equation that I used to develop my "Goal Calculator" in the spreadsheet. It will actually use the real income and income growth based on your collection schedule!

I think the only thing his spreadsheet doesn't do is predict the weather! :)

[mnju_03]

I think the only thing his spreadsheet doesn't do is predict the weather! :)

No no...if you look closely between lines 141 and 212...it does.

[Paulio]

I just want to say a big THANK YOU to Ramshutu and White Frog. I'm grateful that we have 2 excellent contributors like you.

[white frog]

I think the only thing his spreadsheet doesn't do is predict the weather! :)
Actually it does... It predicts that the weather will be the exact opposite of what the weather man says it will be!

[mnju_03]

Actually it does... It predicts that the weather will be the exact opposite of what the weather man says it will be!

There's an app for that.

[Max Power]

Given that cash isn't worth **** at upper levels, I will just let my eyes glaze over and upgrade the building that I think is the coolest at the time.

[cookie monster]

First, no argument that the ROI metric isn't the thing to look at when valuing buildings or upgrades. As it's calculated it's not even "ROI." A return on investment is a percentage and you can't measure it without a fixed time period.

Second, don't take credit (Ramshatu factor) for basic financial equations.

[mnju_03]

First, no argument that the ROI metric isn't the thing to look at when valuing buildings or upgrades. As it's calculated it's not even "ROI." A return on investment is a percentage and you can't measure it without a fixed time period.

Second, don't take credit (Ramshatu factor) for basic financial equations.

Who pissed on your cookies!?

[Ramshutu]

Who pissed on your cookies!?

Some men just want to watch the world burn.

[mnju_03]

Some men just want to watch the world burn.

I have a word for them....****s.

[mob]

Ramshutu,

How do you account for timing. The formula is very interesting however it does not factor in the 'lost' hours in between upgrades. Do you wait to collect on a building prior to upgrading or do you lose the time to upgrade immediately? Rather than target - so specifically "the best option", I practice upgrading vertically 2-4 levels at a time to minimize time lost and maximize gains. In the end, with decent planning, I am able to save and hit a couple large upgrades in succession. Typically, I find my economy does not increase steadily and instead it jumps significantly roughly every 3 weeks.

Interested in your feedback...and yours too WhiteFrog.

[Ramshutu]

Ramshutu,

How do you account for timing. The formula is very interesting however it does not factor in the 'lost' hours in between upgrades. Do you wait to collect on a building prior to upgrading or do you lose the time to upgrade immediately? Rather than target - so specifically "the best option", I practice upgrading vertically 2-4 levels at a time to minimize time lost and maximize gains. In the end, with decent planning, I am able to save and hit a couple large upgrades in succession. Typically, I find my economy does not increase steadily and instead it jumps significantly roughly every 3 weeks.

Interested in your feedback...and yours too WhiteFrog.

You can't easily account for it in terms of the formula, other than simply adding to the cost the lost upgrade time. I agree that there is an implicit cost of the number of collection missed that would need to be accounted for. I remember considering this ages ago in a separate thread.

[Ramshutu]

I have a word for them....****s.

Or the Mythebusters.

[cookie monster]

Some men just want to watch the world burn.

And some just want to claim ownership for something that's already been invented.

[mnju_03]

Or the Mythebusters.

I love that show...


And some just want to claim ownership for something that's already been invented.

No, I will not make out with you.

[Ramshutu]

And some just want to claim ownership for something that's already been invented.

If it helps, trolling was around back in '85.

[white frog]

Ramshutu,

How do you account for timing. The formula is very interesting however it does not factor in the 'lost' hours in between upgrades. Do you wait to collect on a building prior to upgrading or do you lose the time to upgrade immediately? Rather than target - so specifically "the best option", I practice upgrading vertically 2-4 levels at a time to minimize time lost and maximize gains. In the end, with decent planning, I am able to save and hit a couple large upgrades in succession. Typically, I find my economy does not increase steadily and instead it jumps significantly roughly every 3 weeks.

Interested in your feedback...and yours too WhiteFrog.
I would almost always consider the time wasted not upgrading a particular building more valuable than the money you'd get from a single collection.

[MajorOffensive]

Hate to say it, but I also posted a thread (http://www.funzio.com/forum/showthread.php?27571-Really-Long-Post-of-the-Day-2-Economy-Quasi-Tramp-Stamp-Style/page1) a while back about this. More than build or upgrade times, Savings Time is often the limiting factor when considering the high level buildings. So I thought I would try to maximize value for the time invested.

One of the problems I have encountered is trying to work expansion costs and serial build-to-upgrade times. For many buildings, the initial build time is shorter than the next couple of upgrades, so you may gain more per day invested for upgrading to level 2 or 3, despite more savings, than you would from just building to level 1. This only makes a difference if you can actually afford them in fairly quick succession, though. Otherwise you may be squandering savings time by not investing it in something else, like a Nightclub upgrade. It is neither a simple nor straightforward metric to use.

Not to mention that sometimes, what appears to be a slightly worse investment short term may shave days off a big savings period later. But that's only provided it doesn't become a money sink; you pretty much need to set a limit on upgrades for higher level B buildings until they only cost you so many days savings. Your highest earning building based on your payout schedule should be your only priority; and for anyone who plays regularly throughout the day, this is the Nightclub. Even collected only 2.6 times a day, it still out paces anything else after an upgrade or two.


Ramshutu,

How do you account for timing. The formula is very interesting however it does not factor in the 'lost' hours in between upgrades. Do you wait to collect on a building prior to upgrading or do you lose the time to upgrade immediately? Rather than target - so specifically "the best option", I practice upgrading vertically 2-4 levels at a time to minimize time lost and maximize gains. In the end, with decent planning, I am able to save and hit a couple large upgrades in succession. Typically, I find my economy does not increase steadily and instead it jumps significantly roughly every 3 weeks.

Interested in your feedback...and yours too WhiteFrog.

Mostly lost income isn't as significant as the boost you get. It comes back to you over time, and normally pretty quickly. The cost of the upgrade normally dwarfs any income lost in a period of a few days to a week. What really gets out of control is the proportion of the cost increases to the income growth per level. Costs grow at a fixed 67% per level, but income growth trails off after level 4 for A type buildings and level 3 for B type buildings. In the end, at level 10 you pay about 100 times the initial cost for a growth 20 or 7 times the base, respectively, IIRC.


I would almost always consider the time wasted not upgrading a particular building more valuable than the money you'd get from a single collection.

Definitely this. You lose potential income while not upgrading buildings. It is better if they are making a little more money while you are saving up for the next upgrade.

[kykboxr]

just gonna say....thats alot of effort to put into a game...you should be on wall street....

I was on wall street. This is MUCH deeper :D

[PawnXIIX]

Bump.

This was too good to ignore. I feel like this should be on the front page. Despite having a slightly higher cost and a build time that was almost 5 times longer it was determined that at my level it's slightly better to build a condo than upgrade an upscale club:

Upscale club level 2:

(3757) / (6680000 / 47369 + 18) = 23.6

Condos level 1:

(6600) / (8000000 / 47369 + 90) = 25.49

When I get to level 108 that is.

[ShawnBB]

I have a conscience and a soul. No wall street for me.

Good point:). So is this thread. Once again, forum enriched my understanding about CC Econ!

Ramshutu,this is a really fascinating concept.
I was considering upgrade in this order,but found out NC will always on top of my list which is very annoying,lol.

Any suggestion on upgrade selection during saving? Because according to proper GFI order, most of my game time will end up in saving NCs.

[RijilV]

I dunno, whenever I use this formula all I get back is I should upgrade my level 1 NC to level 7 right away because of the IPH increase as the NC is upgraded. Interestingly enough it doesn't have me build a second NC until after I've got two level 10 casinos and my upscales to 6.

[Ramshutu]

I dunno, whenever I use this formula all I get back is I should upgrade my level 1 NC to level 7 right away because of the IPH increase as the NC is upgraded. Interestingly enough it doesn't have me build a second NC until after I've got two level 10 casinos and my upscales to 6.

Taking the upscale upgrade compared to the NC, the reason this equation is prioritising the club, is that while they cost about the same, and the UC has half the hourly upgrade worth, it takes half the time (ish) to realise the income because of the build time.

I'm a little surprised about the casinos to level 10 though, as I would have thought unless you are racking in 50 mil a day, the save time would be significant.

[Silvio]

Great metric. I have implemented it into my spreadsheet and it figures prominently in my upgrade selection. While I don't follow any metric religiously (I will always optimize my upgrades based on my life and accessibility to the game), it has provided some defense to some instinct.

Nice work Ram! Always appreciate some well done mathematic analysis!

[Ramshutu]

Great metric. I have implemented it into my spreadsheet and it figures prominently in my upgrade selection. While I don't follow any metric religiously (I will always optimize my upgrades based on my life and accessibility to the game), it has provided some defense to some instinct.

Nice work Ram! Always appreciate some well done mathematic analysis!

While I did work this out independently (I have not read anything else) I would say that it seems some other people have raised similar theories prior to this. So thanks to them too, by proxy!

[RijilV]

Taking the upscale upgrade compared to the NC, the reason this equation is prioritising the club, is that while they cost about the same, and the UC has half the hourly upgrade worth, it takes half the time (ish) to realise the income because of the build time.

I'm a little surprised about the casinos to level 10 though, as I would have thought unless you are racking in 50 mil a day, the save time would be significant.

Yeah, I'm surprised too. Here is what I generated based on "real" IPH (ie I'm not collecting the laundromat every 5 minutes). I built the NC before I probably should have and that's why the system is probably screwed, but as far as I can tell upgrading the NC to level 7 from level 6 at my IPH will take 807 hours. I'm going to work out a program that generates what buildings to build between upgrades, as over the course of 807 hours there are plenty of buildings that will more than pay for themselves. Anyhow, the output bellow is from a script I whipped up that calc's the IPH as each upgrade completes. Also this factors in the reduced build time and reduced upgrade cost items as I have both.


name,level,cost,iph_gain,iph,GFI
Nightclub,2,48146000,48125,164441,105
Nightclub,3,83078800,72187,236628,129
Nightclub,4,142383426,96250,332878,144
Nightclub,5,241732375,120312,453191,150
Nightclub,6,405010465,168437,621628,171
Nightclub,7,677056555,216562,838191,182
Upscale Club,2,4743650,3758,841949,196
Upscale Club,2,4743650,3758,845707,196
Casino,1,60000000,41250,886957,191
Casino,2,72516000,41250,928207,330
Casino,3,122836200,61875,990082,335
Casino,4,207587908,82500,1072582,303
Casino,5,349255323,103125,1175707,257
Nightclub,8,1122327873,264687,1440395,248
Casino,6,583318139,123750,1564145,252
Nightclub,9,1854880276,312812,1876957,239
Nightclub,10,3060692488,481250,2358207,273
Casino,7,970789499,144375,2502582,282
Casino,1,60000000,41250,2543832,245
Casino,2,72516000,41250,2585082,575
Casino,3,122836200,61875,2646957,622
Casino,4,207587908,82500,2729457,586
Casino,5,349255323,103125,2832582,508
Casino,6,583318139,123750,2956332,424
Casino,7,970789499,144375,3100707,338
Casino,8,1608082685,165000,3265707,263
Casino,8,1608082685,165000,3430707,274
Upscale Club,3,8011869,5637,3436345,249
Upscale Club,3,8011869,5637,3441982,249
Upscale Club,4,13573640,7516,3449499,219
Upscale Club,4,13573640,7516,3457016,219
Casino,9,2662412440,185625,3642641,208
Casino,9,2662412440,185625,3828266,218
Casino,10,4409460357,288750,4117016,225
Casino,10,4409460357,288750,4405766,240
Upscale Club,5,22950332,9395,4415162,196
Upscale Club,5,22950332,9395,4424557,196
Wedding Chapel,2,2123560,1613,4426171,170
Wedding Chapel,2,2123560,1613,4427784,170
Wedding Chapel,3,3572094,2420,4430204,169
Wedding Chapel,3,3572094,2420,4432624,169
Upscale Club,6,38756447,11274,4443899,165
Upscale Club,6,38756447,11274,4455174,165
Nightclub,1,40000000,24062,4479237,157

[mnju_03]

I have a headache reading all of this... but I love it!

[Crazy Canuck]

Wow some of you guys put a lot of thought into what your going to build and what to upgrade!

All I do is upgrade building that collect every 12, 24 or 48 hours. I have no interest at this time in saving up for the NC since it's collection time makes it harder to collect everytime without being robbed. Sure it's a great IPH boost but that stat means nothing if you can't collect it everytime without missing a collection or getting robbed.

My hood may not be mathematically sound but I love it and it is easy to collect all big ticket building on time.

[Dreno33]

Some Summary points I hope I interrupted correctly:

1) The main flaw in Ramshutu's formula is the "in btwn upgrading."
2) RijilV is going to create a program that calculates Ramshutu's formula AND determine which in btwn upgrades to activate.
3) Mnju is foncused, again.
4) The formula truly reflects the biggest increase by giving rational decisions on the next upgrade that should be considered and done.

[Ramshutu]

Between upgrades is actually quite easy, I think.

You want something with a long upgrade time, that has the minimum cost, for maximum IPH gain.

Off the top of my head (IPH gain * upgrade time) / Cost ^ 2.

This would mean that long upgrade, low cost, high gain buildings would yield higher numbers. I have chosen cost to the power two as cost is really the most important factor. For example, without the power 2, two buildings with the same build time with one building that twice the cost and twice the gain as another would give the same number.

[prostouser]

what about combining ROI and GFI for choosing upgrade/build while collecting money for the Best GFI target?
For example, we can
1. Pick the best GFI. Calculate "Remaining days to save for GFI".
2. Filter our all available actions, if their realization will not improve this "Remaining days to save" value. For example, if their ROI will be big enough. ROI must account for time to build and time to save.
3. Use GFI-metric to pick up the best remaining action (GFI2).
4. If "Remaining days to save for GFI2" is significant we can repeat step 2 to pickup GFI3, GFI4, and so on.

[Ramshutu]

what about combining ROI and GFI for choosing upgrade/build while collecting money for the Best GFI target?
For example, we can
1. Pick the best GFI. Calculate "Remaining days to save for GFI".
2. Filter our all available actions, if their realization will not improve this "Remaining days to save" value. For example, if their ROI will be big enough. ROI must account for time to build and time to save.
3. Use GFI-metric to pick up the best remaining action (GFI2).
4. If "Remaining days to save for GFI2" is significant we can repeat step 2 to pickup GFI3, GFI4, and so on.

Too......much......maths......

These are really two different equations. GFI: The best upgrade including savings is covered in the main post.

The other you are talking about, the most efficient use of upgrade cash to raise up your income with the least investment whilst saving is covered by the post above. That should cover your scenario.

[Plux]

Correction: 3 Metrics in use, ROI vs $/hr/hr vs MUI (Marginal Utility of Income). Mine carries a further hedge that a wall is hit which renders Utility equal to zero. You can upgrade too far and be throwing cash into the bin for an income per hour gain that'll need a year to recover. Great for stats, not for effective income control.

[Ramshutu]

Correction: 3 Metrics in use, ROI vs $/hr/hr vs MUI (Marginal Utility of Income). Mine carries a further hedge that a wall is hit which renders Utility equal to zero. You can upgrade too far and be throwing cash into the bin for an income per hour gain that'll need a year to recover. Great for stats, not for effective income control.

GFI does this implicitly.

[RijilV]

Too......much......maths......

These are really two different equations. GFI: The best upgrade including savings is covered in the main post.

The other you are talking about, the most efficient use of upgrade cash to raise up your income with the least investment whilst saving is covered by the post above. That should cover your scenario.

FWIW this is more or less what I'm doing, though I go for profits over N-time rather than strict ROI. Since GFI typically has me saving up for upgrades while I save up I'll do upgrades on buildings that will turn a profit in the calculated length of time it'll take me to save, so in theory, I actually get there a little quicker and get to upgrade a variety of buildings.


Also once I factored in that I only get 2 full collections on NC and the 10% bank tax, it dramatically changed the build oder WRT NCs - now I'm looking at upscale club upgrades and casino builds before pushing the NC to level 10 - which makes much more sense to me.