jinqs

04-16-2012, 01:30 PM

The ROI calculations are wrong in the infamous Money Buildings spreadsheet found here:

https://docs.google.com/spreadsheet/ccc?key=0AgEHrvnoijXudHFVU2RxYUQzYXYtOURRd0d3M1hVR 2c&hl=en_US&pli=1#gid=0

Basic explanation of the current formula

The formula that it's using is:

Building Time + (Cost of Upgrade / (Old Hourly Income - New Hourly Income))

This is pretty straight forward. What it is figuring out is: How long after you start the upgrade will you have paid for its cost? Take the build time (you haven't started paying down the upgrade while you're waiting for it) and add the amount of time it will take for you to recover the money you spent upgrading the building given the incremental increase to income.

For example, if the building previously made you $10/hour and after the upgrade it makes you $20/hour, you are making $10/hour more than you were before. Suppose the upgrade took 2 hours and cost $50, the ROI with this calculation is 2 + (50/10) = 7 hours.

What's missing

This fails to take into account a substantial cost that is associated with performing the upgrade: the lost income while the upgrade is underway. In the example above, you would have made $20 in those first 2 hours if you had not upgraded the building at all, so the cost of upgrading the building is not actually just the $50 face value. It's the $50 face value plus $20 of lost income. Let me demonstrate with some basic math:

If I upgrade: I spend $50 initially, then make $0/hour for 2 hours and then $20/hour for 5 hours. In 7 hours I have 20 * 5 - 50 = $50 more than when I started.

If I don't upgrade: I spend $0, then make $10/hour for 7 hours. In 7 hours I have 10 * 7 - 0 = $70 more than when I started.

The actual ROI formula should expand out the "Cost of Upgrade" to include the lost income while the upgrade is underway:

Building Time + ((Cost of Upgrade + (Building Time * Old Hourly Income)) / (Old Hourly Income - New Hourly Income))

An actual example

In general this difference shouldn't be that big though, right? Wrong. Consider the upgrade for the Laundromat from level 5 to level 6. For simplicity I'll do the math with non-tycoon. The upgrade takes 12 hours, costs $1298 and raises the hourly income from $900 to $1320. The cost that the current formula takes into account is the flat cost of the upgrade or $1298. The cost that my formula takes into account include the $900/hour that you aren't making for 12 hours for a total of $12098. The cost of doing the upgrade is 9.32 times higher than the current formula accounts for... 9.32 times higher!!!

If we calculate the final ROI using both formulas we get 15.09 hours with the current formula and 40.80 hours with my formula. That's 2.7 times higher than the current formula accounts for.

Impact to optimal upgrade sequence

If you look at the difference this has to the theoretically optimal upgrade order when starting out, it is drastically different. However, I'm not sure how substantial the difference is once you're farther into the game.

Note: In terms of gold buildings, I included only the ice cream shop below because I don't intend on spending money, but I can get that one for free. :)

Recommended upgrade order using incorrect ROI formula:

Laundromat 2

Laundromat 3

Laundromat 4

Laundromat 5

Pizza Parlor 2

Pizza Parlor 3

Ice Cream Shop 2

Laundromat 6

Ice Cream Shop 3

Pizza Parlor 4

Ice Cream Shop 4

Laundromat 7

Gas Station 2

Recommended upgrade order using the correct ROI formula:

Laundromat 2

Laundromat 3

Laundromat 4

Pizza Parlor 2

Pizza Parlor 3

Ice Cream Shop 3

Pizza Parlor 4

Laundromat 5

Gas Station 2

Gas Station 3

Ice Cream Shop 4

Deli 2

Souvenir Store 2

https://docs.google.com/spreadsheet/ccc?key=0AgEHrvnoijXudHFVU2RxYUQzYXYtOURRd0d3M1hVR 2c&hl=en_US&pli=1#gid=0

Basic explanation of the current formula

The formula that it's using is:

Building Time + (Cost of Upgrade / (Old Hourly Income - New Hourly Income))

This is pretty straight forward. What it is figuring out is: How long after you start the upgrade will you have paid for its cost? Take the build time (you haven't started paying down the upgrade while you're waiting for it) and add the amount of time it will take for you to recover the money you spent upgrading the building given the incremental increase to income.

For example, if the building previously made you $10/hour and after the upgrade it makes you $20/hour, you are making $10/hour more than you were before. Suppose the upgrade took 2 hours and cost $50, the ROI with this calculation is 2 + (50/10) = 7 hours.

What's missing

This fails to take into account a substantial cost that is associated with performing the upgrade: the lost income while the upgrade is underway. In the example above, you would have made $20 in those first 2 hours if you had not upgraded the building at all, so the cost of upgrading the building is not actually just the $50 face value. It's the $50 face value plus $20 of lost income. Let me demonstrate with some basic math:

If I upgrade: I spend $50 initially, then make $0/hour for 2 hours and then $20/hour for 5 hours. In 7 hours I have 20 * 5 - 50 = $50 more than when I started.

If I don't upgrade: I spend $0, then make $10/hour for 7 hours. In 7 hours I have 10 * 7 - 0 = $70 more than when I started.

The actual ROI formula should expand out the "Cost of Upgrade" to include the lost income while the upgrade is underway:

Building Time + ((Cost of Upgrade + (Building Time * Old Hourly Income)) / (Old Hourly Income - New Hourly Income))

An actual example

In general this difference shouldn't be that big though, right? Wrong. Consider the upgrade for the Laundromat from level 5 to level 6. For simplicity I'll do the math with non-tycoon. The upgrade takes 12 hours, costs $1298 and raises the hourly income from $900 to $1320. The cost that the current formula takes into account is the flat cost of the upgrade or $1298. The cost that my formula takes into account include the $900/hour that you aren't making for 12 hours for a total of $12098. The cost of doing the upgrade is 9.32 times higher than the current formula accounts for... 9.32 times higher!!!

If we calculate the final ROI using both formulas we get 15.09 hours with the current formula and 40.80 hours with my formula. That's 2.7 times higher than the current formula accounts for.

Impact to optimal upgrade sequence

If you look at the difference this has to the theoretically optimal upgrade order when starting out, it is drastically different. However, I'm not sure how substantial the difference is once you're farther into the game.

Note: In terms of gold buildings, I included only the ice cream shop below because I don't intend on spending money, but I can get that one for free. :)

Recommended upgrade order using incorrect ROI formula:

Laundromat 2

Laundromat 3

Laundromat 4

Laundromat 5

Pizza Parlor 2

Pizza Parlor 3

Ice Cream Shop 2

Laundromat 6

Ice Cream Shop 3

Pizza Parlor 4

Ice Cream Shop 4

Laundromat 7

Gas Station 2

Recommended upgrade order using the correct ROI formula:

Laundromat 2

Laundromat 3

Laundromat 4

Pizza Parlor 2

Pizza Parlor 3

Ice Cream Shop 3

Pizza Parlor 4

Laundromat 5

Gas Station 2

Gas Station 3

Ice Cream Shop 4

Deli 2

Souvenir Store 2