I've been playing a lot of a silly little city-building game on my phone, called Airport City. I wrote about it earlier. For anybody who doesn't care about the game, you can stop reading now, because there's not going to be any real content here. No, you can chalk this entry up to one of those frivolous things that I get obsessed with from time to time, kind of like my Tecmo Super Bowl FAQ.
The basic idea in Airport city is that space is limited, and buildings that you build on that space will accrue passengers or money based on timers. Buildings that have quick timers have few passengers to collect, but buildings with long timers will have a lot of passengers to collect. Once they are ready for collection, their timers will stop, and so they won't accrue any more passengers. For instance, the Cottage has a 2 minute timer, but only provides 1 passenger, while the Brazilian Cottage can only be collected every 60 minutes, but provides 6 passengers. I could conceivably get 30 passengers/hour from a Cottage, but only if I collected them immediately every time.
In practice, I check the game when I think about it and have time, and this makes it not immediately obvious which is the better building in terms of space efficiency. When I haven't checked in a while, the Brazilian Cottage is better, but when I check many times an hour, the plain Cottage is better.
So, I did what any OCD gamer obsessed with a ridiculous little game would do: I recorded how often I checked for a few days and did some number crunching to see what buildings provided the best return in exchange for space.
There are other slight issues that make the problem harder. Buildings come in different sizes, either 1x1, 2x2, or 3x3. Almost every building needs to be connected to a road to work. Each building has an electricity cost which requires building power plants to support them. In addition, (almost) every building needs a road adjacent to it.
I recorded when I check Airport City for three days. I did this as faithfully as I could, and though I had to recreate a few checks from memory, I think I got just about all of them. A few of them I had to guess after their time, when I realized that I had forgotten them, but I don't think there are that many. Where these checks lasted longer than two minutes, I recorded two consecutive 2 minute checks, so that the quickest buildings wouldn't get punished for continuous play. After I got the times recorded, I counted the number of times that each building would trigger according to those times.
After this, it was a relatively trivial series of calculations to come up at space efficiency. Where
s is space efficiency measured in passengers per space or money per space
z is the size of the building,
r is 1 if a building needs a road or 0 otherwise,
c is the count of how many times the building was collected in that time,
p is the number of passengers/money that a building provides for each collection
e is the electricity drain of the building, and
15 is the electricity efficiency per tile of coal power plants (60/4, the best space efficiency of the non-greenback power plants)
The equation becomes
s = c*p / ( z + r*1/4 + e/15 )
Or in simpler terms
s = total passengers collected / (size of building + road dependency + electricity drain)
I then normalized this for the best building purchaseable with coins, for ease of comparison. The best building scored 100, and all other buildings scored less. A few bill-based buildings scored higher than 100, but were left out of normalization because they are usually bad purchases (See below)
Anybody who is interested in the specifics can view my Google spreadsheet. Feel free to copy, repost, and modify that for use for yourself.
What did I learn?
Small buildings are always better than their identically-timed larger counterparts.
For example, look at the Brazilian Cottage (1 tile, 6 passengers every hour) versus the Mansion (4 tiles, 18 passengers every hour. Even if you factor in that the larger building has better road efficiency and electricity efficiency, it's not enough to outweigh the extra passengers for the Cottage. Removing the number of collections from the equation since they will be equal for both, a Brazilian Cottage has a space efficiency of 4.34 passengers per space, and the Mansion only 4.04. That's repeated every time that a small building has the same timer as a larger one.
The tradeoff is that single buildings are slightly harder to fit into the plots given, but if you work at it, you can virtually eliminate that concern by cleverly arranging your buildings. For instance, I've worked it so that I only have three spaces that aren't connected to a road in my city, and those are filled by power plants, which don't need roads.
If you have spare bills, buy space, not buildings.
Bills are very hard to come by. You can get them by leveling up, participating in promotions, or purchasing them using real-world money (Anathema!). Though there are buildings that you can buy with bills, the better return is probably to buy a city expansion. After all, an expansion gives you 16 extra tiles, and even though some of those bill-based buildings are the most space efficient buildings, they're still not as efficient as 16 extra tiles, particularly if you can manage to buy an expansion when they're at half cost.
As an example, take the Townhouse, the best of the bill-based population buildings. For my playing habits, when normalized against the best non-bill building at 100, the Townhouse scored 134.0 pop/space, while even the most sluggish non-bill building, the Tower Building, scored 9.3. If you had 16 spaces of Tower Building, you would have 148.8 pop. If you could apply that to the best building, the Side Wing, you'd score 1600.0 pop/space. Unless your expansions are prohibitively expensive, it's almost certainly better to apply your bills to more space and then fill that with new buildings, rather than purchase one of the expensive bill-based buildings. Theoretically, there's a point at which expansions are too expensive to justify this, but even at my current cost of 20 per expansion (non-discounted), I'm much better off using my hard-earned bills to gain space.
The best building is going to depend on your playstyle.
This is obvious, but bears repeating anyway. Above, the conclusions are strictly math-based, and are independent of how much you play. Below, they are only applicable to my playing style. I'd suggest that anybody who wants to find out what their best buildings are should copy my spreadsheet and repeat the experiment. It might be wildly different, depending if you check your app once per day or once per hour.
There's a much wider spread in passenger efficiency than in money.
The Side Wing scored 100 pop/space, while the next best building that's generally available, the House with a Pool, scored only 59.47. By comparison, the Coffee House only outperforms the Grocery Store 100.0 to 89.6 money/space.
Timers 60 minutes or less are better for my playstyle (except for the Eatery).
The Side Wing is easily the most efficient population building, at 5 minutes. It outperformed everything else by almost 2 to 1. After that, there's a cluster of buildings between 45 and 60 pop/space, all of which are under 60 minutes. All the remaining buildings fall under 21 pop/space.
On the money side, all the buildings of an hour or less performed at 64 money/space or better (except the Eatery), and all the buildings of greater than an hour are less than 37 money/space. The Eatery's terrible return of 26.1 money per space is due almost entirely to how little the accumulation curve changes for longer timers. The Eatery gives you 2 coins on a two minute timer, while the Grocery Store gives you 9 coins in 10 minutes. To put that in context, the only way you can beat the Grocery Store with an Eatery in a ten minute period is to check the eatery exactly every two minutes. Money buildings with longer timers show the same type of return.
And that's almost 1500 words on a silly little phone game. Well, hopefully somebody learned something. Should you wish to gainsay anything I've got here, or ask me any questions, don't hesitate to use my contact form.