From towns to understanding food and growth Question... How does it work?

I'm slightly confused as well..   If you build a city on a 2-2-0 tile it can never reach level 3?   I thought with some techs that increase yields and whatever they could.  

it's a bit confusing,

Some stop growing right in the middle of a level and there is no warning to that effect. You have to keep an eye on it.

Hopefully somebody can answer us.

The number of grains your city has determines the amount of available food. To find this amount each grain gets multiplied by a food per grain rating in the city. This rating changes when you build structures in your city that increase food per grain. There are also some structures that increase food per grain in all cities. There are enchantments that can increase this number. Also some enchantments can add grain to a city. Some strategic resources can also increase the base number of grains. As long as you have more food than people you can grow; however a larger food surplus allows a city to grow faster, as does some buildings, some enchantments, and consulates (an upgrade to outposts). At certain population levels, your city upgrades to the next level of cities. As far as I know once a city upgrades it cannot lose city levels.

So if you have a city with only one grain, but you have most of the techs and can build all of the city food buildings, plus have numerous faction wide food buildings you can eventually level the city up. Other than building pioneers and leveling up the city, population has no other uses that I'm aware of (well you can sacrifice them for mama with a spell but that's not what I was talking about). I hope that helps, and if I said something inaccurate please correct me.

From memory, you get a certain amount of food per grain. So in other words if you get 50 food per grain and it's a 2 grain city then you get 100 food. 100 food can support 100 population. If you hit 100 population then that city will stop growing.

Some city improvements give you bonuses to food. So if you built an improvement that gave you +25% food per grain, that would mean that your 2 grain city would now produce 62.5 food per grain, or 125 total (I think the fractions are added as you'd expect). Your city will now grow to a maximum size of 125.

There are a limit to the number of food increasing improvements you can build in a city; Towns get quite a lot more, so can generally grow larger and faster. Some Town improvements increase global food production. So if a Town builds an improvement which increases global food production by +5 per grain, your 2 grain city would now be able to grow to 135. There is a spell which will increase the grain of your city by 1, as well, can't remember what it is off the top of my head.

Growth is determined by a few different things, but one of the biggest factors is the difference between your current population and your maximum population. In other words, if your current population is 25 and your total food is 500, then your city could support 20 times more population than it currently has, and it will get +3 growth (which is the amount it grows in population each turn). Again, from memory, I think you get +1 for having up to double the food your current population needs, +2 for up to treble the food your current population needs, and +3 for more than treble the food your population needs. So in the example above with 135 food, you'd have +3 growth up to 45 population, +2 growth up to 67 population, and +1 growth up to 135 population (when it would go to +0). Something like that, anyway. 

There are various buildings and spells which will alter your growth rate. Getting your capital to upgrade from a village as fast as possible is a valid strategy.

The same mechnic works for materiuals too.

So a 5-2-0 city will grow really fast while its production will lag. While a 1-5-0 city will grow very slowly (or not at all), but can produce buildings/units very fast.

As noted above, spells/buildings can improve towns with low numbers and help them overcome the low starting values.

Of course, all things being equal, a X-Y-2+ location is by far the best considering how important essance is in the game.

So can anyone math up some pratical examples?

Like if you have a 3 grain town how many wells, inns, granaries and other things do you need to make for it to be able to reach level 4?  From that city alone and/or along with other Towns affecting faction per grain?  Practical examples?

I'm getting a headache, where's the cake?

All good information. Thanks all.

A good example would be great.

A practical example isn't really practical, imho. I usually try to reach lvl 2 quickly with new cities, after that, I check if I can make a next level easily, otherwise I build more Pioneers. Population by itself doesn't do anything (as Korn469 said). You can check the big progression bar to see how much population you have, and if you can reach the next level or will need to build a food building.

Anyway, in your example, you need to multiply all 'per grain' buildings and techs with 3, since you have 3 grain. This means you need x100 food. You start with 25 (again, all per grain), so you need 75 more. The first 3 buildings add +50 grain. In total, as the bonuses you see next to their techs are not cumulative. Let's say you have already built these, for a total potential population of 225. How can you get this to 300 for a level 4 city?

- Town buildings that increase food p/g in every city. If you already have 5 towns with at least the first building in the 'food for everybody'-line, you are good to go. The first building, Grocer, gives 5 food p/g to all your cities. 5x5 = 25 (*3 grain) + 225 = 300

- If the city is a town, you can build 'food multipliers', like the well. 225x1.5 = 337.5

- City Enchantments: one enchantment multiplies your food, multiplier depending on Essence. The other, early tech one, adds +1 grain to the city. So in the example, it would be 75*(3+1) = 300

Mind you, I have only talked about max population. Growth is something else. I think Merlinme's figures are correct, but there's even more to it...

City progression population requirements (current level - population required for next level - next level):

lvl1 - 50 - lvl2
lvl2 - 150 - lvl3
lvl3 - 300 - lvl4
lvl4 - 600 - lvl5

Thus, if you have a 3-grain city and you want it to achieve its fourth size category, you need to have a total food per grain of 100. This can come from other towns by means of the Grocer line of buildings (+5/10/20/40 faction-wide food per grain per structure, affecting both the town it's built in and all other settlements in your empire; additionally, the +40 faction food per grain is a 1-per-faction structure), the Garden line of buildings (+15/35/50/60 local food per grain; additionally, the +60 food per grain is only available to Empires), the Well line of buildings (+25%/50%/50%/50% local food production, so there is no population bonus to upgrading beyond the Inn), the Pier line of buildings (+5/5/10/15 local food per grain; additionally, the final upgrade of the Pier is only available to Kingdoms), the Great Mill wonder (+25% local food production), and a couple of spells (+25% food production per essence from Gentle Rain, +1 grain from Nature's Bounty). Possibly also a few other buildings I can't think of right now, and it should be possible to create unit abilities via modding that would add to faction food production, as well. The Well and Grocer lines of buildings can only be built in Towns, and Well line buildings do not provide increasing food bonuses after the first upgrade.

Let's assume that we have an empire of 20 cities, which includes ten Towns, seven Conclaves, and three Fortresses. Five of those towns have Grocers, which together grant +25 faction food per grain (+5 food per grain * 5 grocers). Another two of the Towns have Bakers, which together grant +20 faction food per grain. One Town has a Butcher, for +20 faction food per grain, and one Town has a Brewery for +40 faction food per grain. The other town doesn't have any of this stuff. Thus, from our ten Towns, we have a bonus of 105 food per grain in every settlement our faction has. Neither Conclaves nor Fortresses are capable of affecting the food production of other settlements, so we'll ignore them. This faction-wide food bonus from the Towns is sufficient in and of itself to allow any tile with three or more grain to support a level four city, any tile with two or more grain to support a level three city, and any tile with one or more grain to support a level two city, without including local food bonuses from Garden-line or Pier-line buildings or the city hub itself (which provides 25 local food per grain).

For the most part, though, I agree with Fallenchar that a 'practical' example isn't really useful. The age of your empire and how you've been building it, and the type of city you have, and the amount and focus of your research, are all going to impact what you can do at any given time. I've had games where I could basically ignore food-production centers because I'd built enough Towns with Grocer-line buildings that even my 1-grain cities could reach level five (eventually), and I've had games where if I wanted my cities to grow a size level I'd need more food structures than would reasonably be available to my faction in a worthwhile timeframe.

Also, growth bonuses from food surpluses are essentially the food surplus percentage divided by 100, restricted to be between 1 and 3.

Man I'm kinda getting it.  I appreciate the attempts @Fallenchar.  It's tough to grasp the intracasies of the additions and multiplications going on here.  Definite see the outlines of the Algebra going on ((umm food , growth) * city bonuses) * or + faction bonuses) or something.

So bottom line:

4/3/2 or 3/3/3?

I'm thinking 3/3/3, no?

It's situational, but usually, I'd take the 3/3/3 over the 4/3/2

Both are top sites. 3/3/3 is slightly better, as you can cast a +1 material/grain spell with that extra essence, while getting a bigger bonus from *essence enchantments like Meditation. 

One of the slight quirks of the game is that if you lose population you do not go down city levels. So if you get your city to level 5, it will stay level 5, even if you Sacrifice it down to 10 population. Later in the game when you have a few cities it generally makes sense to have one or two focus on building pioneers (and using Sacrifice, if you have it). I either choose a level 5 town or a town which has reached its highest expected level for the foreseeable future. Playing on higher difficulty levels, cities you've captured off the AI are great for this, as they tend to be very high population. At the point when I can turn 500 population into mana using Sacrifice I generally think I'm well on the way to winning. You can cast Sacrifice multiple times a turn on the same city, so the fact its only half the population at a time is not really a limit. A good city to choose for this is a Town with high growth; with Slums (for example) it's pretty easy to get +6 population growth a turn, and with Sacrifice that is effectively +6 mana a turn. That's on top of the initial bonus of hundreds of mana when you Sacrificed the city's original population.

In all my FE and LH games, I have never had a level 5 city. That fact didn't stop me from conquering the map. I would like to stress the fact that reaching high population or level 5 doesn't help you win games.*

It can be fun, though. Just make sure which cities are worth building up population-wise, and which aren't.

*Admittedly, some city-level up bonuses are very useful. Keep an eye on Joeball's list of level-ups in the other thread!

I've got a city to level 5 a few times, generally by capturing an AI level 4 Town which has Slums. I didn't until I started playing on Ridiculous with the improved AI though, I agree it's not really necessary to win, and certainly not something I particularly aim for.

I'm going to try all I have learned this week end.

I'm gonna play it on high difficulty and see if I can make sense of it.

Thank you all for the information.

3/3/3 always. You get that grain back from Sorcery tech (Nature's Grain or something) at the cost of the extra essence, and more essences boost Gentle Rain and Arcane Forge later on, not to mention troop enchants. 

Use Consulates (outpost upgrade), with that and Gentle Rain getting a level 5 city is easy. (+1 Grain and 25% food per essence) The main problem is production to get there since both consulates and food buildings gets expensive, so Enchanted Hammers, Clay pits etc. are very useful for getting cities up fast. 

Conquering the map is a very different thing to do depending on difficulty. I could probably conquer the map without anything but my Sovereign and starting troops on the easiest difficulty.