Sawmills

[Seravy]

Current ROI is 17 assuming no production bonus, so about 14-15 on the most common terrain.
The ROI it has is not bad, what's bad is the ratio of city hammers (1-3) vs sawmill hammers (6-10) which we want to turn into (6-8) vs (4-6) instead. (all numbers adjusted by maintenance)

1 food is probably still safe (albeit makes Granary worthless until pop 2 but that's fine) but it only yields 1 extra hammer which is nowhere near enough. 2 food would be 3 hammers but the impact of 2 food is already too high on food economy. (even 1 is a big deal, it means you can have 2 extra units per city)

[Seravy]

Let's try to come up with something for housing.

Goals :
-Housing should be the best buy on good terrain up to about 3-5 population after that it shouldn't be as good as basic buildings.
-Housing should not be worth it on bad terrain compared to basic buildings. On the worst places, it shouldn't even be worth it for 1 population.
-Housing should not be worth it at high population.

I see we used 2 hammers = 1 population in the previous thread so let's go with that.

Popgain(per turn)*ROI*2 = BaseProduction

We need to come up with a housing formula (popgain=?) where the ROI in the above meets the goals (better or worse as we want it).

For this we need to know the production so we need to decide on base hammers.

Here comes the tricky part. We also want to decide base hammers based on housing so we can't do it the opposite direction. Basically the more population we can expect from housing, the fewer hammers we need to provide to make up for the missing amount.
Fortunately we have a goal on housing, so assuming we succeed in meeting that goal, we can use that to determine hammers. Even better, we can do the opposite - set the housing goal in a way that it is ideal for the hammers.

But first we need to know how many hammers we want. The change would not affect the output of farmers and workers, so we need to redistribute exactly 8 hammers at 4 maintenance = 6 net hammers. (before terrain)
So we need to divide up 6 in a way that the first half is greater than the second, but the first half also gains a bonus from production provided by farmers and workers. Assuming we want 6 hammer sawmills, at a maintenance of 4 (net gain 4 hammers, literally the same value as a marketplace, before terrain modifier), we'll have 2 hammers left over as base hammers. But we want this to be greater than 4, so at least 6, after including workers and farmers.

That means housing+natural growth needs to provide 4 hammers worth of people under average conditions. (in poor terrain, you'd still be better off buying your buildings for gold first)

We assumed 1 population = 2 hammers so housing would need to produce an extra 2 units of population, on average terrain.

We assumed 2 base hammers, so each city size would have this much production (taxes not included) :
Pop 1 = 3 Hammers
Pop 2 = 5 Hammers
Pop 3 = 5 Hammers (need 2nd farmer, hammers rounding down from it)
Pop 4 = 7 Hammers
Pop 5 = 8 Hammers (need 3rd farmer, hammers rounding up)
Pop 8 = 12 Hammers

Fairly safe to say we are usually losing 5 hammers/turn on average for housing, but this goes up as size grows.
So.. Pogain*ROI*2 = 5. Popgain*ROI = 2.5.

Assuming sawmill average ROI is 15 as currently, Popgain = 0.166 = +170 people a turn.

We need to come up with a housing formula that provides +170 people a turn, on average (+6 racial growth, pop 15 location?) cities, at least up until pop 4.

This also means a changing ratio of farmers to workers (1, 1+1, 2+1, 2+2) so the formula likely should not depend on that (you'll usually have more farmers than workers in the most critical 3 pop part).

A pop 1 city with max pop of 15, gets (15-1)/2 = 7, so +70 growth from terrain and 60 from race, so +130. This shrinks by +5 for each unit of pop gained, so +120 is more reasonable for the middle point.

If we do want housing to still be proportional to native growth, then housing should provide a +142% growth benefit. (Before Builder's Hall)
Buying Builder's Hall might extend the housing to be effective at pop 4 and 5 as well, likely not past those, if the bonus is multiplicative. (1.5*+142% = 213% with BH.)

At this housing rate, we gain +290 people a turn, so it takes roughly 7 turns to reach +2 pop gained (pop 3 total). I believe 7 turns of waiting is a completely fair and even compensation for having 200 gold left over compared to the "buy sawmill" system - You can roughly spend 200 gold on 7 turns of progress in this early part of the game, once the city did reach this size and has the sawmill.

So by housing we reach 3 units of population. At then, we are producing 2 base hammers, +2 hammers from our worker, +1 hammers from our farmer, for a total of 5.

At the intended 17 ROI, the sawmill would cost 4*17 = 68 production.
That means it would take 13.6 turns to build it. That's lower than the intended 17 ROI, so we are (barely) safe. We wanted much better though. The problem here is that we assumed all the tax money comes back to this town, but it might not. So maybe it would be better to encourage housing until +3 people (so hitting 4). We already designed the housing formula to be good up to that amount so we are good on that. It would take about 4-5 turns longer to reach this amount of population, but in exchange for that, it'll be much more convenient to take money out of the city (both more taxpayers and 29% less time for building any basic building - overall worth it.)

So to summarize the numbers...

Base Hammers : 2 (nice, I really didn't want a high amount here)
Sawmill cost : 68
Sawmill production : 6 hammers
Sawmill maintenance : 4 gold
Housing formula : +150% population growth rate. Builder's Hall increases it to +225%. Farmer/worker ratios don't matter.

I'm a bit worried about that housing rate though, it's about twice as good as it used to be. Seeing +800 people growth numbers can easily trick people into thinking housing is worth it on a pop 12 city. We might want to calculate some numbers to ensure our "housing should not be effective..." goals are also met.

Pop 1 city, max pop 8, +4 racial growth. (poor terrain and race)
Would get +70 people, so housing gets +100 on top. So 0.1*ROI*2=3 hammers, ROI = 3/.2 = 15.
Well that's not good. This growth formula is too forgiving and still results in acceptable growth on at least pop 1->2 for a bad race/terrain combo.

Pop 8 city, max pop 25, +9 racial growth (good race and terrain)
Gets +170 people so housing gets +250. So 0.25*2*ROI = 12 hammers. ROI = 12/.5 = 24. Well this is acceptable but would have preferred a number further away. With BH it's still worth doing housing...


Any ideas for a better formula?

[Seravy]

So let's try to summarize...

at +70 people vs 3 hammers, we want ROI>20
at +120 people vs 5 hammers we want ROI=15 
at +170 people vs 12 hammers we wand ROI>30

pop*ROI*2=Hammers
So 40*X>3 => X<0.075.
So housing should be 70 or less people for the first one

30*X=5, X=0.166, we want 170 people here as we already calculated

60*X>12, X<0.200, we want below 200 people here.

That's nonlinear. 
70->70 is a 100%, 120->170 is a 142%, but 170->200 is only 117% again.
Guess we can't get away with a simple housing = (population growth*X%) formula then.

We generally want higher max pop=higher housing, higher current pop = lower housing, and higher racial growth = higher housing as well.

So maybe, Housing bonus = 170 people * (max pop+racial growth-8)/13 * (1.3-0.1*pop) ?

That's really complicated but the basics are trivial to remember (higher max or racial pop = higher growth = higher housing, and higher size = lower housing.). Builder's hall would add 50% extra on top of that. (which probably pushes the above "bad for housing" examples barely over the limit.

The examples would yield +62, +170 and +170, meeting all three criteria.
With BH you'd need to either lose at least a third of your (max pop+racial growth-8) which only really means losing another 2 max pop or racial growth (perfect), or one third of (1.3-0.1*pop) - growing rom size 8 to 10 would do that part. Perfect.

[Nelphine]

I don't like the goals. I don't want to do housing up to pop 5, ever. Not in a max pop 30 stream of life builders hall city with lizardmem or halflings.

I would like to see housing better than current sawmill at pop 1 on an average poor city - say max pop 10. I would be ok with housing being better than a current sawmill at pop 2 for a max pop 23 or better city, or a pop 12 or 15 city with builders hall.

I never want housing, even with builders hall, to be better than a current sawmill at pop 3.

I'm ok with housing at pop 2 being as good as basic buildings, but it shouldn't be better on a pop 10 city.

Pop 3 housing should need a builder's hall to be better than basic buildings, and even require high, 20+ population.

I WOULD like to see ~pop 15-20 cities, with a max pop of 22+ prefer housing over trade goods. More accurately, I think housing should better than trade goods until you reach ~80% of max population.

[Bahgtru]

What a swerve haha. Did you change topic because you made up your mind with sawmills? Is it going to be 1 food and a bit of hammers in every city centre for free and a bit less hammers with the sawmill? That seems lovely btw.

[Seravy]

I never want housing, even with builders hall, to be better than a current sawmill at pop 3.
Pop 3 housing should need a builder's hall to be better than basic buildings, and even require high, 20+ population.

The calculations resulted in that we want housing to be the best (without requiring a building) until pop 4 in average or better cities. If not, we don't have enough hammers. So we can't have this goal otherwise we need weaker sawmill, or more starting hammers.
Do note I used pop 15 spots as the baseline for average. A lot of player cities will be on pop 10-11 places where they probably should stop at 3 instead.

Also, while housing does have the highest ROI, it only produces population. That means gold and hammers, but no research, magic power, etc. So while it is the best thing to build, if you need something else, you will want to switch to those anyway. Furthermore, Housing has a hidden "penalty" - larger population will eventually have more and more unrest, making it less effective. (We might want to make the housing formula also scale down the gains if there are rebels, but even without, the created new population isn't working, making the ROI on it infinite.)
Considering both of these, I don't think Housing past pop 4 will be a thing except maybe in amazing locations (pop 25+) or Klackons. (Klackons already have better ROI by default as their cities are more productive and their growth modifier is high - but they also miss out on more hammers by using it which might balance it)

I did think a bit about things last night after posting.
Housing isn't really a wait time - it's productive with better ROI than anything else you could build. However the "leftover" gold isn't really relevant either, as anything it would be invested into will have equal or worse ROI than previously. (and our problem with sawmills wasn't the ROI but the time it takes to build one without money)
So overall, everything we calculated is still good.


However, the easy lairs. It's ultimately giving the player free money. We already decided we don't want the player to get free money. That's why we have the free settlers instead of simply starting gold. Money can potentially go towards rushing an Armorer's Guild and abusing the system to win early.
So that's a very strong point against having these lairs. On the other hand, the need to reduce the luck factor is real. So the money is OK if you would not find treasure anyway, but it's potentially gamebreaking if you do and get this extra ~500 on top of it. Not sure what to do about that.

[zitro1987]

I don't find the formula very intuitive because it doesn't seem to even consider hammers or workers like in original. That would mean players will have to 'know' to switch all their workers to farmers if housing.

I believe hammers need to contribute to housing efficiency, just like trade goods. This could mean using 'housing' for a 15 pop city with 25 max is not a terrible choice (at least compared to trade goods) because the high production would net a few hundred pop per turn.

[Seravy]

This is the ROI of housing on all the relevant city sizes and (max pop+race modifier) values. Green are where it's better than building a sawmill :
   
And this is with Builder's Hall added :
   

Basing the formula on hammers has an interesting consequence. ROI depends on hammers ad the growth gained. If the growth gained also depends on hammers (lineraly) then hammers no longer matter.

Which means we can come up with a formula ignoring hammers completely. That would be convenient but we already have a good formula...

However, using hammers is also very very bad. It makes Housing have linearly higher efficiency as hammers grow. So basically, you would need to first buy the sawmill, and then have those hammers build population for you. Which is the exact opposite order we are aiming for.

So I say no to using hammers. Note that the original also never used hammers. It did use the worker/population ratio, but since most of the early population are NOT workers and cannot be, that wasn't working well.

Switching to farmers is a problem though, as you are effectively taking out food->gold from the city instead of the hammers, and we assumed those would be lost hammers. So doing that directly increases your ROI. I'd say housing should either force setting maximal workers or consume all extra food.

[Nelphine]

Agreed. It's not intuitive at the moment. I like the 'consume all extra food', but when you have 2-3 wild game spots on a pop 1 city, you might have chosen the location to reduce farmers elsewhere, which kind of defeats that, so I don't think we should consume all food. I don't like forcing farmers because it 'feels' strange, but I can't actually think of a reason why not to do it, so it seems the better option.

I should probably work out a formula myself, as I feel that one is too good for housing, and I want 'with builders hall' to be somewhat less effective than your 'without builders hall' version. 

I'm also on zitros side, that I would really like to occasionally use housing instead of trade goods when all buildings are complete, which means I would try to use hammers. I suspect that won't be possible though - trade goods are too good when you have any kind of decent industry.

[Seravy]

Trade goods have 1/4 the ROI of building anything else due to it converting 4 hammers to 1 hammer in another city.
So for housing to compete with trade goods, it needs to have ROI<60. That reaches about 4 units of population higher than competing with actual buildings. 

Either way, you can't have it more effective at high pop, but less effective at low pop, at the same time, when effectiveness decreasing with higher current pop was the main requirement.

Also, high pop cities produce a lot of hammers, so the wasted production is simply too high for housing to be worth it no matter what the formula (even with the 25% modifier on trade good. All these assume no other buildings, if you already built your production buildings, you'd be wasting about twice as much...).

Besides, I rather not want to take out a calculator and try to figure out whether housing or trade goods is more effective on my pop 15 city that just had 8 pop killed in battle, that's not very fun, and if the breaking point is that high, you'd need to, it wouldn't be possible to do it intuitively (like you could with this system, start with 1-6 based on how good the location and race is, add~2 for builder's hall, 4 if comparing with trade goods, and if current pop is below that, it's worth it. That's easy, you need to stop between 7-12 people.

By the way housing on a high pop city is not worth it for one more reason. It works like a loan. Yes, you get those people now, but you hit the max limit very soon by doing that. Once you did, you no longer have natural growth happen. So the timeframe where those extra people are productive is the turns difference between reaching max naturally and using housing. That might not be enough turns for ROI to happen, and most other investments assume you get that production output for the rest of the game. If it ends in a reasonably low amount of time, it's worse.