Hm,I have two public baths and one marketplace building atm,with roads that shoud be about 120% but what I find is worst of all, if we talk about happiness, is that you have only 50% if you are low wich is not corect it shoud be at least 80% couse max happiness is 120% ......
I didn't understood that with 50%, 80%...
I was thinking at the same thing lately. How much is worth to keep cultural buildings and decorations for 120% productivity. I have done some math and maybe fellow posters here can check if is right.
I will start with my concrete case. I have 27 houses, 5 butchers and 3 tanneries, 6 taverns and some decorations and Gravel roads which gives 10 happiness per square which means that if I didn't have this road I had to build more cultural buildings. My total population is 1857 and available 9 which means that if I want to build something else I have to make houses also. My demand for happiness is 1857x1.4=2599.8 and now I have 2617. This means that is close to the limit so I can't be "accused" to have to many taverns.
For the rest of the math I have used
HaekelHansi guide which is always very helpful.
I have 19 Frame houses and 8 Cottage. I will use for simplicity 27 Frame houses (meaning all the same) and because Frame house has a higher production per square and hour.
At 100%: 60/4=15 Coins per square and hour.
At 120%: 15+20%= 18 Coins per square and hour.
27 houses x 4 squares each = 108 squares occupied by my houses.
108x15=1620 (100%) ; 18x108=1944 (120). This being the total production.
1944-1620=324 this being what I lose if I leave out 120% productivity and I renounce to my cultural buildings and decorations.
324/15=21,6 the squares I occupy building more houses to compensate 120% to 100% difference. 21,6/4=5,4=6 houses.
A tavern occupies 9 squares: 21,6/9= 2,4 taverns.
Now with the production buildings.
5 butchers x 12 sq=60 squares. At a 15 minutes cycle a butcher produces 80 supplies at 100% happines.
80+20%= 96 (120%).
80/12=6.6 supplies per square at 100%.
96/12=8 supplies per square at 120%.
80x5=400;96x5=480. 480-400=80 supplies, the difference of production for my butchers from 120% to 100%.
80/6.6=12.12 squares.
For Tannery is the same amount at 15 minutes the difference is that a tannery occupies 9 squares.
3 tannery x 9 = 27 sq.
80/9=8.88 supplies per square at 100%.
96/9=10.66 supplies per square at 120%.
80x3=240; 96x3=288; 288-240=48. supplies the difference of production for my tanneries from 120% to 100%.
48/8.88=5.4 squares.
I hope I written so you can follow. If you followed we take the squares from the above: 21.6; 12.12; 5.4
21.6+12.12+5.4= 39,12 rounded up 40 squares.
I have 6 taverns x 9 squares = 54 squares. So if get rid of them I get 54 sq and I have to build houses and productions buildings that takes 40 squares to compensate. 14 squares difference in my advantage and I don't lose money and supplies building cultural buildings.
Indeed is interesting and important to do the math for Market place>Shoemaker>Brownstone house. Maybe I will do it and get back to you. But for me after this math happiness boost for productivity is just a mirage. Is true that neighbors can polish some cultural building for instance and you don't have to build so many cultural buildings but is not continuous, may times I found my self without 120% so I don't rely on my neighbors
. And it doesn't matter because the neighbors can also motivate to double the production of a building so... Goods buildings are not affected by this 20% bonus as far as I know...
PS. I forgot to ask. I don't know if you get a penalty for having to less happiness. ???