Forwarded: [City] Gradual happiness bonuses

[DeletedUser103370]

Proposal
Gradual happiness bonuses instead of fixed pre-determined ones.

Have you Checked the Ideas section for the same idea posted by someone else? Is this idea similar to one that has been previously suggested?
NA.

Reason
More reasonable bonus for happiness.

Details
So first, this is the formula now:

Happiness Ratio / Population Mood / Productivity
Below 1.0 / Angry / 50 %
Between 1.0 and 1.4 / Content / 100 %
Above 1.4 / Enthusiastic / 120 %

My problem with this approach, that it doesn't differentiate between players, though their happiness ratio still can be quite far apart. If a player has 0 happiness, he gets the same bonuses as someone with a ratio 0.99. Or for example a player has 1.4, gets the same bonuses as someone with a ratio of 3!
A much better approach would be if the bonuses were not fixed, but completely dependent upon the exact ratio you got! You could still keep the terms used for different states of your happiness, but the bonuses should be calculated dynamically. For example:

Ratio 0.1 = 10% productivity
Ratio 0.2 = 20% productivity
Ratio 1.0 = 100% productivity
...
Ratio 4.0 = 400% productivity
etc.

Thanks to @Prinza the Hunter and @Strategy Master 101 for the logarithmic proposal (in simple words, the bonus modifier will decrease gradually as the happiness gets higher), here is a practical solution:

HPR = Happiness to Population Ratio, HM = Happiness Modifier, HM is a function of HPR

Going from HPR=0.99 to HPR=1.00 will cause HM to go from HM=0.717 to HM=1.00 (Δ=0.283)
Going from HPR=1.00 to HPR=1.50 will cause HM to go from HM=1.00 to HM=1.24 (Δ=0.24)
Going from HPR=1.50 to HPR=2.00 will cause HM to go from HM=1.24 to HM=1.45 (Δ=0.21)
Going from HPR=2.00 to HPR=2.50 will cause HM to go from HM=1.45 to HM=1.62 (Δ=0.17)

Spoiler

Happiness Modifier> = 0.85 * log_2 ( <Happiness Population Ratio> + 1.26 ) - [0.283 if HPR < 1

courtesy of @Strategy Master 101!

Visual Aids
N/A.

Balance
Actually it would be rather fair and balanced this way.

Concerns
Awaiting feedback.

Abuse Prevention
N/A.

Summary
Dynamic happiness bonus calculations.

 

[Prinza the Hunter]

+1

Suddenly going from 100% to either 50% or 120% is silly.

The entire concept of being 120% happy is stupidity in itself (let's see anyone put 120% of a glass's capacity into a glass - the same applies to happiness, effort, and all the other trendy "I want more than 100%" nonsense). That said, I assume I will be unpopular in talking of scrapping anything over 100%, so I will go with the stupidity.

The exponential factor of happiness buildings was a suprise to me (only learnt of it recently from a useful guide) but should apply gradually, even with a formula that is hard to understand.

A logarithmic scale that gives a mood (productivity bonus) of 100% for 100% happiness and a mood of 120% for 140% happiness should be fairly easy and could mean that a mood of over 200% is almost impossible to achieve without stripping out all the buildings it would apply to, something I think is desirable for balance reasons.

 

[DeletedUser103370]

+1

Suddenly going from 100% to either 50% or 120% is silly.

The entire concept of being 120% happy is stupidity in itself (let's see anyone put 120% of a glass's capacity into a glass - the same applies to happiness, effort, and all the other trendy "I want more than 100%" nonsense). That said, I assume I will be unpopular in talking of scrapping anything over 100%, so I will go with the stupidity.

The exponential factor of happiness buildings was a suprise to me (only learnt of it recently from a useful guide) but should apply generally, even with a formula that is hard to understand.

A logarithmic scale that gives a mood (productivity bonus) of 100% for 100% happiness and a mood of 120% for 140% happiness should be fairly easy and could mean that a mood of over 200% is almost impossible to achieve without stripping out all the buildings it would apply to, something I think is desirable for balance reasons.

Yeah there's definitely truth in what you're saying, the problem I see with confined happiness levels, is that there is a big difference between players. For example I know a guy, who has an extra 30k happiness above the 120% enthusiastic, so how could we define the upper limit to differentiate between him, and someone barley reaching 120%?

That being said, I'd happily go with a 0%-100% happiness scale, if it could be done in a way to reflect the individual player's exact happiness levels!

 

[DeletedUser96901]

+1

 

[DeletedUser108047]

As I have my city permanently on 120% happiness via Traz, Atom, Roads and a premium cultural building I won, I'm not personally much in favour of change

Like a few other elements in this game that have been recently queried such as road placement etc... I query whether the current happiness scale is a deliberate attempt by devs to structure play in certain ways. To keep the game in balance (that is a game that is fun and attractive to a wide range of playing styles, a wide range of experience and a wide range of commitment) the happiness requirement forces players to build at least some cultural buildings and not load up their city exclusively with troops or goods etc. Or if they do, restrict their progress in other ways

I'd be reluctant to suggest change without understanding a lot more about how the various elements are meant to work together

 

[DeletedUser96901]

As I have my city permanently on 120% happiness via Traz, Atom, Roads and a premium cultural building I won, I'm not personally much in favour of change

either you have 120% happiness and get 100% productivity
or you have 140% happiness and get 120% productivity

in both cases you would get 20% more with this Idea

 

[DeletedUser108047]

@Test Ament bad choice of words on my part - 140% happiness so 120% productivity.

Yes the proposal would give more. Getting more is not necessarily the point of the OP or what I am concerned about.

I'm not saying it is a bad idea and I get the idea of it being a more flexible/relevant scale of reward, but I remain of the view that there is a lot of deliberate structure in the game that is not immediately explained but I think ensures playability for a broad range of players. There are many checks and balances to ensure that if you want lots of happiness you have to make a sacrifice elsewhere; or if you want lots of coins, you can't get as much goods or supplies etc... I would not want to blindly propose changing the way it works without better understanding how all the elements interact....

I also query whether the proposal would fit with the way the game is being developed. The devs have recently rolled out coin and supply boosts both in the tavern and in kit form as well as motivation kits. In at least one way this is an option to boost return on buildings without worrying about happiness... Rather than rewrite the game structure I think they are more likely to tweak the game by changing the price of some of the tavern boosts etc. it would be very interesting to see how many players are actually using the tavern boosts rather than relying on happiness.

 

[DeletedUser105579]

+1
I can't say I'm completely on board with a linear relation. Look at history - furious populations still worked, and over-happy populations tend to stagnate and make less. I would suggest it be logarithmic:

<Happiness Modifier> = 0.85 * log_2 ( <Happiness Population Ratio> + 1.26 ) - [0.283 if HPR < 1]

Plug that in to your calculators, see what you think.
The math behind it: it is fitted to the points (1,1) and (1.4,1.2), and the additional piecewise part ensures that it passes through (0,0), in addition to causing a significant drop in the modifier from 1 to 1-δ.

Edit: I see a commenter above suggested that it be logarithmic, I promise that I didn't intentionally steal your thunder

 

[DeletedUser103370]

+1
I can't say I'm completely on board with a linear relation. Look at history - furious populations still worked, and over-happy populations tend to stagnate and make less. I would suggest it be logarithmic:

<Happiness Modifier> = 0.85 * log_2 ( <Happiness Population Ratio> + 1.26 ) - [0.283 if HPR < 1]

Plug that in to your calculators, see what you think.
The math behind it: it is fitted to the points (1,1) and (1.4,1.2), and the additional piecewise part ensures that it passes through (0,0), in addition to causing a significant drop in the modifier from 1 to 1-δ.

Edit: I see a commenter above suggested that it be logarithmic, I promise that I didn't intentionally steal your thunder

That math is too much for me, but do I understand right, you mean if you have a much higher happiness it will result in a negative effect?

 

[DeletedUser105579]

you mean if you have a much higher happiness it will result in a negative effect?

HPR = Happiness to Population Ratio, HM = Happiness Modifier, HM is a function of HPR

Nope, the rate that the modifier changes by will decrease.
Going from HPR=0.99 to HPR=1.00 will cause HM to go from HM=0.717 to HM=1.00 (Δ=0.283)
Going from HPR=1.00 to HPR=1.50 will cause HM to go from HM=1.00 to HM=1.24 (Δ=0.24)
Going from HPR=1.50 to HPR=2.00 will cause HM to go from HM=1.24 to HM=1.45 (Δ=0.21)
Going from HPR=2.00 to HPR=2.50 will cause HM to go from HM=1.45 to HM=1.62 (Δ=0.17)
See the effect? As you add more and more buildings past a Happiness to Population ratio of 1.4, you get smaller and smaller returns. In other words, you are better off using that space for something else.

 

[Prinza the Hunter]

+1
I can't say I'm completely on board with a linear relation. Look at history - furious populations still worked, and over-happy populations tend to stagnate and make less. I would suggest it be logarithmic:

<Happiness Modifier> = 0.85 * log_2 ( <Happiness Population Ratio> + 1.26 ) - [0.283 if HPR < 1]

Plug that in to your calculators, see what you think.
The math behind it: it is fitted to the points (1,1) and (1.4,1.2), and the additional piecewise part ensures that it passes through (0,0), in addition to causing a significant drop in the modifier from 1 to 1-δ.

Edit: I see a commenter above suggested that it be logarithmic, I promise that I didn't intentionally steal your thunder

I'm not a mathematician so you can't steal my thunder: I made some attempts at a formula but gave up.

I'm a computing guy, though. I don't know what log_2 is - is this log with a base of 2? Also, I don't understand "
- [0.283 if HPR < 1]" as it doesn't make sense if tacked on the end.

Using terminology from the game:

Do you mean

if AdditionalHappiness < 1 then
Productivity = 0.85 * log_2 ( 0.283 )
else
Productivity = 0.85 * log_2 ( AdditionalHappiness + 1.26 )

Once I grasp the formula, I can generate a table and graph to illustrate.

The developers would obviously decide the exact formula, if they adopt this suggestion, but it would be useful to have something that we, as players, agree is about right.

 

[DeletedUser105579]

I'm not a mathematician so you can't steal my thunder: I made some attempts at a formula but gave up.

I'm a computing guy, though. I don't know what log_2 is - is this log with a base of 2? Also, I don't understand "
- [0.283 if HPR < 1]" as it doesn't make sense if tacked on the end.

Using terminology from the game:

Do you mean

if AdditionalHappiness < 1 then
Productivity = 0.85 * log_2 ( 0.283 )
else
Productivity = 0.85 * log_2 ( AdditionalHappiness + 1.26 )

Once I grasp the formula, I can generate a table and graph to illustrate.

The developers would obviously decide the exact formula, if they adopt this suggestion, but it would be useful to have something that we, as players, agree is about right.

if AdditionalHappiness < 1 then
Productivity = 0.85 * log_2 (AdditionalHappiness + 1.26 ) - 0.238
else
Productivity = 0.85 * log_2 ( AdditionalHappiness + 1.26 )

Let me try to make a picture for it

Spoiler: Here are the data points in blue

Productivity	AdditionalHappiness
0.00041	0.00
0.711436	0.99
0.999874	1.00
1.19971	1.40
1.44914	2.00
1.62412	2.50

When AdditionalHappiness is 0, 1, and 1.4,
Productivity is approximately 0, 1, and 1.2
In order to get a Productivity Multiplier of 2, you would need a Happiness to Population Ratio of 3.849 (clearly inefficient compared to having supply/coin buildings)

I'm not that great with BBcode, so if anyone could explain why there is a lot of whitespace above the table I could fix that

 

[DeletedUser103370]

I see! Yeah that's perfect guys, I put that into the main post @Strategy Master 101 if you don't mind!

 

[DeletedUser105579]

It's all yours