Yearly Percentages

[Khubilai]

When something says "14.02% Yearly" (council jobs, for example) what does that mean exactly? I assume that it means there is a 14.02% chance that the stated thing will happen, but when? Since the context is "yearly" it sounds like this event probability is calculated once every 365 days. When? Could it happen on any day in that year, and if it does, does the 365 day timer then reset?

 

[Djieh]

IIRC, it does in fact mean that you have a 14.02% probability of success within a year. From there, the probability is calculated for every single day within that year so that it could happen on any day.

 

[Khubilai]

So in effect, there is a 14.02% chance of the occurance on any day, as long as that council member is doing that particular job. I still don't get why it's labelled as "yearly".

 

[Kimberly]

So in effect, there is a 14.02% chance of the occurance on any day, as long as that council member is doing that particular job. I still don't get why it's labelled as "yearly".

No, that's not right. The chance on any given day is such, that in a whole year, the chance is 14.02%. The chance of it happening on March 1st, 1089 is very small, but because the dice are rolled fairly often, the chance of it happening in any given year is 14.02%.

Why do they use the yearly value, instead of the real percentage for when it's checked? Because it's much easier for you to work with a yearly percentage than a very small percentage that applies only when the event is checked.

On a side note, I'm not sure if events are actually checked for daily...I know they weren't, in Europa Universalis III.

 

[Khubilai]

Thank you very much, that clears it up nicely!

 

[Ithvan]

I thought they were checked monthly, because daily would mean the events fired much more frequently.

 

[Darkgamma]

Very very low MTTH solves it. 15/365 isn't much.

 

[tuareg109]

No, that's not right. The chance on any given day is such, that in a whole year, the chance is 14.02%. The chance of it happening on March 1st, 1089 is very small, but because the dice are rolled fairly often, the chance of it happening in any given year is 14.02%.

Why do they use the yearly value, instead of the real percentage for when it's checked? Because it's much easier for you to work with a yearly percentage than a very small percentage that applies only when the event is checked.

On a side note, I'm not sure if events are actually checked for daily...I know they weren't, in Europa Universalis III.

I'm no statistician, but if it's .0384% chance per day (14.02/365), then 1-.0384%=99.962% chance of failure. (.99962)^365=86.92% chance of failure per year
1-.8692=.1308
This means that it isn't calculated your way, or else it would be a 13.08% yearly chance of success. Since we can't change the amount of days in a year, all we can do is either change the % chance per day, or the method for calculating yearly chance of success.
It can't be changing the % chance per day, because the % that gives you 14.02% is not (14.02/365); this means that there must be some different formula or method that Paradox uses to calculate this.

Hey, if any mods see this, can you give us the formula you use for this?
I am now super interested.

 

[Darkgamma]

Or maybe you had a statistical error?

 

[riknap]

wait...
aren't these computed monthly?
so a 12% chance yearly is basically a 1% chance monthly?

edit: I realized that was a retarded post, but I'll own up anyway

 

[Kimberly]

I'm no statistician, but if it's .0384% chance per day (14.02/365), then 1-.0384%=99.962% chance of failure. (.99962)^365=86.92% chance of failure per year
1-.8692=.1308
This means that it isn't calculated your way, or else it would be a 13.08% yearly chance of success. Since we can't change the amount of days in a year, all we can do is either change the % chance per day, or the method for calculating yearly chance of success.
It can't be changing the % chance per day, because the % that gives you 14.02% is not (14.02/365); this means that there must be some different formula or method that Paradox uses to calculate this.

Hey, if any mods see this, can you give us the formula you use for this?
I am now super interested.

Well, I don't actually know how event checks are done. I do know that A) they are done more than once a year, and I assume that B) the 14.02% yearly chance is correct. For both of these things to be true, the probability of the event firing each time a roll is done (however often that may be) must low enough to end up with a chance of 14.02% chance of the event firing in one year.

wait...
aren't these computed monthly?
so a 12% chance yearly is basically a 1% chance monthly?

The yearly percentage isn't evenly split over the amount of event checks. Proof:

Because the odds don't change with each check, and the event either fires or it does not, the amount of event firings is binomially distributed. If you check 12 times, and the odds of success each time are 1%, then the odds of the event firing once in a year is binompdf(12,0.01,1) = 0.1074405905, or roughly 10.7%. The odds of the event firing more than zero times are 1 - binompdf(12,0.01,0) = 0.1136151283, or roughly 11.4%.