Luck/Turmoil versus Nothing.

[Squirrelloid]

Originally Posted by chrispedersen

1. Determine number of events.
2. Randomly choose province for event
3. Determine what events can happen (scales etc).
4. Check each possible event see if it happens.
5. Still have events remaining.. go to 2.

1 is almost certainly wrong based on the data I have. If it predetermined the number of events, you'd be unlikely to see a binomial distribution (which you do see). (I mean, I suppose it could calculate the number of events based on a binomial distribution, but that doesn't seem like the kind of thing JK would have bothered to do. In fact, the only reason to do that is to fool people trying to figure out how events are generated.

[chrispedersen]

Originally Posted by Squirrelloid

1 is almost certainly wrong based on the data I have. If it predetermined the number of events, you'd be unlikely to see a binomial distribution (which you do see). (I mean, I suppose it could calculate the number of events based on a binomial distribution, but that doesn't seem like the kind of thing JK would have bothered to do. In fact, the only reason to do that is to fool people trying to figure out how events are generated.

how is rolling four times (step one) not binomial?

[LDiCesare]

The issue with this:

1.Determine number of events.
2. Randomly choose province for event

is that it would take the order/turmoil probability factor out of the equation, or use that of one predetermined province like the capital.
To test it, we'd have to put a capital with +3 order and another province with +3 turmoil and see
- if events are evenly balanced between the provinces
- if the overall probability of events is that of an order 3 province or an order 0.

[Squirrelloid]

Originally Posted by chrispedersen

how is rolling four times (step one) not binomial?

But why would you check that way if you're determining number of events all at once? It only makes sense to determine them independently if you're checking for the event after some other step 1. (Especially given what we know of JK's programming style)

In addition to the problem LDICaesare points out, your method also predicts that empire size has no effect on the number of events seen. I'm pretty sure this is wrong, but I haven't recorded data to test it specifically.

[Finalgenesis]

I've also noticed that events clusters and tend to like certain provinces, often times I get events for the same province 50%+ of the time per turn over a year or so. I think it's easily observable, after two or so years holding 10+ province you should notice that certain province name pops up a lot more often, I usually end up memorizing where the province is base on the name for those that gets an event every other turn or so.

[thejeff]

Because it's based on a %chance of events happening? I suppose you could come up with a complex formula to make the percent bonuses/penalties (from Luck/Misfortune or Order/Turmoil) meaningful, but it would seem easier to just use them multiple times.

On the other hand, the number of events does seem to scale with number of provinces.
On the gripping hand, it doesn't seem to scale at all linearly, which the check each province in turn would suggest.
I ran a test recently, after the discussion about events happening more frequently in low number provinces:
2 Nations on a 602 province map, provinces divided evenly. Both nations T3L3 Dom10. Temples in every province to push dominion up as fast as possible.

C'tis: provinces 1-301
Turn   Events in province
5:     170
6:     68
7:     15,36
8:     172
9:     126
10:    3,84,126
11:    206,96,171
12:    65,283
13:    38,246
14:    280,4,167
15:    269,279,199,2

Midgard provinces 302-602
5:     541
6:     400
7:     326
8:     304,346
9:     570,590
10:    534,320
11:    566,399
12:    313,458,567
13:    458,442

I'm not sure what it proves, but it doesn't seem to be checking provinces in order. Nor does the number of events scale up as fast as I'd expect. I didn't test smaller numbers of provinces, but you get 2 events regularly and 3 occasionally with much smaller empires (30-40 provinces?) If each province was checked independently, until a cap was hit, I'd expect a 300 province maxed out luck/turmoil empire to be hitting the cap regularly.

I also have a hazy memory of one of the developers saying that events were driven by the capital scales, but I wasn't able to find the post again. It was a long time ago.

[Finalgenesis]

Originally Posted by thejeff

I also have a hazy memory of one of the developers saying that events were driven by the capital scales, but I wasn't able to find the post again. It was a long time ago.

Originally Posted by Squirrelloid

First, as thejeff pointed out, if you determine #events before you look province-by-province, then province scales have no effect on how likely an event is. Yet they clearly claim to do so.

I think that it's not too impropable that the luck/turmoil effect on event frequency could be one of those things where either the capital or your pretender scale is used in the event generation formula rather then province-by-province check. This was something I forgot to put in my "clarified post"

[chrispedersen]

Looking at the data I generated, with 50 turns run on a size 4 empire and 50 turns run on a size 8 empire.

With neutral scales, the number of events did not scale between the empire size.

You have the same number of events happening on a size 4 nation, vs a size 8 nation.

Second, I believe the reasons the number of luck events increased so drastically (but not evenly) for +/- luck is because the luck scale increased the number of eligible events in their provinces.

I don't believe its a question of IF a luck event occurs, pick a random event in this territory.

I think its, IF a luck event occurs, check to see if each eligible event in a province occurs.


So, if as I believe there are up to four luck events, and each one has a check to see if it occurs - the actual chance of having an event =4* P(E)*P(EventinProvince)

So changing luck not only increases p(e) it also increases P(eip). This is the only way I can see to account for the doubling of events, and also the consistency that -luck increased the number events more than + luck. While they both may have increased the p(e), the increased the P(eip) unevenly due to the more possible unluck events than luck events.


Second, the same provinces were hit turn after turn with the same events.

Third, some events get turned on on certain turn progressions, 7,10,35, this has a slight dampening on the number of events per turn I posit in the early turns.

However, in the 4 lands test 34 events happened in the first 10 turns, 39 events occured in the last 10 turns.

In the 8 nation test, 34 events happened in the first 10 turn, 43happened in the last 10 turns.

[Squirrelloid]

assuming independent province by province checks with neutral scales, a 300 province territory should have a .9^300 chance for each event not happening, which as you might imagine is vanishingly small. (10^-14)

Ok, so we need a new model. Chris's model doesn't have any effect for empire size, so that clearly isn't right.

thejeff, is that data listing provinces in the order the events happened?

[chrispedersen]

Originally Posted by Squirrelloid

assuming independent province by province checks with neutral scales, a 300 province territory should have a .9^300 chance for each event not happening, which as you might imagine is vanishingly small. (10^-14)

Ok, so we need a new model. Chris's model doesn't have any effect for empire size, so that clearly isn't right.

thejeff, is that data listing provinces in the order the events happened?

I still don't get the criticism.

I'm suggesting first determine how many provinces get event checks. Then run each event check through a provinces event mask.
But I'll do some tests...