Luck/Turmoil versus Nothing.

[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.

[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.

[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.

[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?

[thejeff]

Yes, the order they were listed in the messages.

Do we know the base chance? We certainly don't know what it means.

At least by the end of that test most provinces were T3L3, which should have boosted the chances by 36% (Do we know if that is +36 to the base percent chance, or an increase of 36% of the base chance? I'd always assumed the former...)

I can try to run more turns. See if the data changes.

[Squirrelloid]

I'm assuming its a % increase in base chance, because adding 36% is very clearly too large.

My tests suggest a 10% chance of an event for each of 4 independently calculated events. The distribution of events i saw matched such a binomial distribution. Of course, I only tested with one province, so it does leave open how it works with more provinces.

[Finalgenesis]

From a design point of view, I would think that a diminishing effect on event frequency for additional province to be a reasonable design decision, along with some sort of cap. It looks like the event gen mechanic doesn't check for event province by province, but perhaps roll for whether an event happens, then roll where it occurs among your provinces, then select events up or down the event list base on local luck. The formula itself will probably account for province number as a factor in a diminishing formula, e.g. 4 rolls of "Occurence = 10% + (10% * (x/x+1))" where X is the # of province your have (disclaimer: this is not meant to guesstimate the actual formula, but show how a cap of 19.9999% event occurence in 4 checks might be implemented, along with adding in province # as a dimishing factor, the cap can easily be changed to other percentage).

It is also a reasonable mechanic for event gen formula may also make a 1st event more likely to occur then a 2nd event, though Squirreloid's testing seem to refute this.

Linear relationshop between event frequency and province # wouldn't make sense (Also refuted by thejeff's data, though more sample population would help as 10 turns of data is a bit low, it does however, show that something unintuitive is going on with event generation though)? We know that province # is likely factor from Squirreloid's test I think, as we do see a lot more then 36% event when we had more provinces, also Squirreloid have tested this for quite a few turns, so turn progression may not influence event chance (at least for a solo province). What other factor can account for thejeff's data where the event chance seem to pick up with no change in province #?

@thejeff
For your test, was your dominion spread covering all your provinces? Or was it just spreading out from capital? Or maybe turn # is a factor when there are mutliple provinces... Thanks for your testing data too thejeff, very handy.

[Finalgenesis]

Rereading my post above, I realized that unless you're my clone, it won't be easily understandable. I'll try to lay out my thought process in an easier to understand manner:

Event generation mechanic:

a) 4 single checks for event, roll once only (not once per prov)

-At current, this looks the most reasonable, as thejeff's testing likely show that the check is not once per prov (otherwise he'd max out 4 events a turn, or close). Likely the formula used includes province # as a factor somehow in a dimishing manner, as we can say with some confidence that we DO see more events when we had more province.

b) assign all events to random province

-Of those 4 checks, any success rolled (event generated) must be assigned to a province. Technically this should be random, though many have noticed that this tend to cluster.

c) once event assigned to province, apply luck

-So an event has been assigned to a province, luck have to apply somehow. I'm guessing the event is generated after the province has been selected. The province applies its local luck to the event roll through whatever formula.

thejeff's phenomenon:

This refers to why thejeff's testing seem to show that events occurence picks up as the turn progress. To be fair we need more data to say anything with any credibility, let's leave this aside for now. Something must be different during his t5-9 compared to t10-15 to account for the increased occurence, off the top of my head:

a) Turn #

Well obviously turn # is most visible, would turn progression be a factor in event generation? Squirreloid's testing seem to say otherwise, since his average event frq on a single province was 36% throughout without seeing thejeff phenomenon. However, it is remotely possible that turn # as a factor only kicks in when there is more then 1 province. I see this as unlikely but possible.

b) dominion

The other thing that could be different is the dominion, but I need to know whether thejeff's data had dominion spreading from Cap on T1 only before I can make any conjecture. Test with philosopher and temples may be revealing if so, maybe in thejeff's test scenario wall in dominion so it only occurs at capital, then letting it max or keeping it low to see, then maybe test if dominion being widespread changes anything.

c-z) ???