The random-nation button favors interesting nations

[Thucydides7]

It would appear that the random-nation button slightly favored interesting or more powerful nations over less interesting, less powerful ones. Not only does it subjectively seem so, but statistics over 400 trials agree, with six-sigma confidence.

The number of times the random-nation button was observed to select each nation over about 400 trials at a year 1444 start are as follows.

Independent nations:

1 Aachen
1 Abenaki
3 Aceh
2 Adal
1 Ajuuraan
2 Albania
1 Algiers
1 Alsace
0 Anhalt
0 Ansbach
0 Apache
2 Aq Qoyunlu
4 Aragon
0 Arakan
0 Ashanti
0 Assam
0 Assiniboine
1 Augsburg
2 Austria
3 Ayutthaya
0 Aztec
1 Baden
2 Bahmanis
1 Baluchistan
1 Bastar
2 Bavaria
1 Bengal
0 Benin
0 Blackfoot
1 Bohemia
3 Bosnia
3 Brandenburg
2 Bremen
2 Brittany
5 Brunei
3 Brunswick
5 Burgundy
2 Byzantium
4 Caddo
1 Candar
4 Castile
2 Ceylon
5 Chagatai
3 Champa
0 Cherokee
0 Cheyenne
1 Chickasaw
1 Chimu
0 Chocktaw
3 Cleves
0 Cologne
2 Comanche
3 Connacht
2 Cree
4 Creek
2 Crimea
1 Cyprus
1 Dai Viet
3 Delhi
2 Denmark
1 Dhundhar
0 Dulkadir
0 East Frisia
6 England
3 Ethiopia
0 Ferrara
0 Fox
7 France
1 Frankfurt
3 Friesland
1 Gelre
4 Genoa
3 Georgia
2 Golden Horde
2 Granada
3 Gujarat
0 Gwalior
0 Haasa
3 Hausa
2 Hedjaz
2 Hesse
3 Hungary
1 Huron
0 Illiniwek
1 Inca
1 Iroqoius
3 Jaisalmer
2 Japan
1 Jaunpur
0 Kachar
3 Kanem Bornu
0 Kangra
2 Karaman
2 Kashmir
1 Kathiawar
4 Kazan
1 Kilwa
3 Koch
1 Kochin
3 Kongo
2 Korea
2 Lan Na
2 Lan Xang
1 Leinster
2 Lenape
3 Liege
3 Lithuania
2 Livonian Order
1 Lueneburg
0 Magdeburg
0 Mahican
0 Mainz
3 Majapahit
2 Makassar
3 Malabar
2 Malacca
1 Mali
2 Malindi
0 Malwa
2 Manchu
3 Mantua
3 Marwar
2 Maya
0 Mecklenburg
5 Mewar
1 Mewat
2 Miami
3 Milan
5 Ming
0 Miqmaq
0 Mombasa
2 Morocco
1 Muenster
2 Multan
2 Munster
2 Muscovy
4 Mutapa
5 Najd
3 Navajo
1 Navarra
1 Nepal
1 Nogai
7 Novgorod
2 Oirat
2 Ojibwe
3 Oldenburg
0 Oman
2 Orissa
0 Osage
3 Ottawa
2 Ottomans
1 Oyo
1 Pawnee
5 Pegu
1 Pequot
1 Pima
4 Poland
2 Pomerania
2 Portugal
2 Potawatomi
2 Powhatan
2 Provence
0 Pueblo
5 Qara Qoyunlu
3 Ragusa
1 Ramazan
0 Riga
2 Ryazan
0 Ryukyu
2 Salzburg
2 Savoy
3 Saxe-Lauenburg
1 Saxony
0 Scotland
1 Serbia
1 Shan
3 Shawnee
0 Shoshone
3 Siena
2 Sind
1 Sioux
1 Songhai
0 Susquehannock
0 Switzerland
5 Teutonic Order
1 The Hansa
0 The Knights
8 The Mamluks
0 The Palatinate
5 The Papal State
2 Tibet
7 Timurids
3 Trebizond
3 Trier
4 Tunisia
3 Tuscany
1 Tver
0 Tyrone
1 Ulm
1 Urbino
0 Utrecht
5 Uzbek
2 Venad
3 Venice
1 Vijayanagar
1 Wallachia
3 Wurttemberg
1 Wurzburg
3 Yemen
3 Zapotec

Lesser partners:

0 Modena
0 Naples
6 Norway
0 Sukhothai
3 Sweden
0 Thuringia
0 Tripoli

Vassals:

0 Armagnac
0 Athens
0 Auvergne
0 Bourbonnais
0 Bundelkhand
0 Corfu
0 Date
0 Foix
0 Garjat
0 Gondwana
0 Hatakeyama
0 Holstein
0 Hosokawa
0 Imagawa
0 Jangladesh
0 Khandesh
0 Khmer
0 Lorraine
0 Mazovia
0 Mogadishu
0 Moldavia
1 Mongolia
0 Naxos
0 Orleans
0 Otomo
0 Ouchi
0 Perm
0 Pskov
0 Shiba
0 Shimazu
0 Silesia
0 Sofala
0 Takeda
0 Taungu
0 Uesugi
0 Yamana
0 Yaroslavl

To establish the aforementioned six-sigma confidence, within each of the above three categories, nations were ranked by their initial position on the game's score-comparison ledger. The random-nation button is then found slightly to prefer higher-ranked nations.

If you do not know what this is all about, but have read this far, anyway: There is a random-nation button on Europa Universalis IV's intro screen. The random-nation button steers you gently toward, say, England; away from, say, Pequot. England and Pequot are both possible when you press the random-nation button, but England is apparently the more likely.

 

[otaman1]

I guess random nations isn't so random after all. I've always been wondering why it keeps bringing me to great powers.

 

[Xinkc]

EDIT: Sorry, misread part of the thread. Anyways, I'd like to hear from a dev on whether or not the Random Nation button is weighted.

 

[MaXimillion]

Tripoli is actually a lesser union partner, not a vassal

 

[Castrolol]

Maybe it rolls a dice on provinces instead of nations and therefore is bias towards bigger nations?

 

[Mauer]

Maybe it rolls a dice on provinces instead of nations and therefore is bias towards bigger nations?

I was gonna say this. Anyway nowhere does it say it's full random, maybe it is weighted like random lucky nations.

 

[ahyangyi]

Maybe it's done by randomly choosing a province, rerolling as long as it's uncolonized, then showing you the country owning that province. It's definitely one of the easier ways to write code for this.

 

[murlocmancer]

Maybe it's done by randomly choosing a province, rerolling as long as it's uncolonized, then showing you the country owning that province. It's definitely one of the easier ways to write code for this.

This would make a lot of sense

 

[Wizzington]

The random button weights for size and tech speed, so yeah it's not totally random.

 

[VampireBoot]

The random button weights for size and tech speed, so yeah it's not totally random.

Is it the same code as for random lucky nations?

 

[Wizzington]

Is it the same code as for random lucky nations?

No, less weighted.

 

[Thucydides7]

The random button weights for size and tech speed, so yeah it's not totally random.

This seems a good idea. Consider for example the several North American Indian tribes, all of which are interesting but most of which play pretty similarly. There are several tribes, but only one England. England plays like no other nation.

Under the circumstance, for gameplay variety and for other reasons, one would prefer that the random-nation button select England more often than it selects any particular North American Indian tribe. It does this, which is good.

 

[Fishman786]

You conducted 400 trials on this?


How did you come up with the initial hypothesis?

 

[Stategem161803]

I guess random nations isn't so random after all. I've always been wondering why it keeps bringing me to great powers.

Random != Uniformly distributed

 

[Thucydides7]

How did you come up with the initial hypothesis?

Not knowing which nations the random-nation button might favor, I conjectured something vaguely plausible, as earlier detailed. Along with the trials, this was all that was needed to establish, statistically, that the random-nation button used something other than a flat distribution, which is what I had wished to prove.

Formally I suppose, the hypothesis was that the distribution had indeed been flat. Formally, the statistics disproved the hypothesis.

 

[unmerged(783218)]

Meh. Stacking up datas like that doesn't show anything. You should classifies the countries in different groups and run analysis of variance test to confirm your hypothesis.

 

[Cymsdale]

Meh. Stacking up datas like that doesn't show anything. You should classifies the countries in different groups and run analysis of variance test to confirm your hypothesis.

Are you ignoring the fact that a dev confirmed his conclusion?

 

[Thucydides7]

Since a developer has confirmed, further discussion of analytical technique is merely of academic interest. So, for academics:

I considered withholding my data, since it is bulky; but had I withheld it, readers would rightly have disbelieved that I had in fact gathered it. So I posted it.

Statistical pedantry is fairly useless in cases like this, since it does not really matter whether Student's T (or whatever) or just a Gaussian distribution is used over 400 samples; but skepticism is good. I certainly do not claim to be a master statistician. Skeptics could either (a) analyze my data as they like or (b) gather their own data. Skeptics could even adopt alternate, plausible definitions of interesting. Regardless, skeptics who take the trouble to complete the exercise can hardly but find what I did; namely, that the random-nation button favors interesting nations.

As to the statistics themselves: Ranking the independent nations 1 through 210 as earlier explained, for a flat distribution, the average rank returned by the random-nation button ought to have been 105.5. The average rank was observed however to be 86.3. Of course, one must complete enough trials to make such an average statistically significant, which I did. I used a population deviation sqrt(N) rather than a sample deviation sqrt(N-1), and I used it on a Gaussian distribution, since specialized distributions are not very relevant over 400 samples. The rms deviation per sample from the mean was supposed to be 210/(2*sqrt(3)), which is right for a continuous flat distribution, though of course is only an estimate for the unknown distribution in question. I did not adjust my deviation per sample to the observed mean, but you can do that if you like; it won't matter much. And if you do not know what this is all about, that's all right. I am no master statistician, either. But for readers who are master statisticians, why, they now have my data and a basic explanation of my technique, so they can do the math, themselves, if they wish.

None of this is important, of course. We are talking about a video game, after all. I had a question, though, Google found no answer, I was curious, and I knew just enough about the science of statistics to carry out an experiment, so that is what I did. Next time someone is curious about the random-nation button and interesting nations in Europa Universalis IV, Google can find this answer for them.

Update: Since it came up, in case anyone cares, adjusting to the observed mean changes the confidence interval from 6.3 to 6.4 sigma. And if someone wants yet more refined statistics, why, they have my data and can calculate whatever statistics they like, themselves. They can apply a nonheuristical ranking, use Student's T, analyze variance, whatever they like. (My guess is that no one will, but they can, if they like.) The conclusion though is not likely to change, though: the random-nation button indeed favors interesting nations.

Since this is not an academic journal but a video-game forum, and since I am not an academic, I had better leave it there.

 

[unmerged(783218)]

Are you ignoring the fact that a dev confirmed his conclusion?

No. But I was expecting a bit more rigorous treatment of datas before coming up with any conclusions.
Statiscal treatment could have proven that being a vassal/under a PU doesn't interfere, and show a correlation between tech, size and occurence.
But that was a mere grumpy scientist's observation to say that you should not come up with conclusions without any statistical treatments.

Also, the dev said there is a weighting, but not to wich extand. We could hypothesize a formula and test it with the datas :laugh:

 

[Thrake]

No. But I was expecting a bit more rigorous treatment of datas before coming up with any conclusions.
Statiscal treatment could have proven that being a vassal/under a PU doesn't interfere, and show a correlation between tech, size and occurence.
But that was a mere grumpy scientist's observation to say that you should not come up with conclusions without any statistical treatments.

Also, the dev said there is a weighting, but not to wich extand. We could hypothesize a formula and test it with the datas :laugh:

Well, please prove me that being a vassal or a PU doesn't interfere.