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Sunday, May 24, 2015

The one true EU4 idea group ranking

kitten on the keys by Chris Blakeley from flickr (CC-NC-ND)

People just love to discuss EU4 idea groups, and to be honest almost everything they say is completely wrong.

I have no intention of joining this making stuff up contest, so instead here's a ranking that's as close to correct as it's possible to get.

The algorithm not only gives meaningful relative rankings, it gives meaningful absolute values - expressed in monarch points.

I've written it a while ago, but I'm posting it now, as next patch will mess with the values.

The Algorithm and its limitations

Value of +1 monarch point per month is 1, and that's the unit everything is expressed in. As dip/adm are far more valuable than mil, they're both worth 1.1 and mil is just 0.8, so they average to correct value.

The game has huge number of bonuses, and they're reduced to other bonuses based on some sensible assumptions. Algorithm has simple models of income, spending, military power, envoy use, monarch point budget and so on, and given such assumptions vast number of bonuses can be reduced to just a few.

The ranking has serious limitations, which are completely unavoidable:
  • Assumptions used to calculate point values are based on a typical country, at typical point in the game - maybe extra colonists wouldn't be much use for you as Ulm and maybe you really value galley combat strength over everything else as 1444 Byzantium, but ranking merely expresses how good those bonuses would be on average
  • Algorithm is completely linear. It tries to estimate how good +1 of some bonus would be, and makes linear extrapolation from there. Some bonuses are better in multiples (-10% galley cost is weak, but -100% galley cost is pure exploit territory), some are weaker in multiples (like you really need that 6th missionary most of the time), the algorithm just tries to estimate how much value would an extra one have for a typical country. The game is helpfully linear, so two +10% bonuses are identical to +20% bonus, but that's not the same as being twice as good.
  • Algorithm for the same reason ignores any synergies or anti-synergies between different bonuses.
  • Algorithm just focuses on bonuses, it ignores all events, decisions etc. based on idea groups.
  • Algorithm ignores order of bonuses, so it doesn't care if good ones are early or late.
There are also limitations which could be improved upon:
  • Assumptions and numbers are reasonable ballpark estimates, but they don't have amazing precisions, and you could easily tweak them getting somewhat different rankings.
  • After we reduce handful of bonuses to some values like "5% higher income", "10% more powerful armies", or "1 extra diplomat", how do they compare with universal unit of +1 monarch point/month? Numbers I've chosen here could definitely be challenged.
  • There is not enough distinction made between "X" and "base X". For many things it's just fine, but "trade income" and "base trade income" are typically quite far from each other, so good ballpark estimate of trade income would still give wrong estimates of how much trade income bonuses are worth, as they apply to base trade income instead.
  • There could be bugs.
Fortunately it turns out that numbers algorithm returns are not even close - some ideas are drastically better than some others, which makes worries about precision less important.

A few examples

The whole algorithm is on github. Here I'll just present some examples of the kind of reasoning it uses.

Algorithm estimates that typical country spends 40% of its budget on land forces, and 50% of its army budget on infantry, so -10% infantry cost is equal to -4% army cost, or +2% extra money.

Algorithm estimates that you'll be hitting +1 stability button once every 15 years, and its base cost is 100 (actual cost is irrelevant due to how bonuses stack). So -X% stability cost bonus is worth +X adm points every 180 months. In other words -10% stability cost is estimated as +0.055 monthly admin or +0.061 average monarch point (as adm mp is worth 1.1 mp).

Algorithm calculates that throughout the game you'll spend 4 points a month for base cost of techs - this is surprisingly robust, as we know how many years there are in game, how many techs start to end, and what it's base cost (600/tech). It doesn't need to know how much you're paying for actual techs, bonuses are applied to base cost. So -10% tech cost is worth as much as +0.4 bonus to each monarch point, or +1.2 points/month total.

Algorithm estimates that diplomats spend 25% of their time travelling, colonist 10%, and merchants 1% (missionaries just teleport), and average country has 2 diplomats, 2 merchants, and 1 colonist, so -X% envoy travel time is comparable to +2 * 25% * X% diplomat, +2 * 1% * X% merchant, and +1 * 10% * X% colonists.

Algorithm estimates that usually stability is what you'll be using papal points for, so 100 papal points is about as good as 100 adm. Then it converts +1 yearly papal points to +1/12 montly adm points, and takes 50% as good guestimates how likely you are to be able to take advantage of that. That 50% is somewhat dubious, as much fewer than 50% of countries are Catholic, but typically European countries get this kind of bonuses.

Algorithm estimates that for a typical country, 25% of infidel provinces are heretics, and 75% are heathens, so +1% missionary strength against heretics is worth as much as +0.25% against everyone.

Algorithm estimates that extra siege pip speeds up sieges by 17% (that's based on some spreadsheet simulations), and 30% of sieges have leaders (that's just a guess), so +1 leader siege is worth 5.1% siege ability.

If you're interested in such calculations, script explains its choices in comments pretty well.

And it all reduces to...

The last step is most arbitrary, covering all things that have no good conversions:
  • +1 colonist - +3 points
  • +1 diplomat - +2 points
  • +1 missionary - +1 point
  • +1 merchant - +1 point
  • +1% missionary strength - +1 point
  • -1 unrest - +1 point
  • -0.1 autonomy - +1 point
  • -10% warscore cost - +1 point
  • +10% money - +1 point
  • +20% siege ability - +1 point
  • +10% defensiveness - +0.1 point
  • +10% military power - +1 point
  • +10% manpower - +0.3 point
  • +25 colonial growth - +1 point
  • +0.5 point for every minor ability (like infiltrate administration, reduced stab impact etc.)
  • +1 point for extra CB (religious CBs are treated as 2 different CBs)
  • +1 annual legitimacy - +0.5 point
  • +1 annual republican tradition - +1 point
  • ability to explore - +2 points
  • +1 advisor pool size - +1 point
  • +1% hostile attrition - +1 point
  • 10% better relations over time - 0.2 points
  • -10% AE impact - 0.2 points
  • +1 diplo rep - +1 point
A lot of bonuses like prestige, IA, fervor, heir chance, trade range, interest, ship recruitment speed, enemy core creation, spy offence etc. are ignored completely as either far too situational to be of use to a typical country, or basically pointless.

To help with those numbers I took decisions and policies like "+1 missionary strength +1 unrest" (maybe yes, maybe no - so these bonuses are worth about the same), "+1 colonist for -1 dip" (so ridiculously good so they removed it in patch), which is not terribly scientific, but it's a good starting point.

Idea groups

And here's the ranking of idea groups:
  • 11.76 Exploration Ideas
  • 9.54 Religious Ideas
  • 8.23 Diplomatic Ideas
  • 7.58 Expansion Ideas
  • 5.22 Humanist Ideas
  • 4.80 Influence Ideas
  • 4.50 Plutocratic Ideas
  • 4.14 Trade Ideas
  • 4.10 Aristocratic Ideas
  • 3.62 Espionage Ideas
  • 3.58 Defensive Ideas
  • 3.42 Innovative Ideas
  • 3.40 Quantity Ideas
  • 2.40 Offensive Ideas
  • 1.94 Economic Ideas
  • 1.66 Administrative Ideas
  • 1.35 Quality Ideas
  • 0.96 Maritime Ideas
  • 0.56 Naval Ideas
As you can see every single military idea is total crap, and naval/maritime are just ridiculously bad. I don't expect anybody to possibly be surprised by top 5.

National ideas

And here's the ranking. Personally I'd value Russian, Spanish and American ideas above Najdi - Najdi ideas are very good, but its +5% missionary strength is perhaps not worth 5x as much as +1% missionary strength bonus would be, so algorithm's linear character arguably overestimates it.

Only one country has ideas which algorithm estimates as (within margin of error) worse than default ideas, and I totally agree with this assessment.
  • 10.85 Najdi Ideas
  • 10.49 Muscovite Ideas
  • 10.36 Spanish Ideas
  • 10.10 American Ideas
  • 8.88 Colonial Ideas
  • 7.54 Jerusalem Ideas
  • 6.96 Byzantine Ideas
  • 6.92 Norwegian Ideas
  • 6.86 Bremen Ideas
  • 6.74 Austrian Ideas
  • 6.55 Manchu Ideas
  • 6.49 Sukhothai Ideas
  • 6.42 Mapuche Ideas
  • 6.42 Assamese Ideas
  • 6.39 Canadian Ideas
  • 6.38 Carib Ideas
  • 6.32 Teutonic Ideas
  • 6.32 Bosnian Ideas
  • 6.29 Native Ideas
  • 6.24 Iroquois Ideas
  • 6.15 Kievan Ideas
  • 6.08 French Ideas
  • 5.84 Lan Xang Ideas
  • 5.79 Kanem Bornuan Ideas
  • 5.73 Québécois Ideas
  • 5.63 Romanian Ideas
  • 5.55 Divine Ideas
  • 5.51 Kurdish Ideas
  • 5.41 Cherokee Ideas
  • 5.38 Malayan Sultanate Ideas
  • 5.37 German Ideas
  • 5.36 Provençal Ideas
  • 5.34 Palatinate Ideas
  • 5.32 Armenian Ideas
  • 5.27 Krakowian Ideas
  • 5.26 Shawnee Ideas
  • 5.20 Japanese Ideas
  • 5.11 Tibetan Ideas
  • 5.09 Knights Hospitaller Ideas
  • 5.07 Welsh Ideas
  • 5.03 Ajuuraan Ideas
  • 5.01 Mossi Ideas
  • 4.95 Savoyard Ideas
  • 4.92 Vindhyan Ideas
  • 4.91 West African Ideas
  • 4.88 Central Indian Ideas
  • 4.86 Novgorod Ideas
  • 4.86 Trebizond Ideas
  • 4.79 Javan Ideas
  • 4.78 Lithuanian Ideas
  • 4.67 Karamanid Ideas
  • 4.58 Hungarian Ideas
  • 4.56 Songhai Ideas
  • 4.53 Sinhalese Ideas
  • 4.48 Moldavian Ideas
  • 4.47 Papal Ideas
  • 4.45 Hausan Ideas
  • 4.45 Tapuian Ideas
  • 4.44 Bulgarian Ideas
  • 4.44 Ragusan Ideas
  • 4.43 Athenian Ideas
  • 4.42 Polotskian Ideas
  • 4.42 Fulani Jihad Ideas
  • 4.40 Danish Ideas
  • 4.40 Irish Ideas
  • 4.39 Sumatran Ideas
  • 4.35 Client State Ideas
  • 4.34 Circassian Ideas
  • 4.33 Pskovian Ideas
  • 4.31 Transylvanian Ideas
  • 4.26 Finnish Ideas
  • 4.24 English Ideas
  • 4.23 Horde Ideas
  • 4.22 Ryukyuan Ideas
  • 4.18 Afghan Ideas
  • 4.15 Scottish Ideas
  • 4.13 Siberian Ideas
  • 4.10 Italian Ideas
  • 4.10 Polish Ideas
  • 4.09 Montenegrin Ideas
  • 4.06 Prussian Ideas
  • 4.04 Swahili Ideas
  • 4.03 Dai Viet Ideas
  • 4.01 Ashanti Ideas
  • 4.00 Ethiopian Ideas
  • 4.00 Chinese Ideas
  • 3.99 Ryazan Ideas
  • 3.98 Huron Ideas
  • 3.96 Bohemian Ideas
  • 3.96 Kongo Ideas
  • 3.92 Nepali Ideas
  • 3.90 Siddi Ideas
  • 3.90 Tarascan Ideas
  • 3.89 Hejazi Ideas
  • 3.89 Wallachian Ideas
  • 3.87 Ayutthayan Ideas
  • 3.85 Breton Ideas
  • 3.81 Bavarian Ideas
  • 3.79 Bahmani Ideas
  • 3.77 Mesoamerican Ideas
  • 3.77 Anatolian Ideas
  • 3.74 Zaporozhian Ideas
  • 3.71 Vijayanagar Ideas
  • 3.70 Yaroslavlyian Ideas
  • 3.69 Khmer Ideas
  • 3.68 Brazilian Ideas
  • 3.67 Holstein Ideas
  • 3.63 Mexican Ideas
  • 3.63 Arabian Ideas
  • 3.61 Shan Ideas
  • 3.55 Chachapoyan Ideas
  • 3.54 Kazani Ideas
  • 3.52 Taungu Ideas
  • 3.51 Portuguese Ideas
  • 3.51 Pueblo Ideas
  • 3.47 Mughal Ideas
  • 3.45 Milanese Ideas
  • 3.43 Ottoman Ideas
  • 3.41 Khivan Ideas
  • 3.41 Wurzburgian Ideas
  • 3.40 Aztec Ideas
  • 3.39 Daimyo Ideas
  • 3.37 Ruthenian Ideas
  • 3.35 Venetian Ideas
  • 3.33 Air Ideas
  • 3.33 Candarid Ideas
  • 3.30 Hamburger Ideas
  • 3.29 Malian Ideas
  • 3.28 Swedish Ideas
  • 3.27 Theodoro Ideas
  • 3.22 Saxon Ideas
  • 3.22 Indian Sultanate Ideas
  • 3.22 Jaunpuri Ideas
  • 3.20 Croatian Ideas
  • 3.17 Hessian Ideas
  • 3.17 Naxian Ideas
  • 3.17 Serbian Ideas
  • 3.16 Dutch Ideas
  • 3.14 Berber Ideas
  • 3.11 Guarani Ideas
  • 3.10 Couronian Ideas
  • 3.10 Ming Ideas
  • 3.09 Muiscan Ideas
  • 3.09 Navarran Ideas
  • 3.04 Tuscan Ideas
  • 3.03 Beninese Ideas
  • 3.03 Cypriot Ideas
  • 3.02 Korean Ideas
  • 3.01 Tverian Ideas
  • 3.01 Bengali Ideas
  • 3.01 Arawak Ideas
  • 3.00 Granada Ideas
  • 3.00 Gujarati Ideas
  • 2.99 Creek Ideas
  • 2.99 Punjabi Ideas
  • 2.96 South Indian Ideas
  • 2.90 Danziger Ideas
  • 2.86 Georgian Ideas
  • 2.84 Silesian Ideas
  • 2.82 Incan Ideas
  • 2.77 Italian Ideas
  • 2.70 Chimu Ideas
  • 2.67 Permian Ideas
  • 2.64 Timurid Ideas
  • 2.55 Chickasaw Ideas
  • 2.42 Omani Ideas
  • 2.41 Dahomey Ideas
  • 2.38 Mogadishan Ideas
  • 2.35 Hanseatic Ideas
  • 2.32 Charruan Ideas
  • 2.31 Maratha Ideas
  • 2.31 Mamluk Ideas
  • 2.22 Pacific Northwest Ideas
  • 2.20 Orissan Ideas
  • 2.18 Aymaran Ideas
  • 2.16 Smolenskian Ideas
  • 2.04 Persian Ideas
  • 2.02 Rajput Ideas
  • 1.92 Swiss Ideas
  • 1.91 Pomeranian Ideas
  • 1.87 Burgundian Ideas
  • 1.87 Tupi Ideas
  • 1.79 Neapolitan Ideas
  • 1.73 Gutnish Ideas
  • 1.72 Andean Ideas
  • 1.60 Caucasian Ideas
  • 1.51 Albanian Ideas
  • 1.44 Aragonese Ideas
  • 1.34 Default National Ideas
  • 1.30 Genoese Ideas

7 comments:

Anonymous said...

Your flat values are just flawed.

Colonist should be at best 2, and diplomat at best 1,5.

You should have realised something went horribly wrong when espionage wasnt in last 3.

taw said...

Anonymous: I'm aware that internet thinks espionage is awful and military ideas are amazing, but calculations say otherwise, and I trust calculations.

Weight changes you mentioned are reasonable, but they wouldn't really change ranking that much.

Jessica Reyes said...

It's so cool that there's even an algorithm used. I'm glad that my teacher who teaches me polish using Skype at http://preply.com/en/polish-by-skype mentioned this. I totally agree with the ranking.

Anonymous said...

Really cool concept but the other anon has a point. The flat values grossly overvalue diplomats and undervalue manpower, morale and discipline.

Anonymous said...

Really cool idea but i guess the problem is raking idea groups without context - exploration may be good, but in some situations its useless. From my perspective when you're talking about which are the better idea groups you're looking for the ones that hold the most value regardless of the situation you are in, which is why the military ones tend to be the ones that stand out. Similarly some idea groups kind of overlap to the point in which it would be detrimental to take both of them, Religious and Humanist for example, and in those cases the weaker idea group becomes significantly less optimal.

Also, you can't defend espionage and not try to back it up :P. I cannot see how its a case of people hating it more than it deserves, I've tried to find the vaule but those ideas are useless.

And in case you're wondering, its a tie between religious and quantity for the best idea group, regardless of the situation they are both incredible and they are probably the only two idea groups that don't have something completely awful tucked inside them somewhere.

Peter Novák said...

Great attempt on summarizing it all, but there are some really serious flaws to the values.

For instance modifying papal influence by a chance to be a catholic has no logic, since every nation having this is catholic. Also on the same note - stab costs 100 if not modified, the further stability over 1 cost much more and those are the ones you spend your papal influence on - hence its value is amore than a bit off.

Advisor pool +1 cost equals one point? Really? I never found it even remotely useful.

Missionary equals one missionary strength? Now this is completely wtf. This is true only if your positive missionary strength is equal to the number of missionairies, which is likely never. Also these two are extremely interdependent.

But especially, all your claims about military being useless are based on making 10 percent increase worth 1 point. This is really ludicrous. I mean, seriously, do you think that having two diplomats a two diplomatic reputation is worth having 60 percent stronger armies? Is there any argument you can base this assesment on?



Anonymous said...

I disagree with MIL MP being the least valuable. A single MIL tech advantage can win battles and even wars for you. Especially the ones that give boost in both morale and tactics. For instance, tech 4 Korea can single-handedly take on tech 3 Ming. That's how important MIL MP is. Dip MP should've been the one with 0.8 value. There's no other use for it aside of reducing WE and annexing vassals, and usually your provinces end up with high production points because there's no other way to spend that overflowing DIP points.