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So, I’m doing some tests about the breakthrougs to see how they work. Before we go any further let me explain some thing: The tests were made without deep scan, but I'll do some latter tests with deep scan, since they take longer I'll have to wait a bit, so this thread, so far, makes statistics of ONLY early game.


What I found out with my tests:

1 - All breakthrough anomalies are predetermined by the game;
2 - Each map has its own anomalies and they are ALWAYS in the same places;
3 - Most maps I saw have between 6 and 8 breakthrough anomalies;
4 - For some odd reason I don't know yet all sponsors share the same anomalies places except Europe;
5 - Paradox Sponsor share the same anomalies places than others with a few more, those few more aren't the same anomalies that Europe has.


Methodology:

The methodology I used is divided in 2 steps, the first step is to determine where the anomalies are, the second step is to determine the percentage of each breakthrough to see if they have the same weight or if there are some more rare than others.

I used the map 1N107E to do the major tests, but in order to verify if Europe is different than the others in all maps I also run tests in 10N100E.

In 1N107E the anomalies are on: A0, E3, F1, G1, I3 and J6 for International Mars Mission, USA, Blue Sun Corp, China, India, SpaceY, Church of the New Ark and Russia. For Europe the anomalies are on: D9, E3, F1, G1, H7 and J0. For Paradox Interactive the anomalies are A0, E3, F0, F1, G1, I3 and J6.

Please notice here that the Paradox has all the same anomalies than the others except Europe plus one more which is F0. Also notice that Europe shares half of the points which are E3, F1 and G1, the other 3 aren't the same, which are D9, H7 and J0.

The second map I used to see if this applies in Europe only is the 10N100E, the points are on: A1, A4, B9, C4, C5, C8, E0, F6 and G8 for International Mars Mission, USA, Blue Sun Corp, China, India, SpaceY, Church of the New Ark and Russia. For Europe the anomalies are on: A1, A4, C4, C8, E0, F6, G7, G8 and G9. For Paradox Interactive the points are on: A1, A4, B9, C4, C5, C8, E0, F6, G7, G9 and J6.

Notice here that this map has 8 points instead of 6, since I didn't do the deep scan I dont know if this map has less anomalies in deep scan than the other, but for a early game this map has a higher possibility of good anomalies than the other one since you have straight access to 8~10 anomalies. Notice here also that once again Europe has points that aren't the same the rest of the sponsors, and also notice that Paradox share points with the others with a plus extra. Also notice here that Paradox has 10 points, which represent 2 extra instead of 1 on the other map, so I think the game calculates it based on a percentage.

Now that we know the points are fixed on the map I'll pass to the methodology I used to get the results:

1 - Started with 50 probes or the maximum I could (Paradox can only 40) and scanned all the map;
2 - So I wrote down the sectors the anomalies are;
3 - I restarted the game with 10 probes and 4 explorers on the map 1N107E;
4 - I scanned all the anomalies 5 times with each sponsor and wrote it down in a Google Sheet;
5 - This represented 305 scanned anomalies;

I also found out that if you restart the game without returning to main menu most of the anomalies with remain the same but switching places, but if you return to the main menu you'll get new anomalies, so each time I restarted a game to scan I returned to main menu.

Now lets see the statistics about the scans:

In my tests I found out that the most common breakthrough is Vocation-Oriented Society while the most rarer is: Nocturnal Adaptation, followed by Dome Streamlining, Neo-Concrete, Service Bots, Soylent Green and Superconducting Computing.

You can see the whole test here.