Can't vassalise due to insufficient base tax?

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After making clear how tax base works, I have renewed my study. As a sidenote, tax base includes your capital bonus, temples and half of your vassal's tax base.
The examples are no longer restricted to OPMs.
Observing from the Ottomans, after annexing Albania. Tax base=100.
Country name; tax base; opinion modifier
Connacht; 4; +30
Naxos; 5; +30
Munster; 6; +30
Mecklenburg; 7; +29
Urbino; 8; +2
Liege; 9; -17
Aachen; 10; -31
Magdeburg; 11; -41
Salzburg; 12; -49
Serbia; 13; -55
Brunswick; 14; -59
Yemen; 15; -63
Oman; 16; -67
Pomerania; 17; -69

My conclusion: if target state has a tax base smaller than 7% of yours, then a +30 opinion bonus will apply. If target state has a tax base larger than 12% of yours, then you need to have huge positive buffs to offset the 50+ opinion penalty. If the tax base ratio is between 7% and 12%, then the vassalization will be somewhat similar to 1-3 province states pre-1.2.
 
Thank you for your analysis, I'm also playing an Ottomans game and vassalisation of Tripoli was really smooth, while I cannot vassalise Tunisia because of this modifier. I guess it's because of of Tunis' high tax base. So the solution for this is both to expand and to build temples?
 
I have compiled 3 more sets of data, to reveal the rough extent of vassalization you can do, especially for huge blobs:

1. Hungary, game start, 58 tax base.
Country name; tax base; opinion modifier.
Albania; 3; +30
Connacht; 4; +30
Naxos; 5; +30
Munster; 6; +3
Mecklenburg; 7; -21
Urbino; 8; -36
Liege; 9; -47
Aachen; 10; -55

2. France, a game into 1682, 857 tax base.
Tax base; opinion modifier.
10; +30
20; +30
22; +16
24; -1
26; -14
29; -29
30; -33
32; -40

3. France, a game into 1820, 3623 tax base.
Tax base; opinion modifier.
16; +30
33; +30
39; +30
44; +22
45; +17
46; +13
62; -33
72; -48
77; -53
106; -71
 
Nice data bleakie!
Unless someone pop up and reveal the answer this is a very interesting math problem to figure out.
From these numbers it certainly look like the 'break-even' point is somewhere around the square root of your tax base. I have to try more to figure out the scaling and intersect...
 
Nice data bleakie!
Unless someone pop up and reveal the answer this is a very interesting math problem to figure out.
From these numbers it certainly look like the 'break-even' point is somewhere around the square root of your tax base. I have to try more to figure out the scaling and intersect...

It seems that the square root of tax base is the point for a -30 modifier. It matches all the 4 sets of data.

And the break-even point is 80% of the square root of tax base.
 
Nice data bleakie!
Unless someone pop up and reveal the answer this is a very interesting math problem to figure out.
From these numbers it certainly look like the 'break-even' point is somewhere around the square root of your tax base. I have to try more to figure out the scaling and intersect...

This is all that is so great about the EU players. 4 minutes after an extensive data collection on the impact of tax base on diplo-vassalising is posted, someone else figures out that the square root is the probable factor.

Great work both of you! Now, if we could just lure Kanitatlan out of retirement to do the combat math ;)
 
What is a resonable amount of positive modifiers you can expect to get? Because looking at those values it seems only very rich/large nations will be able to diplo-vassalize anything that isn't an OPM.
 
What is a resonable amount of positive modifiers you can expect to get? Because looking at those values it seems only very rich/large nations will be able to diplo-vassalize anything that isn't an OPM.
Threatened/Friendly attitude +10, superiority in military +20, diplomatic reputation +1 per point, trust for single digit boost.
I doubt you can get more than +45 without counting the tax base.
 
This penalty seems excessively large in comparison to the other modifiers to vassalization, particularly at the stage where it kicks in. I'm playing a game as an almost fully formed France right now and with a base tax of over 200, I can't vassalize Lorraine, which only has 2 provinces that have 12 base tax total.

I think either or both of the size of the modifier and the calculation for when it is applied need some adjustment. Or they need to readjust the other modifiers to compensate for it somewhat. As it stands, peaceful expansion in certain regions is nearly impossible.
 
This penalty seems excessively large in comparison to the other modifiers to vassalization, particularly at the stage where it kicks in. I'm playing a game as an almost fully formed France right now and with a base tax of over 200, I can't vassalize Lorraine, which only has 2 provinces that have 12 base tax total.

I think either or both of the size of the modifier and the calculation for when it is applied need some adjustment. Or they need to readjust the other modifiers to compensate for it somewhat. As it stands, peaceful expansion in certain regions is nearly impossible.
If Lorraine has 2 temples, its tax base is 16 with the capital bonus. That means 256 tax base will yield a -30 modifier, which should be good enough for you to diplo-vassalize Lorraine. Try to gain a few more dozens of tax base, and the change will be quite dramatic when it comes.
 
Just a note on the trust, it can actually go a lot higher. I currently have +38 trust bonus with an Orthodox Yemen holding Ethiopia & Aden. I'm not sure of the exact base taxes involved, but I hold Italy, Greece, Tunis, Tripoli, Syria with the Mamluks & Hedjaz as vassals. Sums up to -74 base tax modifier (I haven't finished temples everywhere yet either) with -10 for different religions. With +38 trust, +20 mil, +13 dip rep, +10 threatened I have +81. With either the +5 dip rep event or a change in religion they would be vassalisable.
 
Vassal Number = 1.5 * (Vassal Base Tax)^2
([Vassal Number]-[Your Base Tax])/ [Vassal Number]* - 90
Capped at 30

For all the datapoints except 2, this fits, just pulled some numbers out of my ass, I'm too tired to do math

3 30 58 13.5 296.6666667 30
4 30 58 24 127.5 30
5 30 58 37.5 49.2 30
6 3 58 54 6.666666667 6.666666667 --doesn't fit here
7 -21 58 73.5 -18.97959184 -18.97959184 --or here, ninja edit
8 -36 58 96 -35.625 -35.625
9 -47 58 121.5 -47.03703704 -47.03703704
10 -55 58 150 -55.2 -55.2



10 30 857 150 424.2 30
20 30 857 600 38.55 30
22 16 857 726 16.23966942 16.23966942
24 -1 857 864 -0.729166667 -0.729166667
26 -14 857 1014 -13.93491124 -13.93491124
29 -29 857 1261.5 -28.85850178 -28.85850178
30 -33 857 1350 -32.86666667 -32.86666667
32 -40 857 1536 -39.78515625 -39.78515625



16 30 3623 384 759.140625 30
33 30 3623 1633.5 109.6143251 30
39 30 3623 2281.5 52.91913215 30
44 22 3623 2904 22.28305785 22.28305785
45 17 3623 3037.5 17.34814815 17.34814815
46 13 3623 3174 12.731569 12.731569
62 -33 3623 5766 -33.44953174 -33.44953174
72 -48 3623 7776 -48.06712963 -48.06712963
77 -53 3623 8893.5 -53.33614438 -53.33614438
106 -71 3623 16854 -70.65325739 -70.65325739
 
There is a simpler representation for the formula.
Adjusted power ratio = [Your tax base] / [Target tax base]^2
Attitude modifier = 60 * Adjusted power ratio - 90, capped at +30.

I use Xesttub's equation as the base model, and fit the available data set for the correct parameters.

I'm not sure of the exact base taxes involved

You can check your tax base in the economy tab.
 
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way to exploit:

- start as Norway (4 colonists nation);
- Sell all provinces except one to Sweden;
- Moove your capital to America;
- Colonize and core all America & have the biggest tax base in the world;
- Vassalize & annex them all.
:laugh:
 
... snip...

I'm a little lost in these calculations.

Is adjusted power ratio = [Your tax base] / [Target tax base]^2

or is it adjusted power ratio = [Your tax base]^1/2 / [Target tax base] ?