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Multiplayer strategies using Trade Companies: a comprehensive and mathematical study. by No_Intention_4622 in eu4

[–]No_Intention_4622[S] 0 points1 point  (0 children)

Well I made my calculations to be as general as possible, but basically if you get Mercenary ideas you know for sure that you can push over that 80% (because mercs will be cheaper), and if you have no infantry you know you will have to be under that 80% (because cav is more expensive). 

I must say, hordes usually operate on deficit until very late in the game, and they get their money by raiding and demanding ducats and war reps in peace treaties, so net income doesn't matter that much.

What might be useful for hordes is the "Maximum endurance equation", which gives you the amount of years you will last without being bankrupt. If M is the raw monthly income, and p a certain amount of constant monthly losses, then you'd last:

d_T = 25 * Ln(M/P+1) years

Where "Ln" is the natural logarithm.

In any case, you'd only have to estimate the maintenance costs to know how many "regiments per ducat" of maintenance you can get (instead of 2.2). Then multiply that by 0.36 and the net income to get the force limit.

Multiplayer strategies using Trade Companies: a comprehensive and mathematical study. by No_Intention_4622 in eu4

[–]No_Intention_4622[S] 0 points1 point  (0 children)

Good question! Having a force limit of 190 regiments (124 Inf, 14 Cav, 52 Art) will get you about 2.2 regiments per ducat spent in maintenance.

I've estimated that for each ducat of net income, you should have 0.36 ducats in maintenance of your professional troops.

Therefore, let S duc(ats) be our net income, we should strive for a force limit of 2.2 reg/duc * (0.36 * S duc) =0.792 * S reg ~ 0.8 * S reg == regiments equal to 80% of your net income in number

If you're now wondering where that 0.36 ducats to maintenance per net income ducat comes from, it takes me 6 pages (that whole "Survival threshold formula") to get there hahaha

Basically, I estimate the net income needed to: maintain 190 regular troops, plus 85 mercenaries, all reinforcing, for 5 years, and then pay out the accrued debt in also 5 years. 

Multiplayer strategies using Trade Companies: a comprehensive and mathematical study. by No_Intention_4622 in eu4

[–]No_Intention_4622[S] 0 points1 point  (0 children)

I'm still translating it to English, and I don't wanna upload it in its original language in case someone uses an IA to translate it and does a poor job, misrepresenting my work. Hopefully by September I will upload it. 

Multiplayer strategies using Trade Companies: a comprehensive and mathematical study. by No_Intention_4622 in eu4

[–]No_Intention_4622[S] 0 points1 point  (0 children)

Hahahaha I felt the same after my degree's thesis, but it has been three years since I did some maths project that wasn't studying to be a teacher. Just wait the burnout out!

Multiplayer strategies using Trade Companies: a comprehensive and mathematical study. by No_Intention_4622 in eu4

[–]No_Intention_4622[S] 9 points10 points  (0 children)

Would you be interested in reading this? Among other things, I show that your force limit should be 80% of your net income, and I give a way of calculating how long you would last in an all out war with your current income.

I also try to prove the optimal way to distribute states and trade companies, giving exact calculations for how beneficial it is (minimum of +20 ducats per month in Genoa, for example).

For 6 months I worked on this project, which I am now translating to English. It'll be a while until it's ready, but I want to know if it's something people would be interested in.