Sovereignty

Sovereignty is the most general indication of a Khan's power. Several factors determine a Khan's sovereignty; the primary factor being the attributes of advisors. Sovereignty may also be gained from heirs and marrying off heirs. The overall sovereignty S of a player is simply the sum of attributes (S, equivalent to sovereignty) of all advisors a and heirs h. The heir calculation includes all heirs: married heirs, unmarried heirs, growing heirs, and heirs' spouses.
S \equiv \sum_{a}{S_a} + \sum_{h}{S_h}
==Advisor Attributes==
The sovereignty S_a for an attribute a is the sum of the talent B_T, consort B_C, presence B_R, pet buff B_P, equipment B_E, outfit B_O, and legion B_L bonuses:
S_a = B_T + B_C + B_R + B_P + B_E + B_O + B_L
The bonuses can be calculated as follows, where L is the current advisor level, s denotes advisor star level, :
B_T = g(s,c) T [\frac{(L-1)(L+2)}{50}+2] + k(s,c)\\
B_C = B_T b_{s4}(L_{s4}) + \sum_{i=1}^{3}{B_{si}(L_{si})}\\
B_R = B_T b_R\\
B_E = b_{e4}(B_{e1}+B_{e2})\\
B_P = B_{LP} + \sum{B_{tP}}
==Star Bonuses==
The star bonuses, dependent on star level s and advisor colour c consists of two types, a percentage bonus g_a(s,c) and a fixed bonus k_a(s,c). Each advisor has different values for both of these for every attribute a. A table for these values for a 5-star advisor s=5 is shown here:
c 	g_1(5,c)	g_2(5,c)	g_3(5,c)	g_4(5,c)
Green 	0.96 	1.10 	1.34 	1.44
Blue 	 	 	 	
Purple	1.17 	1.32 	1.61 	1.72
Gold 	1.34 	1.49 	1.80 	1.91
Red 	1.50 	1.66 	1.99 	2.11
c 	k_1(5,c)	k_2(5,c)	k_3(5,c)	k_4(5,c)
Green 	16.12 k 	19.76 k 	24.44 k 	25.48 k
Blue 	 	 	 	
Purple	96.72 k 	118.56 k	146.64 k	152.88 k
Gold 	362.7 k 	444.6 k 	549.9 k 	573.3 k
Red 	1.254 M 	1.536 M 	1.902 M 	1.981 M
==Heirs==
Details can be seen in Heirs.