Real examples of corruption.
Here are the formulas. I have removed factors which don't apply to our case (communal corruption, commercial trait, etc).
Nopt = 20 * (.8 + 3/8*Nwe + 0.25*Ni )
Cd = (0.5^Ni * Gd) / 50
Cr = R / (2 * Nopt)
C = Min( Cd + Cr, .9 )
Where:
Gd = distance from nearest corruption-reducing building
Nwe = 1 if FP, 0 otherwise
Ni = 1 if court, 0 otherwise
Cd = Corruption from distance
Cr = Corruption from rank
C = Total corruption
With FP, no court, Nopt = 20 * (.8 + .375 ) = 23
W/O FP, no court, Nopt = 20 *.8 = 16
With FP, court, Nopt = 20 * (.8 + .375 + .25 ) = 28
W/O FP, court, Nopt = 20 *(.8 + .25 ) = 21
Assume a city with a rank of 16 and a distance of 5 from the FP and 25 from the capital. Then:
No FP
Cd = 25 / 50
Cr = 16 / 32
C = 90% (cap)
Remote FP
Cd = 25 / 50
Cr = 16 / 46
C = 85%
Local FP
Cd = 5 /50
Cr = 16 / 46
C = 45%
No FP, court
Cd = 12 / 50
Cr = 16 / 21
C = 90% (cap)
Remote FP, court
Cd = 12 / 50
Cr = 16 / 56
C = 41%
Local FP, court
Cd = 2 /50
Cr = 16 / 56
C = 32%
As can be seen, a remote FP has almost no effect on corruption unless you add a court, which would have to be cash-rushed.