Originally posted by BGMaxi:

tax efficiency calculation is different if you are Emperor: as emperor, all fiefs of the empire will be considered, if you are only lord (or ruler but not emperor) only the ones you own (I added this because as emperor you get taxes from the governors, so to balance this that you dont get too easily too rich)
Tax inefficiency is also depending on various other stuff, I try to make a summary:
*minimum needed centers are: hard: 2, normal: 4, easy: 6
this is modified by your ministers relation (if you have one): if it is higher than 50 points 3 is added (e.g. on normal you would now need 7 centers)
and if relation is lower than -5 points 2 is substracted (e.g. on normal you would need 2 centers)
if you have hired additional tax collectors, 2 points are added

*efficiency loss per center: hard: 8, normal: 7, easy: 6,
if relation with minister is higher than 50 it is substraced by 1, if it is lower than -5 it is added by 1

*if your number of owned centers (or number of empire centers) if creater than the threshold, tax inefficiency will be calculated:
Let x be the ratio lost, y the number of owned centers that value for tax inefficiency (if you are not emperor castles and villages count 1 and towns 2, if you are Emperor only towns count)
and let z be the number of centers needed as calculated in the first bullet point, then we have:
and let w be the efficiency loss per center (as in the second bullet point)
x = (y-z)*w, (x is the percentage you lose), if x should become creater than 50 it is set to 50, so you can maximally lose 50%, so x will be in an intervall [0, 50]

so the money you lose will be calculated this way: tax_inomce * x / 100

But due to diplomacy, you can get some money back!

If you have a chamberlain, you can get 10% of the lost money back
this is additionaly modified by the following:
if you have hired additional tax collectors, another 15% points are added,
if you have conducted a census (only possible as emperor) another 3% points are added,
if you your relation with your minister (if you have one) is higher than 80 another 3% points are added (if it is higher than 50 only 2% points are added if it is higher than 10 only 1% points are added)
kingdom policies also make a difference (depending on if you are king or lord)
if king: you get additional 5 points per centralisation level (e.g. highest centralisation gives you +15, lowest centralisation gives you -15)
and serfdom (I renamed it to slave policy or something like that):
if allmost all are slaves you gan 9 points, if allmost all are free you gain -9 points
if you are lord:
for highest centralisation you gain -15 points for lowest +15

Example: you have a chamberlain + census + more than 80 relation with minister + highest centralisation + allmost all slaves + additional tax collectors you gain 10+15+3+3+15+9 = 55% back (which should be the maximum)

The percentage value in the brackets is only displayed if you have a chamberlain (quaestor) and it shows how much of the tax loses you get back (in the previous example it would be 55%)