So the base Refinery Yield is 50% as always, Structure/Rig Bonus is then added additive giving the following: BaseYield + StructureBonus + RigBonus, this will make the Base Refining yield of a Tatara: 57%, you then apply any SecurityMod/skill-based/implant bonus’ multiplicative (as you did in your post)
Max Refining yield in Highsec using a Tatara Refinery, is: 57 * 1.15 * 1.1 * 1.1 * 1.04 = 82.48812% = 82.49% (Rounded up)
Max Refining yield in Lowsec using a Tatara Refinery, is: 57 * 1.06 * 1.15 * 1.1 * 1.1 * 1.04 = 87.43741% = 87.44% (Rounded up)
Max Refining yield in Null/WH space using a Tatara Refinery, is: 57 * 1.12 * 1.15 * 1.1 * 1.1 * 1.04 = 92.38669% = 92.39% (Rounded up)
You’re correct in that the Tech 2 rig makes the base refining yield 53% (or in other words adds +3% to the base 50%) same with the Structure bonus, it adds +2% (for the athanor) to the 53% and that sums up to 55% before all the multiplicative(s) apply
I can get 72.4% yield from an unbonused Raitaru (in highsec) with Reprocessing Service module and/or in NPC stations, so if what you say is true, it hardly makes it worth it to even make Refineries with the huge price tag that goes with building them (mostly with Tatara, though).
I took a look at Singularity and I’ve got 76,3% for T1 Rigged Tatara in NullSec. With base chance is only 52%. What the hell? I can’t see any security modifier applied at all.
So the base is 59%. Anything close to it based on security is 53% * 1,12 = 59,36%. And result would be 82.97% which is not correct.
I. 59% / 1,12 = 52,67% the value without applied SS. Base value for citadel with rig is 51%. So 51% * 1,031 = 52,67 and here it is the 1,031 coeff for 4% tataru bonus. Meeh.
Though provided table is good I’m trying to correctly reproduce formula for my calculator.