LastFootnote said:Although I agree with your conclusions, your math is extremely fuzzy. You cannot simply solve for the relationship between A and B because the plus signs in your equation aren't actually addition. Even if they were, these are the actual inequalities:
1 + A + A + A = 1+ 3A ≥ 100%
1 + A + B ≥100%
From these, you cannot determine that 2A = B.
These are not really inequalities. We know that A is the minimum amount you can raise the stage by. We know that 1+ 3A=100. There is no way in hell you can get 100% with less than 3A because you can't raise stages by a smaller interval, and based on how they always coded these in the past you reach the top stage and then any additional stages keep you at the top. We also know that both A and B are integers. We also know that 2A = B from the stages (both get you 50%) but I derived it from the 100 relationships because when I first did this the 50% were uncertain. Thus with that I can once again prove that 1+ A + B = 100.
Even without knowing that both 1+2A and 1+B were 50%, I can still prove 1+ A + B is 100%. The reason is because the stages are discrete. Because you have to be able to get to all of the stages with A alone you know that going from 1 + B to 1 + B + A will land you exactly on 100%. I agree that these could have been inequalities if we found that focus energy somehow worked outside of the normal crit stages, but all of our testing and evidence has turned up to the contrary.
Also as far as the plus signs not being additons my calculations are not for percentages they are for stages. Perhaps instead of 100% I should have used some variable to represent the stage at which we reach 100% (lets call it C). Your right in that we are not adding together percentages, but we are adding together stages. Each stage number we end up with is associated with a percentage.
Stage 1 + 3A = C is associated with 100%. If A were actually 7, then B would be 14, and
1 + 3(7) = 21 = C
1 + 7 + 14 = 21 =C
You would only be able to reach stages 1, 7, 14, and 21, making there still functionally 4 stages.