Uhh, I made a mistake in calculation. I used >=2 for rares instead of =2.
Also I didn't look at how it scales up with more skill, it should grow or at least stay equal to 100%.
Human,
Skill/very rare/rare/total/percent
400/13.39/24.48/390.15/ ~100%
600/32.31/28.52/698.55 / ~116%
AI
Skill/very rare/rare/total/percent
210/21.28/27.45/350/~83%
300/29.46/28.52/437/~72%
400/38.00/28.08/520/~65%
So while the goal is met for the human, in case of AI the efficiency actually drops as skill rises and even starts too low.
No wonder - The generated advantage is a ^ shaped line - the closer we are to "all very rares" the slower the amount can grow in absolute value, which means even less in relative. Basically, the AI already starts above their "peak efficiency" while the human does not, mainly because they have the skill modifier (their 200 skill is worth 400 in reality).
So maybe the skill should still incorporate the difficulty multiplier? Assuming we remove the flat "+X" for difficulty, that would make their tables literally identical to the human, except the positioning :
200/13.39/24.48/390.15/ ~100%
300/32.31/28.52/698.55 / ~116%
...
Yeah I think this is what we should do.
...wait, no. For the AI we assumed only two triggers instead of 3 so...
200/13.39/24.48/253.43/ ~63%
300/32.31/28.52/465.7 / ~77%
That's not good. Let's try adding the a flat +5.
200/26.62/28.35/407.95/ ~102%
300/46.29/26.59/595.85/ ~99%
Not much growth there, in fact it's already shrinking but not significantly. I think that's acceptable, as we used fairly conservative assumptions for the AI (there'll be a lot more than 2 triggers if there are more than one other AI remaining in the game)
also the number of triggers increases with skill because higher own skill usually means higher skill on the other players as well, which raises effectiveness in an way not included in the calculations. If everyone is at twice the skill, the actual effectiveness is double because there will be 2x as many triggers - we just didn't care about this case as the main intended use is strong wizard vs weaker wizard. Where maintaining around 100% is fine - it's 100% of our own skill so at higher skill it is a higher absolute advantage.
So I believe the final formula should be
(Skill including AI modifier/30)+5 if AI.
(we might want to also scale the "5" on difficulty? Not sure if needed.)
Also I didn't look at how it scales up with more skill, it should grow or at least stay equal to 100%.
Human,
Skill/very rare/rare/total/percent
400/13.39/24.48/390.15/ ~100%
600/32.31/28.52/698.55 / ~116%
AI
Skill/very rare/rare/total/percent
210/21.28/27.45/350/~83%
300/29.46/28.52/437/~72%
400/38.00/28.08/520/~65%
So while the goal is met for the human, in case of AI the efficiency actually drops as skill rises and even starts too low.
No wonder - The generated advantage is a ^ shaped line - the closer we are to "all very rares" the slower the amount can grow in absolute value, which means even less in relative. Basically, the AI already starts above their "peak efficiency" while the human does not, mainly because they have the skill modifier (their 200 skill is worth 400 in reality).
So maybe the skill should still incorporate the difficulty multiplier? Assuming we remove the flat "+X" for difficulty, that would make their tables literally identical to the human, except the positioning :
200/13.39/24.48/390.15/ ~100%
300/32.31/28.52/698.55 / ~116%
...
Yeah I think this is what we should do.
...wait, no. For the AI we assumed only two triggers instead of 3 so...
200/13.39/24.48/253.43/ ~63%
300/32.31/28.52/465.7 / ~77%
That's not good. Let's try adding the a flat +5.
200/26.62/28.35/407.95/ ~102%
300/46.29/26.59/595.85/ ~99%
Not much growth there, in fact it's already shrinking but not significantly. I think that's acceptable, as we used fairly conservative assumptions for the AI (there'll be a lot more than 2 triggers if there are more than one other AI remaining in the game)
also the number of triggers increases with skill because higher own skill usually means higher skill on the other players as well, which raises effectiveness in an way not included in the calculations. If everyone is at twice the skill, the actual effectiveness is double because there will be 2x as many triggers - we just didn't care about this case as the main intended use is strong wizard vs weaker wizard. Where maintaining around 100% is fine - it's 100% of our own skill so at higher skill it is a higher absolute advantage.
So I believe the final formula should be
(Skill including AI modifier/30)+5 if AI.
(we might want to also scale the "5" on difficulty? Not sure if needed.)