This week's formula!
OK, tried something slightly different this time. I only got 5 solutions from the using the new skills I added this week. And none of those worked for every test set of skills I had set aside (ie. not used to generate the solutions).
This lead me to believe that if there is a solution then I need to start varying things by less than integers. I tried this and even varying everything by 0.25 it would take months to run. So instead it occurred to me that the average of any number of solutions is also a solution - that way I can generate at least some of the decimal solutions. I weakened the error bounds very slightly to increase the number of solutions I got and then took the average of them all! Gave quite good results actually
Agility..................2.8690%
Courage...............2.3333%
Dexterity..............1.9683%
Perception:...........2.7619%
Serendipity:..........1.1746%
Coolness:..............3.4286%
Aim......................2.9048%
Combat Reflexes.....2.9841%
Marksmanship........10.2698%
Weapons Handling...6.5397%
Combat Sense........6.2063%
Commando............2.8095%
Rifle/Handgun........39.7500%
LWT/BWT/PWT........14.0000%
I'm pretty sure the numbers are all now in roughly the right ballpark for each skill. Obviously its unlikely they're really so messy though
It gives results in agreement with every data set I've received (to sensible limits) apart from 2 reasonably significantly (1 of which I think the data may be flawed, 1 of which is a little unusual due to rifle being the users secondary weapon) and 2 minorly (Kyl and Demonikos, both of which posted on skill unlocks for which we're a little less confident of than HA changes).
Also works nicely for Belphegor above
But it might be getting closer, its still not quite there. New skills on HA changes or pro-standing changes still sought after (particularly people with very high skills or very low skills, but everything helps!).
I have a few things I'm going to try over the weekend and next week. There are also a few issues to resolve, the ones I'm most concerned about:
(i) Should agility be capped at 10000, 400 or something else.....I'm going to try 400 sometime (effectively multiplying agility by 25) although this will require some guesswork as not everyone early on posted agility, but its not too hard to guess reasonably well hopefully...
(ii) I'm pretty sure the formula is the same for LWT/BLP/plasma etc. (sorry Stormer...prove me wrong
). I don't have quite the same confidence about rifle and handgun. Pingo posted some numbers which suggest rifle/handgun needs to be a little more than 39.75%. I also have some numbers sent to me that suggest rifle/handgun needs to be a little less than 39.75%! Both cases though the difference is caused by something like 10 skills in 3000 so I'm not quite sold yet. If some people who've posted rifle skills but not handgun skills, you're handgun skills would be useful on a HA change to decide one way or the other.
Event (a): Handgun and Rifle formulas turn out to be different. Not the end of the world. I have loads of rifle data so we would just concentrate on that. Also means integer solutions would be possibly back on the cards, meaning computation may not be such an issue. Would need yet more data to get meaningful results though.
Event (b): Handgun and Rifle formulas are the same. Seems more elegant to me somehow and I'm still half-tempted to believe its the case. But then the solution is definitely not integer and computation is going to be a problem. Although my averaging method may solve this to some extent
As more and more exact data comes in the option to try for a solution directly may become possible (ie. by inverting a big whacko matrix in Matlab, I may do a test on this sometime but I still don't have enough exact and reasonably independent data to really do this properly yet).
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