Chef Archive
Thread: Experimentation Initial-Value Formula
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MuttonJedi
Thu Apr 22, 2004 5:46 pm
#1
In my quest to make the best food I can, I have been trying to come up with some formulas to predict the results I will get with specific resources without having to go out and collect samples and try each combination. I tend to experiment my foods on filling, flavor, and nutrition. Dividing my points this way, I rarely hit the experimentation caps for my resources, so I am specifically interested in predicting the initial combine values I will get, as those are what really determine my final results.
I don't keep up with all of the crafting forums, but in the little looking I did, I was unable to come up with anything reliable. So I started with the assumption that the initial experimentation values were proportional to the maximum values, and tried to determine the correct ratio. But I ran into a few cases where this just didn't work. My problem appeared with a couple of brandies I made with different types of berries:
#1. Fruits with 829 DR and 979 PE, and berries with 876 DR and 823 PE. These give an initial combine with 7 charges (small glass), at 25% quantity experimentation.
#2. Same fruits, but berries with 824 DR and 843 PE. These give an initial combine with 6 charges at 24% experimentation.
Now consider the experimentation caps for these two brandies. For #1, the average DR is 852.5 and the average PE is 901. Using the 0.25*DR+0.75*PE formula gives a rating of 888.9 (and I verified that the experimentation cap was 88%). For #2, the average DR is 826.5 and PE is 911. The 0.25*DR+0.75*PE formula gives 889.9, just slightly better than #1 (again 88% cap). So, somehow the combination with (marginally) better stats gave me one less charge.
To explain this, I made more items than i care to admit and plotted out the initial combine values vs. stats, and I came up with a formula that fits everything I have seen so far:
Initial Exp Value = 7.5*(E/1000)*(A/1000)+7.5*(E/1000)*(B/1000)+15*(E/1000)
Where, A and B are the average stats used for an experimentation line, and E is the result of the experimentation formula. In this case, A=DR, B=PE, and E=0.25*DR+0.75*PE.
Plugging my stats above into this formula shows why I got the results I did:
#1. 7.5*(888.9/1000)*(852.5/1000) + 7.5*(888.9/1000)*(901/1000) + 15*(901/1000) = 25.2
#2. 7.5*(889.9/1000)*(826.5/1000) + 7.5*(889.9/1000)*(911/1000) + 15*(889.9/1000) = 24.9
I have been rounding most of my numbers to one decimal place, but further testing appears to indicate that the weighted average stats are truncated before being used in the experimentation formula, while the actual experimentation percentages are not truncated except for display. So, looking only at my first brandy the full calculation goes like this:
Average DR = (829+876)/2 = 852.5, truncate to 852.
Average PE = (979+823)/2 = 901
Experimentation rating = 0.25*852 + 0.75*901 = 888.75
Initial Value = 7.5*(888.75/1000)*(852/1000)+7.5*(888.75/1000)*(901/1000)+15*(901/1000) = 25.1998..
Of course, without seeing the actual code, I can't be entirely certain the formula is correct. It has been working for me so far, but I would be very interested if anyone runs into a case where it doesn't fit.
Mutton
I don't keep up with all of the crafting forums, but in the little looking I did, I was unable to come up with anything reliable. So I started with the assumption that the initial experimentation values were proportional to the maximum values, and tried to determine the correct ratio. But I ran into a few cases where this just didn't work. My problem appeared with a couple of brandies I made with different types of berries:
#1. Fruits with 829 DR and 979 PE, and berries with 876 DR and 823 PE. These give an initial combine with 7 charges (small glass), at 25% quantity experimentation.
#2. Same fruits, but berries with 824 DR and 843 PE. These give an initial combine with 6 charges at 24% experimentation.
Now consider the experimentation caps for these two brandies. For #1, the average DR is 852.5 and the average PE is 901. Using the 0.25*DR+0.75*PE formula gives a rating of 888.9 (and I verified that the experimentation cap was 88%). For #2, the average DR is 826.5 and PE is 911. The 0.25*DR+0.75*PE formula gives 889.9, just slightly better than #1 (again 88% cap). So, somehow the combination with (marginally) better stats gave me one less charge.
To explain this, I made more items than i care to admit and plotted out the initial combine values vs. stats, and I came up with a formula that fits everything I have seen so far:
Initial Exp Value = 7.5*(E/1000)*(A/1000)+7.5*(E/1000)*(B/1000)+15*(E/1000)
Where, A and B are the average stats used for an experimentation line, and E is the result of the experimentation formula. In this case, A=DR, B=PE, and E=0.25*DR+0.75*PE.
Plugging my stats above into this formula shows why I got the results I did:
#1. 7.5*(888.9/1000)*(852.5/1000) + 7.5*(888.9/1000)*(901/1000) + 15*(901/1000) = 25.2
#2. 7.5*(889.9/1000)*(826.5/1000) + 7.5*(889.9/1000)*(911/1000) + 15*(889.9/1000) = 24.9
I have been rounding most of my numbers to one decimal place, but further testing appears to indicate that the weighted average stats are truncated before being used in the experimentation formula, while the actual experimentation percentages are not truncated except for display. So, looking only at my first brandy the full calculation goes like this:
Average DR = (829+876)/2 = 852.5, truncate to 852.
Average PE = (979+823)/2 = 901
Experimentation rating = 0.25*852 + 0.75*901 = 888.75
Initial Value = 7.5*(888.75/1000)*(852/1000)+7.5*(888.75/1000)*(901/1000)+15*(901/1000) = 25.1998..
Of course, without seeing the actual code, I can't be entirely certain the formula is correct. It has been working for me so far, but I would be very interested if anyone runs into a case where it doesn't fit.
Mutton
sciguyCO
Thu Apr 22, 2004 6:31 pm
#2
Wow, and I thought my math explanations got scary!
Two questions: were those all great success assemblies? I haven't seen any situations where an amazing gives better starting results, but a "good" or "moderate" success on assembly should give lower values. Also, does that hold up with the other experimentation lines? Quantity is 75% PE and 25% OQ, I wonder if those might've implicitly made it into the constants you have.
I'm horrible at function fitting, and I had been going on the assumption that the initial percentage was a function solely of the final percentage. What you found is non-linear, and even if you use resources that end up with the same E value, the starting percentage would differ depending on the actual A and B.
I'll play around with some non-food stuff to see how generic it is. A quick guess would be that for something like harvesters (that depend on UT, SR, and HR) there'd be a third C term, and the multiplier would be 5 instead of 7.5. And for crafting tools (depend only on CD), there'd be just A with a multiplier of 15.
Bravo!
MuttonJedi
Thu Apr 22, 2004 7:15 pm
#3
Yes, this was only for great success assembly. I ignored anything else including amazings, although I never saw a difference with amazing/great either.
I have tried this with all four experimentation lines on brandy. It seems to work with the 66%/33% ones as well. I haven't tried any 3-stat items, but I actually started using single-stat items (survival knives, clothing repair tools, and lube-oil fishing poles). For those the formula 15*Stat^2+15*Stat fit very well (well, divide stat by 1000 again). I also did wood-only Karkan Ribenes, where some of the terms disappear from missing stats.
The curves are not very pronounced, so it really only makes a difference on values that are near an integer boundary.
Mutton
I have tried this with all four experimentation lines on brandy. It seems to work with the 66%/33% ones as well. I haven't tried any 3-stat items, but I actually started using single-stat items (survival knives, clothing repair tools, and lube-oil fishing poles). For those the formula 15*Stat^2+15*Stat fit very well (well, divide stat by 1000 again). I also did wood-only Karkan Ribenes, where some of the terms disappear from missing stats.
The curves are not very pronounced, so it really only makes a difference on values that are near an integer boundary.
Mutton
sciguyCO
Thu Apr 22, 2004 7:16 pm
#4
Ignore my second question. Forgive me for doubting you, it works wonderfully, all four categories, all different items.
I did some playing around with single-stat items, and it works with 15 * A (leaving off the B term). I don't have any aluminum on hand, so I can't try with harvesters.
I'll bet the general form is this:
15 *[ Average( contributing_stats ) / 1000 + 1 ] * E / 1000
Average() would just be the standard mean (or is it mode? I can never keep those straight), no weighting. Since brandy has two stats, it was dividing by 2, giving the 7.5 constants. And since E / 1000 is the maximum percentage, there is a relationship with that, just not the linear one I was looking for. Since E depends on A and B (and C if used), the starting percentage is a 2nd order function, so it's fairly flat at low values, sloping up more as the stats get closer to 1000.
Assuming stats of 1000, you end up with a starting value of 30%, which I'd seen before as the max initial percentage (probably determined with crafting tools made from 999 or 1000 CD copper).
How did you end up getting that? I tried all kinds of weird things, but fitting known data toa general function has never been something I'm good at.
MuttonJedi
Fri Apr 23, 2004 3:59 pm
#5
Yeah, I bet you are right about the general formula. I might just have to train up engineering to try that 
As for how I found it, I did make quite a few items to collect data, but it was mostly wild guesses when the data didn't look quite linear. I happened to try plotting 1000*initial value/stat vs. stat (doing single stat items first) and that came out as a nice straight line. The line went from 0,15 to 1000,30 so I had 1000*I/S = 15 + 15*S/1000 and rearranged from there. To extend to two-stat items I made Karkan Ribenes with wood/hide/bone only and did the same thing over to see how the two-stat formula looked with one stat missing. For quantity on the Ribenes, I got 1000*Initial value/OQ = 3.75 + 1.875*OQ/1000 and it was more guessing from there to fit the two formulas together.
What has me stumped now is trying to get the final stats from the experimentation values. Well, getting them exactly, LOL. Looking at brandy buff sizes, the 150-240 range you have seems right, and it looks linear except for a couple points that just don't make sense. From +168 at 20% to +230 at 90% the buff goes up in 2 point intervals except at 67% where it does +208, +209, +211, +214. I just can't imagine how those two odd numbers get in there.
Mutton
As for how I found it, I did make quite a few items to collect data, but it was mostly wild guesses when the data didn't look quite linear. I happened to try plotting 1000*initial value/stat vs. stat (doing single stat items first) and that came out as a nice straight line. The line went from 0,15 to 1000,30 so I had 1000*I/S = 15 + 15*S/1000 and rearranged from there. To extend to two-stat items I made Karkan Ribenes with wood/hide/bone only and did the same thing over to see how the two-stat formula looked with one stat missing. For quantity on the Ribenes, I got 1000*Initial value/OQ = 3.75 + 1.875*OQ/1000 and it was more guessing from there to fit the two formulas together.
What has me stumped now is trying to get the final stats from the experimentation values. Well, getting them exactly, LOL. Looking at brandy buff sizes, the 150-240 range you have seems right, and it looks linear except for a couple points that just don't make sense. From +168 at 20% to +230 at 90% the buff goes up in 2 point intervals except at 67% where it does +208, +209, +211, +214. I just can't imagine how those two odd numbers get in there.
Mutton
sciguyCO
Fri Apr 23, 2004 6:57 pm
#6
MuttonJedi wrote:
What has me stumped now is trying to get the final stats from the experimentation values. Well, getting them exactly, LOL. Looking at brandy buff sizes, the 150-240 range you have seems right, and it looks linear except for a couple points that just don't make sense. From +168 at 20% to +230 at 90% the buff goes up in 2 point intervals except at 67% where it does +208, +209, +211, +214. I just can't imagine how those two odd numbers get in there.
Well, I got the ranges assuming that the experimental percentages worked like this:
Final stat = min + (max - min ) * ExperimentalPercentage
The odd points you noticed are likely where the rounding down causes the same buff value to show up at multiple percentage values, like 70% (213.0, displays +213) and 71% (213.9, still displays +213). Although I never noticed if odd buff values showed up, maybe it rounds to the closest even?
Still, it tends to be close enough for government work.
LemyDaBigHairyWookie
Sun Apr 25, 2004 5:13 am
#7
This is the formula I use in my crafting to figure my expected Percentages... i've never gone so far as to catalog what % gives what attribute stats(with minor exceptions such as Base Resists on armor layers)
({[(Res1Qual1 x Qual1%) + (Res1Qual2 x Qual2%)] x Res1Unit} + {((Res2Qual1 x Qual1%) + (Res2Qual2 x Qual2%))x Res2Unit}] / TotalUnits
-Assuming Brandy Quantity schematic and random resources-
({[(834PE x 75%) + (843DR x 25%)] x 20} + ({[(923PE x 75%) + (727DR x 25%)] x 20}) / 40
855.125 total unit/schematic weighted resource value
Max Experimentation% is .01 x weighted value for 85.5%
Starting Assembly % will be .30 xMax Experiment % for 25.6%
The game DOES figure on the hidden percentages and that would account for the variances in the buffs you see at the Shown Experiment %... (I see it all the time in stacked experimentation such as weapons/armor)... Its very possible it rounds to closest even on this schematic (I'm not in position to run gobs of tests on this)... What is displayed for buff is what is used in the final BioE multiplier from what I've seen so far however...
sciguyCO wrote:
The odd points you noticed are likely where the rounding down causes the same buff value to show up at multiple percentage values, like 70% (213.0, displays +213) and 71% (213.9, still displays +213). Although I never noticed if odd buff values showed up, maybe it rounds to the closest even?
Message Edited by LemyDaBigHairyWookie on 04-25-2004 07:19 AM
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