IIQ/IIR: MF Balance and Diminishing Returns guide (v2.2)
" Not yet, but I'll try. Thanks for your comment, intangible_s. - Attack and Spell DPS Calculator (view-thread/977942)
- IIQ/IIR balance guide (view-thread/725812) | |
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I did some followup on your work. (if somebody has already done this... oops)
I tried to find the true "C" equation, given the IIR IIQ values you provided, and the subsequent actual multiplier to the amount of rares and uniques received from the control group (where you have no IIR and IIQ bonuses). For ease of math, assume when i say IIR and IIQ I really mean (1+IIR/100) and (1+IIQ/100) respectively I am taking a regression approach to this--- problem is there are so few samples! only 13! So I had to make a very simple model. The model proposed in the original post has a large error to the actual C values. So for reference, the average error of the original equation is: Error = 4.218721564. Let's see if I can do better. I decided to take three different models and share the results.
FIRST APPROACH: explicit regression equation <Math Alert>
This is the "if I were programming it, how would I have done this" approach. And I've found some evidence I may be correct. My inspiration came from this post https://www.pathofexile.com/forum/view-thread/28697#p414204. "Increased Item Quantity[...] gives more items.More drops means more chances to roll currency instead of gear." This lead me to believe the equation should look like  . where f(IIR) is some function of the IIR.I thought immediately that if I were to program it-- i would keep the ratio of rares:uniques the same, but start decreasing the amounts of whites/blues (depending on the monster maybe blues:rares:uniques ratio would also be maintained) To test this thought I did linear regression on the ratio of rares:uniques. Where x=C values (your model) and y=averageUniques/averageRares
graph is here (big)
 As you can see-- there is no positive trend between "C" and the ratio of uniques to rares! so now I can propose my equation. Here, let p = % of drops that are rare or unique before any IIR or IIQ bonus. (IGNORE THE tick, my bad)  Basically what i'm doing here is lowering the amount of whites, and increasing the amount of rares. This limits IIR so that bigger values will have larger diminishing returns Also notice: WE DON'T KNOW P!! and it might be different depending on what you're fighting! So I just did the regression on p, since it's the only unknown final equation = IIQ*f(IIR) =  I found the best error was: Average Error = 0.2961646339 Where p = .42 (see spoiler for explaination of p, should be adjusted by what enemy is dropping) Much better than 4.128
SECOND APPROACH: What if i'm wrong about how IIR works?
What if it takes in two arguments, like f(IIR,IIQ)? Well, then I should discover f(IIR,IIQ) through symbollic regression! Symbolic regression is an evolutionary computation algorithm, basically designed to guess the equation to a set of numbers. I used ECJ library to come up with the results, toyed with settings until i found something nice with low error.  fun fact: when I punished it for making strange equations like this (i had a measure for that-- too much detail for this post) -- i ended up getting my equation i proposed in the first approach :) final equation = IIQ*f(IIR) =  Average Error: .256 (WARNING: lower error not necessarily good! that equation is pretty strange, use as approximation only)
THIRD APPROACH: What if i'm wrong about EVERYTHING! (pure symbollic regression)
I just plugged it into ECJ and let it gooooo Again, just because this has lower error doesn't necessarily make it better. This is because the more complex the model you have, the more it could "overfit" the data. Which just means that it may not generalize to new values! which is what we're most interested in here. We only have 13 samples, so overfitting is easy to do. final equation =  Error = 0.114959915 Feel free to use which ever equation you think is best to figure out how you should assign IIR and IIQ (i'm personally a fan of the first equation) I double your bid. IGN:paranoidcoder Last edited by paranoidcoder on Jan 31, 2017, 4:27:42 PM
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paranoidcoder, so what's "Final Tally"? What are optimal values for IIQ / IIR?
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0/0 and just rng master!
In order to get rid of clearspeed meta cap global movement speed at 100% but make all skills instant so everything feels great.
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" While I dont pretend understand the maths I do have massive anecdotal experience with drops for example pre loot filters I could with almost 100% accuracy tell how many maps would drop on a map just from the loot distribution of the first magic monster pack. In short IR seem to need a very large number to have any meaningful results as the inherent baseline RNG variance is so large while IQ seems to be an additive number on top of the baseline variance so needing a smaller number to be effective. What the sweet spot is who knows. "Blue warrior shot the food" Last edited by maxor on Feb 1, 2017, 11:24:14 AM
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" (SKIP TO THE BOTTOM IF YOU JUST WANNA PLUG IN SOME NUMBERS) Basic summary: Well if you believe my equation, it looks like the closer you can get to equal, (IIQ=IIR), without sacrificing your total IIR+IIQ value, the better off you are( this is approximate). (side note: if you only care about currency, or value currency more in drops, you're going to want a lot more IIQ, IIR does not effect currency) More stuff: I made some adjustments to the equations yesterday (IIQ = 1+ 1/2 * in-game-IIQ/100 and IIR = 1+ 1/2 * in-game-IIR/100) Here's what I think the curve looks like for "normal" monsters [p=.01 y=IIR, x=IIQ] (Darker colors are LOWER multipliers, scale is X100 (3.0 = 300 IIR in game) )  Equation online if you wanna plug in some numbers http://www.wolframalpha.com/input/?i=(1%2Bx%2F2)*((1%2B(y%2F2))%2F((1-.01)%2B.01*(1%2By%2F2))),+from+y%3D0..3+and+x%3D0..3 Here's what I think it looks like for legendary monsters [p=.1 y=IIR, x=IIQ]:  http://www.wolframalpha.com/input/?i=(1%2Bx%2F2)*((1%2B(y%2F2))%2F((1-.1)%2B.1*(1%2By%2F2))),+from+y%3D0..3+and+x%3D0..3 Summary So for normal monsters -- looks like IIR and IIQ are about equal in value. If you count currency drops-- you probably care more about IIQ then. For unique monsters, you care a bit more about IIQ than IIR. But IIR certainly does help and it is easier to find. But if you could choose between 300IIQ and 300IIR, you'd take the 300IIQ. If you want to compare two builds using my method, you'd just plug it into the equation below, and see which number is bigger. (use p=.01 for normal monsters, p=.1 for unique monsters)  Whichever build has the bigger C is the better MF (using this method, not guaranteed to be correct! But seems to fit the data pretty well) P.S. the 10x multiplier to p for uniques seems to be in line with the increased rarity modifier for uniques in this file: http://pathofexile.gamepedia.com/Modifier:MonsterUnique4 Keep in mind in creased rarity related to monsters has been said to be different than the players -- i think in this case it modifies our p value I double your bid. IGN:paranoidcoder Last edited by paranoidcoder on Feb 1, 2017, 1:55:14 PM
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How my theory relates to the real numbers
Here's real vs predicted:  NEW AVERAGE ERROR: .19 --- better than one of the regression errors!! pretty damn good if i do say so myself I double your bid. IGN:paranoidcoder Last edited by paranoidcoder on Feb 1, 2017, 1:49:28 PM
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Hello,
i find it interesting to read what science you make of this, and am thankful of that, but paranoidcoder: ? lets get practical here ? what would be a sweet spot ? 100/350 ? |
