Analysis on the effectiveness of increased item quantity and rarity

bah i can only manage 120 iiq and 350 rarity , im so lazy

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LazarusQ wrote:

number of items = base number * (1 + 4.5*IIQ/100)^0.25

It may not be exactly that, but I'd wager it's pretty close. Only thing I don't like is that it's not close to (1+IIQ/100) for small IIQ.

What makes you think that the designers know enough or care enough about mathematics to have introduced the natural (1 + IIQ/100) condition for small IIQ? What makes you think they just didn't quickly google "diminishing returns" and through that just implemented a function for "number of items"/"base number" that is positive for all x >= 0, has the condition f(0) = 1, its derivative is positive and its second derivative is negative?

What makes you think for sure that they cared about making sure the extremities such as "number of items"/"base number" behaves as (1 + IIQ/100) for small IIQ?

Something else that you may not have noticed: your suggested function has no limit as IIQ goes to infinity. A reason for why you want a limit to exist: in case you accidentally create an item/buff that is bugged in the sense that it gives an insane amount of IIQ, like 10^1000% IIQ. If the function is appropriately bounded, the damage a such bug can cause is so small that you may not even need to make a server reset from backup.


Just look at the formula:

Y = "Number of items"/"base number" = 1 + (70/100)*(1 - exp(-IIQ/70))

*As you notice: when IIQ goes to infinity, Y goes to 1 + (70/100) = 1.7

*The condition Y(0) = 1 is met since Y(0)= 1 + (70/100)*(1 - exp(0)) = 1+ (70/100)*(1-1) = 1

*Taylor-expanding to the first order around IIQ = 0 yields:
Y(IIQ) = Y(0) + Y'(0)*(IIQ-0)/1! + Ordo(IIQ^2) = 1 + (70/100)*(1/70)*IIQ + Ordo(IIQ^2) =
= 1 + IIQ/100 + Ordo(IIQ^2)

I.e. Y(IIQ) behaves as 1 + IIQ/100 for small IIQ like wanted.
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Who do you think will control whether or not the hidden formulas for the game are well-done? Do you think Chris has the mathematical background to rigorously challenge them? XD Even if he had it, would he have the time to do it?

It is more likely that as long as the game is playable and not "fucked up", the bosses of whoever created the hidden formulas will never ever evaluate them. Therefore it is in the interest of the hidden formula creators to never ever release them publicly because that would just make them open for criticism from their bosses if there is enough public uproar, criticism that their bosses would not bother them with if they keep the formulas hidden.

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mazul wrote:

What makes you think etc.

Er... well, I was just making a guess given the data that I have and the mechanisms for diminishing returns of other stuff in the game. This doesn't constitute proof, obviously, but it would make sense if the guy who coded those mechanisms is the same, which is not so improbable, considering that GGG is not a huge company.
Also, I have a nice compelling plot. I tried 1 + (70/100)*(1 - exp(-IIQ/70)) in it and it doesn't fit. Do you want to have another go ?

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LazarusQ wrote:

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mazul wrote:

What makes you think etc.

Er... well, I was just making a guess given the data that I have and the mechanisms for diminishing returns of other stuff in the game. This doesn't constitute proof, obviously, but it would make sense if the guy who coded those mechanisms is the same, which is not so improbable, considering that GGG is not a huge company.
Also, I have a nice compelling plot. I tried 1 + (70/100)*(1 - exp(-IIQ/70)) in it and it doesn't fit. Do you want to have another go ?

I don't have your data in numbers, and no, I will not extract them from your graph by pixel analysis.

For the reddit thread of the thread starter he had following data for %IIQ:

%IIQ => % Effective IIQ
0 => 0
20 => 16.79
40 => 30.14
60 => 39.69
80 => 47.35
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Since humans tend to like "Nice numbers", it is more likely that someone created with weight 70 rather than weight 71. More likely that something is an integer in a designed formula than it having decimals, etc.

So it makes sense to see which of weights 70, 75, 80 and so forth gives the "best fit".
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For y = % "Effective IIQ" as function of x = % IIQ, the corresponding suggested "proper" formula (proper in the sense that is bounded for all IIQ >=0, it behaves "correctly" for small %IIQ and uses "nice numbers")

y = 70*(1 - exp(-x/70)) yields following:

0 => 0
20 => 17.40
40 => 30.47
60 => 40.29
80 => 47.67

which is close enough to the data from the reddit thread for % IIQ to not be able to be utterly dismissed. How rounding effects are implemented through GGG's code can very much explain small difference between their theoretical formula and their simulated results.

All I can take away from this thread and the mathematicese spoken here is that when running high IIQ maps having high IIQ on gear is more or less pointless. But that is very good to know.

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Jojas wrote:

All I can take away from this thread and the mathematicese spoken here is that when running high IIQ maps having high IIQ on gear is more or less pointless. But that is very good to know.

No, IIQ from gear or size of party is supposed to be multiplicative with IIQ from map (see http://pathofexile.gamepedia.com/Partying, under section "effect on loot"). So you should still stack as much as possible.

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mazul wrote:

I will not extract them from your graph by pixel analysis.

Haha ! Never suggested you should. It would be utterly pointless. I didn't post the data because its format is a bit messy for the moment, but I will if you want.

Anyway, since we're all trying to infer game mechanics from very limited information, we all may have different priors as to what kind of formulae would be more proper. You think exponentials because it's bounded, I think powers because look at armour and evasion. If the problem is that it might diverge, there's probably a hard cap on it, like on everything else in the game.

From what we know, there is no way to say whether you're right or I am, or (very probably) neither. You're absolutely welcome to share your reasoning with the community, as I did mine, and constructive criticism is always welcome. The operative word being constructive.

Thanks for the post, mho, 40 iiq and 200 iir just for me is a sweet spot.

Andy

(see below)

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LazarusQ wrote:

You think exponentials because it's bounded, I think powers because look at armour and evasion.

Exponentials are sums of powers...

My main point was that your reservation against your own formula based on that it doesn't yield appropriate low-iiq results, assumes characteristics about its designers, assumptions I strongly disagree with.

I have, unlike you, no interest in finding their flawed formulas. The formula I provided is a better one due to having advantageous characteristics that GGG's one likely doesn't.

Edit:

As for your "welcome". It doesn't matter to me whether or not you welcome anything XD.

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mazul wrote:

Exponentials are sums of powers...

Yes, this is totally relevant to the discussion.

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mazul wrote:

My main point was that your reservation against your own formula based on that it doesn't yield appropriate low-iiq results, assumes characteristics about its designers, assumptions I strongly disagree with.

Well, my reservations were not that strong, actually, I'm pretty happy with my results.

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mazul wrote:

I have, unlike you, no interest in finding their flawed formulas. The formula I provided is a better one due to having advantageous characteristics that GGG's one likely doesn't.

So you may have misunderstood the topic of this thread. In any case, I think GGG are hiring at the moment, you should send them your CV.

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mazul wrote:

As for your "welcome". It doesn't matter to me whether or not you welcome anything XD.

Aww, man, don't say that, you know that was the whole reason for my existence. What am I supposed to do, now ?