Drop rates and deck selection

[Jenkar]

I'm not surprised, imo we need way more data for it to be relevant.

On the note about multiplication : what we're calculatin is :
1- (Min (experimental,theorical)/Max (experimental,theorical))
for which multiplyin' your value by 3 or dividin' ours by 3 doesn't change a thing.

[Dark Weaver]

sorry it was Jangoo who was surprised about it, and he talked about absolute error like 10men pointed out.

[Jangoo]

So I went ahead, downloaded the spreadsheet and merged its data with the data from the FG-efficiency-study,
thus effectively doubling the sample-size.

What can I say? ... The two studies averaged each other out towards DWs values pretty friggin well!

Overall, there is a lot less red and yellow in that table now and those values that didn't make it to yellow-status before,
more often than not are now almost identical with DWs. 

My conclusion:
DarkWeavers numbers are the shit!
I will just go ahead and use them to tune the Statmasta now ... 

FG	DarkWeaver	Merged studies	Sample size
Akebono Chaos Lord Dark Matter Decay Destiny Divine Glory Dream Catcher Elidnis Eternal Phoenix Ferox Fire Queen Gemini Graviton Hecate Hermes Incarnate Jezebel Lionheart Miracle Morte Neptune Obliterator Octane Osiris Paradox Rainbow Scorpio Seism Serket	58,63% 38,68% 41,26% 61,41% 44,74% 68,00% 37,58% 37,33% 56,25% 44,43% 50,92% 49,76% 46,88% 54,71% 39,26% 48,34% 59,72% 47,36% 37,75% 37,84% 47,07% 48,15% 59,71% 57,22% 48,19% 36,10% 36,54% 41,99% 48,29%	56,86% 40,71% 38,40% 59,74% 43,54% 80,80% 34,02% 35,07% 43,42% 50,28% 51,94% 44,39% 45,88% 56,29% 30,99% 45,51% 54,13% 39,29% 37,37% 34,45% 41,14% 44,83% 54,74% 54,75% 52,16% 31,78% 37,21% 41,46% 42,92%	204 140 125 154 294 125 97 211 76 177 206 223 85 167 71 334 109 252 281 209 333 203 137 179 324 107 129 164 219

---

As for the "tripled error" thing:

Whatever the mathematical explanations behind it, tripling DWs first column is the only way to make sense of these numbers for practical purposes.
Nobody really wants to know how big the chance is to win ONE card in howevermany spins ... You'd wanna know how many cards you win from a FG
once you win the game. Since it will always be three spins ... why split around with the probabilities?

[Polari]

As for the "tripled error" thing:

Whatever the mathematical explanations behind it, tripling DWs first column is the only way to make sense of these numbers for practical purposes.
Nobody really wants to know how big the chance is to win ONE card in howevermany spins ... You'd wanna know how many cards you win from a FG
once you win the game. Since it will always be three spins ... why split around with the probabilities?

Like I said earlier, the way you've done this works for the purposes of comparing the two numbers, but I don't think you understand what these numbers actually represent. They lie on a scale from 0 to 3 and it's bound to get confusing at some point if you're going to denote them as percentages or refer to them as probabilities.

[moonlighting]

if you want to calculate the "expected number of cards you win in x games", then you should use darkweaver's first column and multiply by 3.

and if you want to test " the probability of winning one card in one spin", you should use the number of cards won / number of games won / 3

[Jangoo]

What those various numbers imply is in fact crystal clear to me guys ...


Except for one thing:

Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?

[Dark Weaver]

Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?

No, it’s because the first column multiplied by 3 is not a probability that it can be > 100%
What the first column ×3 means is what moonlight said, even I called it probability but it isn’t and I was wrong.
y% chance to win a card in one spin is easy to interpret, each time you spin the reels there are y% chances you’ll win a card. It also means that in n spins you expect to win n×y% cards.  If you multiply y% by 3, it doesn’t mean anything, it is not the probability to win a card in 3 spins, it’s just a probability multiplied by 3 which is just a number.
To interpret the number, you can say that winning a game always give 3 spins, so in 3×n spins you expect to win 3×n×y% cards, which is equivalent to say : in n winning game you expect to win n×(3×y%) ; and with n=1, you have the meaning of the number, 3×y% is the number of cards you expect to win in 1 game (which obviously has nothing to do with a probability).
Suppose a FG has a 60% probability to drop a card in 1 spin :
you win on average 0.6 cards per spin
you win on average 1.8 cards per game
In the first case the probability is equivalent to the number of cards wins because 0.6 = 0×0.4 + 1×0.6 , for the second case 1.8 = 0×(0.4)³ + 1×(0.4)²(0.6)×3 + 2×(0.4)(0.6)²×3 + 3×(0.6)³
And putting 1.8 in % (180%) has no sense, you can just put 180 for the average in 100 games.

[10 men]

Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?

Yes. First column x 3 is not a probability but the expected value. That is fine because the expected value is what you're looking for - "If I pick this deck up and click on False God, how many cards/Electrum can I expect to win?"

The expected value for one win is calculated by calculating the expected value of one spin which in turn is the probability to win one card in one spin.

[Jangoo]

Great guys ... thanks.


This thread and study has really helped a lot. 

[Rainmaker]

To interpret the number, you can say that winning a game always give 3 spins, so in 3×n spins you expect to win 3×n×y% cards, which is equivalent to say : in n winning game you expect to win n×(3×y%) ; and with n=1, you have the meaning of the number, 3×y% is the number of cards you expect to win in 1 game (which obviously has nothing to do with a probability).
Suppose a FG has a 60% probability to drop a card in 1 spin :
you win on average 0.6 cards per spin
you win on average 1.8 cards per game
In the first case the probability is equivalent to the number of cards wins because 0.6 = 0×0.4 + 1×0.6 , for the second case 1.8 = 0×(0.4)³ + 1×(0.4)²(0.6)×3 + 2×(0.4)(0.6)²×3 + 3×(0.6)³
And putting 1.8 in % (180%) has no sense, you can just put 180 for the average in 100 games.

This is wrong.
This probability distribution is called Binomial:

If your probability of success is p=0,6; and you have 3 oportunities then:

B(p=0,6/n=3/r=?) = (r/n) * p^r * (1-p)^(n-r)

r=1 means the chances of winning only 1 card in 3 spins; the r/n = r!/(n-r)!
Which explains the different sorting: (w=win, f=failure)
w.f.f - f.w.f - f.f.w

r=2 means the chances of winning 2 cards in 3 spins:
w.w.f - w.f.w - f.w.w

r=3 means the chances of winning 3 cards in 3 spins:
w.w.w

r= means the chances of winning 0 cards in 3 spins:
f.f.f

B(r=0) + B(r=1) + B(r=2) + B(r=n=3) = 1 (sum of all probabilities).

The chances of winning AT LEAST 1 card would be:
 B(r=1) + B(r=2) + B(r=3)
Which is the same as:
 B(r=1) + B(r=2) + B(r=3) =1-B(r=0) =

[Dark Weaver]

I don’t know what you are trying to say nor what is wrong for you, also I know what a Binomial distribution is.
If you want me to be more explicit :
1.8 cards = 0cards × (probability to win 0 cards) + 1card × (probability to win 1 card) + 2cards × (probability to win 2 cards) + 3cards × (probability to win 3 cards)
this is not a probability, probability distribution or whatever, it is the average number of cards won per game (or 3spins)
And yes, (probability to win x cards) is a Binomial distribution so what ? we can say that the expected value is n×p (n is the number of experiments and p the probability for a success) which in this case is 3 × 0.6 or that the expected value is the sum of the expected value of the n Bernouilli trials in this case 0.6 +0.6 +0.6
I used the old fashion Expected value definition, and it is plainly correct.

[Bhlewos]

Dunno if it might help, but I used Xeno's XenoSim (http://elementscommunity.org/forum/index.php/topic,31602.0.html) to calculate droprates, and got these results (http://elementscommunity.org/forum/index.php/topic,31106.msg427170#msg427170).

So according to runs of 10k each, the 5 FGs with the highest droprates are Divine Glory, Decay, Octane, Jezebel, and Akebono. Make of that what you will.