Some EC day2 analisis

Regarding disciplines

Did you just count which decks would've had ACCESS to certain disciplines or did you count the actual cards in each deck that used the discipline.

A Ventrue voter deck might not have a single dom card in the deck (unlikely that no bounce would be included but still...)

2 Ankha:

1) You failed to read sign after probability analisis.
2) Analisis of 1/14 and 20%/35% is totally the same one, so you have to drop both or like both
3) "backwards" probability extruction are totally wrong in any sample size, but still can be used for some general conclusions (that if you got moustache than you got much more chance to became NBA star that if you got big boobs, reverse of this for other industry )

Whole point of it was not to calculate probabilities, but to show, that mythes about brokennes of some disciplines/strategies got nothing to do with real situation at the top level of the game, so active members of comunity can consentrate on more pressing meters to solve.

Lönkka wrote:

Did you just count which decks would've had ACCESS to certain disciplines or did you count the actual cards in each deck that used the discipline.

Card use, obviously. It's kinda dumb to make conclusions from access (Lutz decks with potence ftw!).

Obviously for finals decks we have more detailed information, for others I have to guess, but generally I think example of ventrue deck without dom and other such strange things is kind of not possible in ec day2 situation.

So 35 out 0f 40 were educated guesses...

*sigh*

Ankha wrote:

elotar wrote:

Of course, having a dom deck have a greater influence on the outcome of the result (being in final), but the method is the same: you can't extract probabilities from one event.

Maybe you wanted to compute something like:

There are 14/40 : 35% of dom decks
In the final there is 1/5 : 20% of dom decks

and compare those results. So there is slightly less dom decks in finals that there should be. The trouble is that you have only 5 players in final, so rounding is necessarily extreme since there should be 1.75 player in final. Fractions of players are hard to obtain. If there had been 2 players, there would have been 40% of dom decks, which is above 35%. It wouldn't have meant anything neither.


You can't tell anything significant from these numbers because they are too little.

It is true that elotar's probabilities were wrong, and it is completely true that if there are 40 decks and 14 out of them have dominate, then chance that at least 1 will ge to the final round is cca 90% assuming that these are chosen randomly.

So when you do that kind of calculation you simply assume that players come to table they all get a number from 1-40, these are put into hat and referee will randomly choose 5 without replacement. This gives you no information whatsoever on whether dominate is stronger or weaker than other disciplines.

However, not everything is lost yet! I propose this experiment.

Let's as a thought experiment start with assumptions:

1. Each deck has equal probability to get into the final round.
2. There is no selection bias (i.e. its not that better players choose dominate because they want to win, or that they don't choose the dominate because they are unconsciously compassionate and want to give other players better chance etc. etc.)

(I know that these are unlikely to hold but bare with me).

Base on this assumption I generated 1000 trials where there were 14 dominate decks and 26 others, and I assumed the they got to the finals completely on random, and thus I generated 1000 possible finals, conditional on the original distribution of decks.

Now the experiment is this:

If the number of dominate decks in finals, is significantly higher, than you would expect if everything is completely random, that would show that that dominate is clearly OP (since this would imply that deck with dominate has higher than pure random chances, conditional on distribution of entrants and no selection bias, to get into the finals).

If the number of dominate decks in finals, is significantly lower, than you would expect if everything is completely random, that would show that that dominate is weak.

If you cannot significantly distinguish that datapoint from the random distribution that was drawn from the entry data, then you cannot say that dominate is better or worse than other disciplines.

Now these are the results from my simulation:

Out of 1000 simulations there were:

131 finals with 0 dominate deck
302 finals with 1 dominate deck
334 finals with 2 dominate decks
173 finals with 3 dominate decks
56 finals with 4 dominate decks
4 finals with 5 dominate decks

(see histogram in drive.google.com/file/d/0B00nqfllsuM_dXhEX3dkQnNqVzQ/view?usp=sharing)

And here is some descriptive stat:

Mean 1,733
Standard Error 0,034480428
Median 2
Mode 2
Standard Deviation 1,090366865
Sample Variance 1,1888999

So clearly, because in actual finals there was just 1 dominate deck, but the most likely outcome was that there will be 2, the hypothesis that dominate is OP based on the aforementioned assumptions, is out of the window.

Now with H0: dominate is equally good than other disciplines.
and with HA: dominate is worse than other disciplines.

To decide between these two hypotheses we can compare the probability that the real tournament was from our distribution which is simply based on the trials 302/1000 = 0.302 or 30.2%

and apply conventional significance criteria (i.e. Reject HA if probability is higher than 1% or 5% or 10%). We can reject HA, at all conventional significance levels.

So how you should interpret my results?

1. You cannot reject the H0 that all disciplines are equally good, conditional on that there was no selection bias, and all players are equally good.

But we know that those assumptions are unlikely to hold.

So what can we say given that we reject the aforementioned assumption? We can say this:

The evidence (from this single tournament) is not inconsistent with the hypothesis that dominate is not stronger than other disciplines. Further studies needed (give me grant money EU! ).

PS: sorry for long post.

1muflon1 wrote:

Out of 1000 simulations there were:

302 finals with 1 dominate deck
334 finals with 2 dominate decks
173 finals with 3 dominate decks
56 finals with 4 dominate decks
4 finals with 5 dominate decks

So 131 of finals without dominate?

So, generally, we can't use your analisis on popular disciplines like dom/aus - nearly any results short of 5 in a finals will be possible.

Try this with "tier 3" disciplines, like nec, with 7.5% presence in the pool and 20% in the finals. It may be more interesting.