Hi all. I am following very often Ranior, Lumin, EconSean live agricola gaming on Twitch and then I would like to give my point of view, since they often ask the community to do it.
From a subjective point of view i definitevely think both Big Country and Begging Student should be banned as soon as possible.
From an objective point of view I formulated my own way to determine if a card should be banned or not. I worked in particle physics and I applied a first rough estimation method for the significance that a card has to be considered too strong with respect to the average.
As an example I used the AB decks data Lumin showed in his post (the first table he published in the following post https://boardgamearena.com/forum/viewto ... 6&p=101625).
In principle, the probability P that a card has to be found among the played cards of the winner ("win-play probability") can be expressed as:
P=(x*y)/(z*w) where:
x=total number of cards drafted in a game (56 as in Lumin's table)
y=probability that a card has to be played in a game
z=number of players (4 as in Lumin's table)
w=total number of cards in the deck (94 as in Lumin's AB deck table)
Then P=0.1498*y
From the table Lumin posted I inferred the total number of games he analyzed. 331 was the averaged number of times a card was drafted, so that multiplying 331*(94/56) ,where 94 is the total number of the cards in the table (minor+occs in the AB deck), I obtained 555 games.
Thus 555*0.1498*y=83.139*y is the "win-play value" that each card should have after 555 games.
y can span from 0 to 1 since it's a probability value. If we consider y=1 it's like taking in account all the possibile combos that have led that card to win. As a matter of fact, when y=1 this means that in every game we assume that all occs and minors are played. Therefore, 83.139 can be considered as the maximum "win-play value" a card can have in 555 games, taking in account all the possible combos.
83.139 can be considered as a "background value". The significance S that a card has to be considered stronger with respect to the background can be computed in this way:
S = (k-z)/sqrt(z) where:
k=win-play value from the data for each card
z=maximum win-play value for the dataset analyzed (in this case 83.139)
This significance S is telling us how much a card can be considered significantly different from the max strenght a card can typically have.
The only card that showed more than 3 sigma (which is the standard value used in physics) is Big Country. 3 sigma means that with a 99.7% confidence level we can consider Big Country significantly different from all the other cards in terms of capability to let you win.
In the table Lumin showed Big Country had 118 win-play value which corresponds, in this framework, to 3.8 sigma.
I am looking forward to have more data from CD decks in order to evaluate the significance for Begging Student and other CD cards.
Suggestions and comments are welcome, bye!
From a subjective point of view i definitevely think both Big Country and Begging Student should be banned as soon as possible.
From an objective point of view I formulated my own way to determine if a card should be banned or not. I worked in particle physics and I applied a first rough estimation method for the significance that a card has to be considered too strong with respect to the average.
As an example I used the AB decks data Lumin showed in his post (the first table he published in the following post https://boardgamearena.com/forum/viewto ... 6&p=101625).
In principle, the probability P that a card has to be found among the played cards of the winner ("win-play probability") can be expressed as:
P=(x*y)/(z*w) where:
x=total number of cards drafted in a game (56 as in Lumin's table)
y=probability that a card has to be played in a game
z=number of players (4 as in Lumin's table)
w=total number of cards in the deck (94 as in Lumin's AB deck table)
Then P=0.1498*y
From the table Lumin posted I inferred the total number of games he analyzed. 331 was the averaged number of times a card was drafted, so that multiplying 331*(94/56) ,where 94 is the total number of the cards in the table (minor+occs in the AB deck), I obtained 555 games.
Thus 555*0.1498*y=83.139*y is the "win-play value" that each card should have after 555 games.
y can span from 0 to 1 since it's a probability value. If we consider y=1 it's like taking in account all the possibile combos that have led that card to win. As a matter of fact, when y=1 this means that in every game we assume that all occs and minors are played. Therefore, 83.139 can be considered as the maximum "win-play value" a card can have in 555 games, taking in account all the possible combos.
83.139 can be considered as a "background value". The significance S that a card has to be considered stronger with respect to the background can be computed in this way:
S = (k-z)/sqrt(z) where:
k=win-play value from the data for each card
z=maximum win-play value for the dataset analyzed (in this case 83.139)
This significance S is telling us how much a card can be considered significantly different from the max strenght a card can typically have.
The only card that showed more than 3 sigma (which is the standard value used in physics) is Big Country. 3 sigma means that with a 99.7% confidence level we can consider Big Country significantly different from all the other cards in terms of capability to let you win.
In the table Lumin showed Big Country had 118 win-play value which corresponds, in this framework, to 3.8 sigma.
I am looking forward to have more data from CD decks in order to evaluate the significance for Begging Student and other CD cards.
Suggestions and comments are welcome, bye!