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[jotheonah]

This seems like a potentially useful thing, but when I go to the card stats I can't make heads or tails of them. I'm not a math person and I don't understand what each column means and how to interpret the numbers therein.

And I know some people on this board are really good at explaining things, including math things.

[rrenaud]

From http://councilroom.com/win_rate_diff_accum.html

(maybe I should add this blurb to the pop buys page?)

Win rates

Win rate is a generalization of winning probability for multiplayer games.

A win in a 2 player game is worth 2 points, a 3 player game is worth 3, and so on. Someone who plays only 2 player games and wins every time will have a winrate of 2; a 2-player gamer who loses every game has a winrate of 0; a 2-player gamer who wins exactly as often as expected (half wins, half losses) has a winrate of 1.

The win rate of an event is the average number of points for that event. So an event that is uncorrelated with winning will have a win rate of 1.0, and events correlated with winning have a win rate of > 1.0, and losing with < 1.0.

[jotheonah]

And when we talk about a card as an event we're talking about ... buying that card? gaining it? having it? playing it? not buying it when it's available?

[Elyv]

And when we talk about a card as an event we're talking about ... buying that card? gaining it? having it? playing it? not buying it when it's available?

Depends on which column you look at.

[The Adventurer]

Yea I don't get it all either. What would be most useful would be a non jargonny, veeeery simple and illustrated legend, clearly following each column one at a time. Not just detailing the "shadier" ones, but all of them.

...and as I expected, people respond to these kind of questions quickly, without much detail or explanations, and dismiss it, like Elyv just did (not an insult, just a fact).

Is there anyone who would be generous of his/her time and kindly go through every column I would see on my own player page, stats per card grid, and define and give a clear example of how this works? Would be very useful thank you

[theory]

I think documentation is something we need to work on, but Elyv's response is accurate: "win rate given gain" is win rate given that you gained the card, and "win rate given avail" means win when it's available, and so on.

I'll ask rrenaud to fully rehash the technicalities of how the numbers are generated, and then I'll try to write up a clearer legend.

[jotheonah]

That would be awesome.

[HiveMindEmulator]

The really confusing one is "effect with": "the number of standard deviations better than expected you perform when you buy or gain the card". Over what distribution are the expectation and standard deviations taken over? Your win points in all games including those without the card? Or the win points of people who bought the card in all games including those not played by you? Or something else?

[DStu]

So we are talking about the popular buys page:
From left to right:
Card should be clear
Avaiability is the total number of games where this card appears
Buys is the average number of cards of this type that is bought in a game where this card appears
Gains is the same for gains (by other means than buys)
%+ is the percantage of the games where this card appears where it is gained (or buyed) at least once
Trashes/returns is the same as Buys/gains for trashed cards or returned to supply (Ambassador)
Win Rate with is the winrate of the players that have gained the card. A rate of 1 means 50% in 2player. The +- gives the amount of certainy, not really important, the more games appear where the card is bought the more certain you can be
Win Rate without is the same when you don't gain it.
Turns and Turns(C) gives the number of turns the game last when this card is present.

For your personal site than everything again for your games.
+
Winrate given Avail: What's your winrate when this card is present.
Effect With: Tells you somehow how much better you are when you buy this card than average. The average is calculated kind of I don't know how.
Effect Without: The same when you don't buy

So for your Adventurer:
The card was present in 584019.0. On average, when it's present, 0.26 of them it was buyed by each player, 0.02 gained by other means. In 21% of the games it was bought/gained at least once.    0.01 Adventurers where trashed on averages and 0 returned.
Winrate with Ad. is 0.93 (so below th average of 1), without it's 1.02. Game length on average is 20.95, 23.30 when Colonies are present.
You yourself have played 44 games with Adventurer, your winrate when the card is on the board is 0.90. On average you buy 0.39 Adventurers when they are on the board and gain 0.11 by other means. You gain it at 31.8% of the games. You trash/return 0.09/0.05 Adv. on average. When you buy it your winrate is 0.50 (so only half as much as expected), when you don't it's 1.08. Your effect with therefore is -1.48(pretty much negative), without it's 0.34 (moderately positive). Average number of turns where 20.15 (Colonies 23.38).

[theory]

The really confusing one is "effect with": "the number of standard deviations better than expected you perform when you buy or gain the card". Over what distribution are the expectation and standard deviations taken over? Your win points in all games including those without the card? Or the win points of people who bought the card in all games including those not played by you? Or something else?

The way "effect with" works is this.  My personal "leverage" for, say, Mountebank, is my win rate when I buy/gain Mountebank minus my overall win rate.  The general population's "leverage" for Mountebank is their win rate when they buy/gain Mountebank minus 1.00 (the global population's win rate).  "Effect with" is how much those two leverages vary, measured in terms of stdev.  (Effect without is derived in a similar way.)

[Elyv]

So, a couple examples of how to use those stats(or at least, of how I use them). I'm using myself, because I'm narcissistic like that(and because I know where the numbers came from). Some of what I say may be wrong, because this is largely stuff I've worked out on my own.

My win rate if copper is available is 1.28. That means that I tend to get 1.28 win points per game, and because I play almost exclusively 2-player, means I win an average of 1.28/2.00=64% of my games. Note that this has absolutely nothing to do with player skill, so the fact that it's higher than, say, chwhite's or WanderingWinder's winrates(both of whom are better than me) probably comes from a combination of me playing about 10% of my games against an IRL friend who I'm better than and playing automatch +/-20 for a long time instead of the +/-15 or +/-10 that I think both of them use.

My winrate with outpost is 1.71 and my Effect With is 3.86. Does that mean I have some insane insight into the card? Well, not really; if we look at %+, I only gain it in 18.5% of games where it's available, because I use it mostly as a win more type of card, to turn a 90% win into a 95% win when you're using minions or something, which means I get almost exclusively in games I would've won anyway.

Speaking of minion, my effect with minion is -2.10. Is it because of bad luck or something? Well, no; there's something I don't get about how to play the card, and the only reason my winrate is still >50% with it is people occasionally do silly stuff(This game probably being the best example of that, there is no way I should have won that game).

My effect without hamlet is 2.66, but my effect with is -0.56. However, I also get Hamlet in 91% of games, so what that means is that when I think my deck doesn't want hamlet, I'm usually right, but I'm not very good in games where I should be buying them(which I believe is most games).

My effect with Ambassador -0.76. That's because I've bought it a lot, but the winrate is still below what councilroom expects(which I think is my overall winrate times the winrate the population as a whole has with ambassador, so 1.28*1.04=1.33).

[HiveMindEmulator]

The really confusing one is "effect with": "the number of standard deviations better than expected you perform when you buy or gain the card". Over what distribution are the expectation and standard deviations taken over? Your win points in all games including those without the card? Or the win points of people who bought the card in all games including those not played by you? Or something else?

The way "effect with" works is this.  My personal "leverage" for, say, Mountebank, is my win rate when I buy/gain Mountebank minus my overall win rate.  The general population's "leverage" for Mountebank is their win rate when they buy/gain Mountebank minus 1.00 (the global population's win rate).  "Effect with" is how much those two leverages vary, measured in terms of stdev.  (Effect without is derived in a similar way.)

Standard deviations of what? My withrate with? My winrate given avail?

[rspeer]

Standard deviations of what? My withrate with? My winrate given avail?

Standard deviations of differences of differences of win rates -- as in, the weird statistic you have left after you take all those differences. It's not really important; what's important is you get a number and if it's over 2 or under -2 it probably means something.

I made "effect with" and "effect without" because I wanted to aggregate all the stats together to answer this one question: In situations where you gain (or don't gain) this card, do you tend to play better than usual, or worse than usual? If you try to think about how all the numbers factor into those questions, your head will hurt.

It's probably not a very good statistic. It has weird artifacts sometimes. Here's one that comes to mind: player skills and card effects don't really add together. tat wins 54% more games than the average player. And players who buy Followers win 54% more than average. So tat with a Followers would need to win 108% more than average, just to get an effect of 0. Since that's both unreasonable and completely impossible in 2-player games, tat's effect with Followers is very, very low.

Anyone who's confused by this page, the fault isn't yours, it's ours. It is the least comprehensible page imaginable, and I added two particularly confusing columns to it on my own whim.

[HiveMindEmulator]

I know it may not be particularly important, but I'm curious about the actual formulation so I can decide if/when any of these "weird artifacts" are occuring. It's the standard deviation of win differences taken over all players? i.e.
if W_a = player a's win rate with - player a's average win rate
W_avg = \sum_i{W_i}/(total # players), where the sum is over all players, i.
the squared standard deviation in question is then
\sum_i{(W_i-W_avg)^2}/(total # players) ?
Or is the sum over something else, like all cards?

[rspeer]

The sum is over all games in which the events in question occur.

Every win rate is a random variable, which we describe with its mean and... well, I've been saying standard deviation, but I think this is actually standard error of the mean (SEM), which is the stdev divided by the square root of the number of games. Anyway, that's the +/- part shown on all the stats.

Let me change the notation a bit, and focus just on the "effect with" case:
W_pc is the win rate of a given player when gaining a given card. (So take all the win values from all the games you play where you gain Smugglers, for example, and find the mean and SEM.)
W_p* is the win rate of that player over all their games.
W_*c is the win rate of all players over all games where they gain that card.
W_** is the win rate of all players over all games, which we can replace with the constant 1.

The effectiveness is measuring (W_pc - W_p*) - (W_*c - 1). When you subtract these random variables from each other, you subtract their means, and you add their squared SEMs. This gives you a new random variable that I call "Effectiveness", or "Effect" because that page is already desperately low on horizontal space.

Then to get one value you can sort by, I divide the mean by the SEM.

The more I describe this, the shoddier the statistics sound. I mean, the things we're measuring aren't even normal distributions, they're mostly a Bernoulli distribution made of 0s (you lost) and 2s (you won a 2-player game). But I feel like it still manages to communicate something, I probably won't spend the time to do it right, and if we took it out of Council Room people would miss it.

[jotheonah]

Well I've certainly learned a lot. Including to maybe not take the stats TOO seriously. Still I'm really grateful to have isotropic, let alone council room and this blog, so i'm sure as hell not complaining.

[DrHades]

What does the "Win Prob" at the end of an game report at Council Room means?

[rrenaud]

The win prob stuff is totally broken right now.  For sometime it gave an okay to bad estimation of who was going to win the game, but then hinterlands came out and I didn't update things, so it's horribly, horribly broken.

OTOH, I'll finally start fixing things on councilroom again soon.

[HiveMindEmulator]

The more I describe this, the shoddier the statistics sound. I mean, the things we're measuring aren't even normal distributions, they're mostly a Bernoulli distribution made of 0s (you lost) and 2s (you won a 2-player game). But I feel like it still manages to communicate something, I probably won't spend the time to do it right, and if we took it out of Council Room people would miss it.

I don't think it's that bad. Game results are Bernoulli, but you're trying to estimate the parameter p of the distribution, which is a constant, your estimate of which is random and roughly normal after a large number of games.
The statistic is also positively correlated with win rate with, negatively correlated with the public's win rate with and your overall win rate, which are properties you want in the statistic. The only question is if dividing by the SEM is the right thing to do. This makes this statistic's magnitude negatively correlated with your number of games played.

[rspeer]

The SEM is already negatively correlated with your number of games played. Dividing by it makes it positively correlated. Which is the whole purpose: to emphasize statistics with more evidence behind them.

[toaster]

Perhaps the most useful shorthand to know is that for 2 player games, win rate / 2 = win percentage.