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[timchen]

If you look at my council room stats, it shows that explorer is one of my worst cards, judging from the win rate given availability. My win rate with explorer is ~1.25, whereas my average win rate is around 1.4.

Now, this fact itself is already very strange. The explorer is a highly irrelevant card. Let's say in 85% of the board the correct way of play is just to ignore it; and in 80% of the boards, I will ignore it correctly. For those boards my win rate should be around 1.4, maybe increasing a little bit due to the misjudgement of my opponent.

Therefore, in order to have an average win rate of 1.25, in those games that matters, I must have a win rate of ~0.65. That is, I lost 2/3 of the game when the explorer is relevant and on the board. Does that mean I judge this particular card terribly wrong?

Maybe not... it is way more likely just a statistical anomaly.

[DG]

How can your "win rate without explorer" be so much less than your avaerage? It's most likely that you're over buying it or under buying it and losing games because of it. My guess is obviously under buying it and opponents are finding some advantage from explorers being in the set that you're not. I'd take that conclusion rather than say "I know the explorer is irrelevant therefore the statistics are wrong".

Following on from that, if you're only buying the explorer at the most favourable moments then you should have a good "win rate with  explorer". However this isn't the case so you're probably framing it in the wrong decks or expecting it to play differently than it actually does. Maybe you need to go back and have a look at a few game logs and see what's happening. Everyone has a few cards they think they understand when there's actually more to learn.

[WanderingWinder]

How can your "win rate without explorer" be so much less than your avaerage? It's most likely that you're over buying it or under buying it and losing games because of it. My guess is obviously under buying it and opponents are finding some advantage from explorers being in the set that you're not. I'd take that conclusion rather than say "I know the explorer is irrelevant therefore the statistics are wrong".

Following on from that, if you're only buying the explorer at the most favourable moments then you should have a good "win rate with  explorer". However this isn't the case so you're probably framing it in the wrong decks or expecting it to play differently than it actually does. Maybe you need to go back and have a look at a few game logs and see what's happening. Everyone has a few cards they think they understand when there's actually more to learn.

Or maybe it's not so much that he's under-buying it, but more that everybody realizes it sucks, which means everyone ignores it, correctly, which brings everyone one step closer to the parity win rate of 1.00, which looks like he's making a mistake, whereas really it's just a card that he doesn't have as much advantage over his opponents on, not so much 'cause he plays it badly as because it's easier for them to play well.
That was far too verbose, but I hope my point got across.

[popsofctown]

Maybe the presence of a card that unusually weak has a subtle, negative psychological effect for you.  For instance, the other 5's might look comparatively more powerful, or the presence of a weak treasure based card might make you pick up villages when you ought to get silver.

Maybe you always start buying Duchies once an opponent does and Explorer is one of the only cards that punishes you pretty hard for that if your deck is slimmer.

Could be lots of things.

[DG]

Or maybe it's not so much that he's under-buying it, but more that everybody realizes it sucks, which means everyone ignores it, correctly, which brings everyone one step closer to the parity win rate of 1.00, which looks like he's making a mistake, whereas really it's just a card that he doesn't have as much advantage over his opponents on, not so much 'cause he plays it badly as because it's easier for them to play well.

That's possible, however my win rate with the explorer used to be over 1.4 with a modest (30%?) purchase rate. I'm guessing that if I can find some success with it then so can someone else.

[timchen]

I guess I didn't state the problem clear enough-- the point is that I assume in a large portion of games, explorer will just be a card sitting there. In those games, I should be able to get a win rate at least the same as my average since I choose not to buy it correctly.

Now the total average of my win rate of the card is 1.25. This must mean in those games that explorer can be relevant , I have to have a horrible win rate. If I assume there are 1/4 games where explorer can be relevant, then in those games my average win rate has to drop to 0.8. Sure, 0.8 win rate is not that low against some good player at explorer, but certainly I didn't pick my opponents to play with explorer, and I have my win rate at 1.4 over the same ensemble of opponents.

By statistical anomaly, I just mean, if you look at the standard deviation of the win rate and calculate the standard deviation of the win rate of the games where explorer is relevant, in the example I gave it becomes 0.8+-0.6. The other way to say the same thing is that the win rate it self is 1.25+-0.14, but at one standard deviation it is already 1.4. This implies in average we would find one card in six to have this kind of phenomena. Since I am looking at my worst 10, finding one of them have such statistical anomaly is probably not so surprising.

[WanderingWinder]

I guess I didn't state the problem clear enough-- the point is that I assume in a large portion of games, explorer will just be a card sitting there. In those games, I should be able to get a win rate at least the same as my average since I choose not to buy it correctly.

But this is faulty analysis, based on bad assumptions. You don't just magically win 70% of your games. You evaluate cards and/or boards better than other people. And I'm guessing you don't have as much of that advantage in games with explorer. Because even though you can make the correct decision on explorer, everybody else can, too.
Does that make sense?

[Voltgloss]

Some other salient data:

- Your "Effect Without" Explorer is -2.67, which is your second-lowest stat out of all cards (after Rabble at -2.69).  This is far lower than your "Effect With" Explorer (-0.59), suggesting that the majority of your Explorer losses come in games where you erred by ignoring it.

- Your "%+" stat for Explorer is 9.1, which is fourth-lowest out of all cards (after Counting House, Stash, and Thief).  However, your "effect without" those other three cards is either positive (0.80 for Counting House; 0.02 for Thief) or much less negative than Explorer (-0.65 for Stash).  So, for those other cards, you are correct to ignore them far more often than you correctly ignore Explorer.

- The only cards for which you have worse "Win Rate Given Avail" than Explorer are Hinterlands cards that you've played very few games with (comparatively), and therefore their Win Rates are held down by high variance.  Out of all the cards for which your stats have a decent sample size, Explorer is your worst.

My conclusion?  It seems you are starting from a faulty premise:

The explorer is a highly irrelevant card. Let's say in 85% of the board the correct way of play is just to ignore it; and in 80% of the boards, I will ignore it correctly.

The stats suggest instead that Explorer must be relevant in significantly more games than you think.  And in those games, you tend to ignore it incorrectly more often than not.

[rrenaud]

Volt, if what you say is true, then you should be able to find game logs in which he lost because of Explorer misplay.  I am skeptical that there are going to be clear instances where he missed an Explorer buy that caused him to lose.

I love data, but don't be a slave to it.  As Tim noted, sometimes there is no real signal in data, and you are just looking at noise.  This is even more likely to happen when you are sorting and selecting the top (or bottom) of the distribution.

[WanderingWinder]

Some other salient data:

- Your "Effect Without" Explorer is -2.67, which is your second-lowest stat out of all cards (after Rabble at -2.69).  This is far lower than your "Effect With" Explorer (-0.59), suggesting that the majority of your Explorer losses come in games where you erred by ignoring it.

In fact, that's not what that suggests at all. What that suggests is that he gets much less benefit out of ignoring it than other players do, and that's probably because he's making the SAME decisions more often than not with this card, but with other cards, he's making better decisions than they are.

[DG]

Volt, if what you say is true, then you should be able to find game logs in which he lost because of Explorer misplay.  I am skeptical that there are going to be clear instances where he missed an Explorer buy that caused him to lose.

Don't be so sceptical. I've looked at these sorts of figures in the past and tried to persuade myself that islands had very few ways to be played and wouldn't really affect win rates. I'd lost a lot of games where I appeared to be playing exactly the same island and money deck as my opponent and lost through poor shuffles. After some consideration, and looking at other people's good island stats, I realised that I was completely wrong and needed to time island purchases better and shape more suitable decks for them.

[Voltgloss]

Volt, if what you say is true, then you should be able to find game logs in which he lost because of Explorer misplay.  I am skeptical that there are going to be clear instances where he missed an Explorer buy that caused him to lose.

http://councilroom.com/game?game_id=game-20111014-234302-fd633c36.html

In which Mean Mr Mustard wins 36-30, opening Silver/Silver and buying two Explorers on turns 5 and 6, otherwise playing Big Money.  timchen opened Silver/Woodcutter; his only $5 buy was on turn 5, when he bought Venture/Silver with $8 and two buys.  Explorer was played four times, for 3 Silvers and a Gold.

http://councilroom.com/game?game_id=game-20101204-105812-6d323d79.html

In which Knave wins 43-32, despite splitting the Minions 4-6, after opening Tactician/Embargo and buying an Explorer on turn 3.  timchen opened Quarry/Silver and used $5 turns to buy Minions and Duchies until both piles emptied, after which he bought Silvers and Conspirators.  Explorer was played five times, once to gain a Gold around timchen's Embargoing the stack.

http://councilroom.com/game?game_id=game-20111205-202423-a810ec28.html

In which busta limes wins 45-21, opening Feast/Silver and using the Feast to get an Explorer on turn 3.  timchen opened Black Market/Lighthouse and used $5 turns to buy Royal Seals.  Explorer was played five times, producing 5 of busta limes's 6 Silvers.

http://councilroom.com/game?game_id=game-20111026-232400-2af8f8c5.html

In which Elm wins 33-30 after opening Explorer/nothing to timchen's Spice Merchant/Shanty Town.  timchen used $5 turns to buy two Governors (which his opponent also buys) and, on turn 5, a Silver.  Explorer was played five times for 4 Silvers and, in the last turn, a Gold needed to buy the final Province.

http://councilroom.com/game?game_id=game-20110517-184723-ceb8df5f.html

In which Finnians wins 37-33 after opening Explorer/Lighthouse to timchen's Silver/Silver.  timchen used $5 turns to buy two Libraries.  Explorer was played five times for 4 Silvers and a Gold.

http://councilroom.com/game?game_id=game-20110401-185620-4449a2e5.html

In which Andy Latto wins 34-17 after opening Explorer/Secret Chamber to timchen's Militia/Ambassador, and despite losing Ambassador tennis quite badly (having 11 Coppers and 5 Estates at the end).  timchen used $5 turns to buy a second Ambassador and two Council Rooms.  Explorer was played five times for 4 Silvers and a Gold. 

http://councilroom.com/game?game_id=game-20110205-161011-ae4dfd4d.html

In which Jack Rudd wins 36-33 after opening Warehouse/Quarry (to timchen's Warehouse/Silver) and getting an Explorer on turn 3.  timchen used $5 turns to buy Duchies (turns 9 through 11; note however that two of those were double-Hoard turns, making the Duchy buys very attractive).

And finally, more for laughs than anything else:

http://councilroom.com/game?game_id=game-20110222-093254-d5d707ef.html

In which Nagetier wins 47-17 after both players open Silver/Chapel.  Where do the Explorers come in?  Because they are the only $5 on the board, and Nagetier's plan relies on using Expand to turn them into Provinces.  Obviously this result doesn't have much to do with Explorer itself - it doesn't actually get played until turns 30 and 34, although to be fair it does produce coin needed to buy a Province or a Duchy on each of those turns.

Some other salient data:

- Your "Effect Without" Explorer is -2.67, which is your second-lowest stat out of all cards (after Rabble at -2.69).  This is far lower than your "Effect With" Explorer (-0.59), suggesting that the majority of your Explorer losses come in games where you erred by ignoring it.

In fact, that's not what that suggests at all. What that suggests is that he gets much less benefit out of ignoring it than other players do, and that's probably because he's making the SAME decisions more often than not with this card, but with other cards, he's making better decisions than they are.

My error; I misspoke by neglecting those cases wherein both players make the same decision on whether to buy Explorer.  To resolve this, I reviewed timchen's list of games where Explorer was on the board, which reflects that:

- 91 games in which NEITHER player ended with Explorer in their decks, and timchen WON.
- 54 games in which NEITHER player ended with Explorer in their decks, and timchen LOST.
- 5 games in which BOTH players ended with Explorer in their decks, and timchen WON.
- 1 game in which BOTH players ended with Explorer in their decks, and timchen LOST.

So when both players make the same Explorer-buy decision, timchen is winning about 63.6% of the time.

But when the players make different decisions, we see:

- 20 games in which timchen did NOT have Explorer at the end, his opponent DID, and timchen WON.
- 15 games in which timchen did NOT have Explorer at the end, his opponent DID, and timchen LOST.
- 4 games in which timchen HAD Explorer at the end, his opponent DID NOT, and timchen WON.
- 4 games in which timchen HAD Explorer at the end, his opponent DID NOT, and timchen LOST.

Now timchen's win rate is down to 55.8%.  Still better than average, certainly, but not as good as timchen's win rate where Explorer is around and both players evaluate it equally.  This data still suggests to me that timchen is somewhat less adept at evaluating Explorer's importance on any given board than he is at evaluating most other cards' importance. 

[timchen]

Wow, thanks for the analysis! I am really impressed that somebody is willing to look into my games, as even myself is too lazy for that...

It's interesting to see how I can't recall the games you linked at all; I probably played too much...
Unfortunately, I cannot observe a common pattern in the games. The first game is one of the games that I should have taken an explorer but just forgot; the second is due to his opening of tactician (and embargo it immediately after it) and has nothing to do with the explorer; the third is interesting but again not really have something to do with explorer, I probably messed up myself due to the misuse of black market, lighthouse, and cellar. The fourth has something to do with Farmlands. Maybe explorer do have a synergy with farmland I don't know; but in this game governor is probably going to dominate over it. The fifth one is probably luck; I like my library more than the explorer. In the sixth and eighth game, I probably played with ambassador too much without good effect; In the seventh game, it seems I lost to venture (which I didn't go for because there's no trashing); but it's possible that explorer combos with venture in a good way I didn't see, judging from the fact that he took 5 Provinces in 15 turns.

[Anon79]

- 91 games in which NEITHER player ended with Explorer in their decks, and timchen WON.
- 54 games in which NEITHER player ended with Explorer in their decks, and timchen LOST.
- 5 games in which BOTH players ended with Explorer in their decks, and timchen WON.
- 1 game in which BOTH players ended with Explorer in their decks, and timchen LOST.

So when both players make the same Explorer-buy decision, timchen is winning about 63.6% of the time.

Sounds like noise. When both players ignore Explorer, your winrate is lesser than your usual winrate - maybe you improved over time, and Explorer being an older card shows up more often when you were not as good?

[timchen]

Indeed. Thanks for mentioning. From the data mentioned, the games when both of us did the same decision on explorer, my win rate is only 1.27. I don't think there is an explanation why this number is so different from my average aside from statistical fluctuations. The time dependence is unlikely, as there are quite a number of cards sharing this property.