SilkRoad 0.402 0.433 0.031
I think this will be because if Silk Road is good it can be mirrored.
Or at least a few will be denied.
So a lot of the time if you are the only player to buy one, it was a late game $4 hand that you wish was a duchy.
That sounds right to me. Do you have a Pirate Ship theory that fits the data? Only thing I can think of without combing through lots of actual games is when a Top 20 player buys it, he or she buys it relatively late and has a way to play it 2 or 3 times per turn in an engine, uses it to "mast" an opponent by taking down the money then grabs $2-3 every turn (maybe times 2 or 3) and is immune to the mirror because their deck has no money.
Meanwhile, there are some cards where Top 20 players actually outperform their overall win rate (given as 65% here) when they alone gain, although the caveat here is that for some of these cards, overall win rate on the board that contains them could be overall higher or lower than 65%.
Card All Top20 Diff
Swindler 0.474 0.652 0.178
Bank 0.463 0.653 0.190
Duchess 0.494 0.653 0.159
PearlDiver 0.498 0.654 0.156
Remodel 0.472 0.654 0.182
Mystic 0.509 0.655 0.146
BandofMisfits 0.478 0.658 0.180
Woodcutter 0.474 0.661 0.187
CandlestickMaker 0.519 0.662 0.143
Haggler 0.478 0.662 0.184
Ill-GottenGains 0.545 0.663 0.118
Smithy 0.461 0.664 0.203
BanditCamp 0.512 0.667 0.155
Fortress 0.483 0.667 0.184
JunkDealer 0.497 0.667 0.170
Moat 0.435 0.667 0.232
Scavenger 0.506 0.667 0.161
Trader 0.410 0.667 0.257
WanderingMinstrel 0.516 0.667 0.151
Worker'sVillage 0.498 0.667 0.169
Gold 0.468 0.669 0.201
Harem 0.499 0.671 0.172
Quarry 0.505 0.674 0.169
Masterpiece 0.606 0.676 0.070
Venture 0.487 0.677 0.190
Copper 0.520 0.678 0.158
Torturer 0.484 0.679 0.195
Altar 0.513 0.680 0.167
Mandarin 0.455 0.680 0.225
Cellar 0.441 0.681 0.240
FishingVillage 0.495 0.681 0.186
Watchtower 0.493 0.681 0.188
Highway 0.505 0.683 0.178
Marauder 0.445 0.683 0.238
Embassy 0.517 0.685 0.168
TradingPost 0.497 0.687 0.190
Crossroads 0.523 0.688 0.165
Embargo 0.466 0.689 0.223
WishingWell 0.575 0.690 0.115
So some of these cards are ones that lower-rated players (that is, players overall) do well with when they are the sole gainers as well (e.g., Wishing Well, Crossroads, Highway, Altar, Copper (?), Quarry, Embassy, Scavenger and Mystic). Except for Copper, all of those basically make sense to me since they can work well with building up engines, so any time you are building one and opponent isn't or you are building a better one...makes sense. And gaining Embassy curses your opponent. :-)
But others of these cards seem to be just more magic in the deck of a Top 20 player, the top ten of those in sorted order:
Card All Top20 Diff
Trader 0.410 0.667 0.257
Cellar 0.441 0.681 0.240
Marauder 0.445 0.683 0.238
Moat 0.435 0.667 0.232
Mandarin 0.455 0.680 0.225
Embargo 0.466 0.689 0.223
Smithy 0.461 0.664 0.203
Gold 0.468 0.669 0.201
Torturer 0.484 0.679 0.195
Venture 0.487 0.677 0.190
Moat does not top this list, but would have been a good guess. :-)
Finally, there are cards that the Top20 just crush with if they are the only ones to gain them:
Card All Top20 Diff
Colony 0.786 0.935 0.149
Goons 0.682 0.875 0.193
Province 0.667 0.853 0.186
Butcher 0.674 0.853 0.179
Platinum 0.593 0.818 0.225
City 0.495 0.809 0.314
Mountebank 0.602 0.807 0.205
BorderVillage 0.581 0.804 0.223
Vineyard 0.653 0.802 0.149
Tournament 0.485 0.800 0.315
I think most of these are pretty obvious. The relative top player advantage with City and Tournament is pretty striking, though.