More Hearthstone Drafting

Sthenno commented on my Hearthstone win odds post about how some streamers he watches would find 8 wins to be a bad result. The HearthArena guys claimed to be averaging 8.5 wins per draft so these claims don't seem terribly out of line. Which means that at least some people are winning at or above 74% across all opponents and decks. That goes way against what I thought was possibly the highest people could be expecting. I was going off of a baseline that 60% was exceptionally good since I recalled LSV and Randy talking about career win percentages during the Vintage Super League commentary and LSV said something about being at 60%. I just looked into it more and his career win percentage is 63.25%. Something has to give here. So I've been thinking about it a fair bit the last few days and came up with some ways that LSV can win significantly less often in his matches than these people are in their drafts.

• LSV's stats are only for games played at the Pro Tour or in a Grand Prix. Hearthstone drafts are against anyone who cares to sign up. I'm sure LSV would actually win more than 63% of his games at FNM!
• Magic matches are best of 3 or best of 5. Hearthstone games are one and done. This actually works out as a factor in the other direction. Someone who won 63.25% of their best of 3 matches would only rate to have won 58.93% of their games. This is assuming a consistent game win percentage across events and game numbers. With sideboarding in Magic I would guess a good player would actually have a higher win percentage in games 2 and 3 than in game 1. Which would actually shift the game 1 number even lower and that's the one most similar to Hearthstone.
• Magic is inherently more volatile than Hearthstone. Hearthstone decks are smaller so you're less likely to get screwed out of a certain kind of card (spot removal/board clear/cheap weenies). Magic also has the land system. I don't care how good LSV is, if he never draws any lands I will be able to beat him! The same is true in Hearthstone to a limited extent if you consider someone who only draws 7 drops all game. They'll be dead before they get to play any of them. Of course if their deck actually has that many 7 drops in it they probably should be losing!
• An individual good deck in a Hearthstone draft will contribute more to your win percentage than a bad one will. Look at someone who goes 12-0 and then 3-3. Their win percentage is over 83% with one awesome deck and one mediocre deck. A similar situation in Magic at the Pro Tour would see a player go 4-0 with the awesome deck and 2-2 with the mediocre deck. Which is a 75% win rate. Even ignoring the silliness with 12 win decks not getting to keep playing... An 11-3 deck contributes 14 games to your denominator while a 0-3 deck contributes only 3 games to your denominator.
• LSV's numbers have been tracked by a consolidated system that pretty much guarantees their accuracy. Numbers self reported by individual players could be fudged. I don't even mean maliciously. I was guessing my own overall game win rate at below 50% but since I didn't keep track of anything there's no reason for anyone else to trust this assertion. Oh, and I watched one of the streamers Sthenno mentioned yesterday and she took actions to fudge her numbers. She drafted a really terrible deck but instead of playing it out she just retired it. It's not clear if she isn't counting that draft in her numbers at all or if she just isn't letting her really bad decks count but either way her stats are inflated because of this practice. She has the gold on hand to draft 20 times without any prizes at all so if she wanted to take a chance on drafting the nut murloc deck she could just retire all the bad ones and obliterate people with the good ones.

At any rate, it's clear enough now that Magic and Hearthstone are different enough that my initial guess of a good win rate in Hearthstone being based on Magic stats was silly. It is also clear that some people are way better at these drafts than I am. I believe while watching her stream she went 5-3, 7-3, 12-1, 3-0, and 7-3. Small sample size and all, but still way better than I would expect across 5 drafts. My terrible decks don't go 3-0-retire! I collect up my 0-3 result and move on.

One thing I did learn while watching her was her mulligan strategy. She straight up explained it when someone asked her about it! She only cares about the first few turns, so she pretty much exclusively throws back anything that costs more than 3. And she takes having the coin into account and plans on using it early in her mulligan strategy. So she might keep 2 3's going second but likely only the best 3 going first. (For those who don't know, in Hearthstone you draw your opening hand of 3 or 4 cards and then can individually mulligan cards by once shuffling any of your cards into your deck and then drawing back up.)

I want to distill that down to some numbers. Pretend the determining factor in who wins a game is having a 2-drop or not. Now I want to look at someone who mulligans everything that isn't a 2-drop against someone who mulligans only 2-drops. (Who wants a 1/2 in their hand when you could dig for a FLAMESTRIKE?!?) So (as I'm wont to do) I mocked up a spreadsheet.

Assuming both players have 7 2-drops then we have the 'win' odds at 41%-6% if player 1 wants the 2-drop and 46%-3% if player 2 wants the 2-drop.

But wait... Why do both people have equivalent decks? Isn't the person who mulligans for 2s more likely to have also drafted 2s? Looking at my 3 recorded decks I've had 4, 5, and 6 2-drops across them. And I was at least aware that I needed to fill my 2 slot. This will not be true for everyone. So let's compare someone with 8 2s against someone with 3 2s. In this case player 1 has a 72%-2% edge and player 2 has a 75%-1% edge.

Hitting your 2 drop isn't a guaranteed win by any stretch, but it does feel like it's going to increase your chances. Getting the first creature in play means you get to start make the decisions on trading creatures or attacking the other player's life total. I can remember one recent game where my opponent played a 3/2 untargetable on turn 2 and then was able to kill or trade with every creature I played while hitting me for 3 until I was dead. If I'd played a 2 power creature on turn 1 in that game I have a much better chance of winning that one.