I want to work out what I could be doing better, but there are two problems here both related to drafting while watching AGDQ. I haven't been streaming my drafts since I don't want to be rebroadcasting sounds from a different stream, and I haven't been concentrating exclusively on the draft or the games because cool stuff would keep happening on the stream I'm watching. Basically, while constructed seems like it was a fine thing to do the drafts feel like a waste in retrospect. I think the best thing to do here is to steadfastly refuse to partake in a draft unless I'm streaming it, at least for the next little while, so I can go back and revisit things afterwards. I'd also like to start keeping track of stats so I know if I'm actually doing bad or not.
The reason it feels like I've been doing bad is I've had a couple of 0-3 drafts recently, on top of a fair number of 2-3 and 3-3 results. But when I stop to think about it more... The overall expected result of a draft is a little under 3 wins. Everyone who signs up for a draft wins some games, but they all contribute 3 losses before they get eliminated. This means for each person that signs up there are 3 wins added to the pool of available wins. Except every now and then someone will go 12-0, 12-1, or 12-2. Those drafts end without providing the full 3 wins to the pool. Overall everyone still expects a 50% record in the long run (every game has exactly one winner) but that means the real expected result isn't 3-3 but more like 2.99-2.99.
And then I think a little more and realize that I've had a 5-3 draft and a 7-3 draft recently to go with those two 0-3 drafts. Which is above average! (Barely!) Super small sample size I know, but my gut feeling that I'm sucking is also based on a super small sample size.
Of course I'd like to think I'm pretty good at games. So being barely above average, if that's actually where I am, is still something I shouldn't be happy with and should be able to fix. I don't believe Hearthstone is just flipping coins, so there has to be an edge to exploit in there somewhere. I just need to actually work at finding it.
I didn't want to draft this morning while a little sleepy but I also wasn't tired enough to go to sleep. So I built a little spreadsheet to work out the odds of different results based on different overall expected win percentages. I can change a couple cells to alter my assumptions and get new numbers. It's got me thinking... Should your win chance change as the draft progresses? On the one hand if your deck is 4-1 then it's probably pretty good. But on the other hand you're now playing against other 4-1 decks, and they're probably pretty good too. Win to get up to 5-1? Your deck rates to be better, but again so do theirs. Lose and fall to 4-2? Your deck rates to be worse, but again so do theirs.
This means assigned a fixed win chance seems reasonable. On the other hand your deck doesn't actually change whether you win or lose at 4-1. It may rate to be worse in the long run but your deck doesn't exist in the long run. Even if you expect to win 75% of the time if you end up with a win you 'got lucky' and did better than expected. If you lose you 'got unlucky' and did worse than expected. But your opponent's decks aren't fixed. They're a nebulous group of potential opponents and it is entirely reasonable to think any given deck of yours is more likely to beat a 4-2 opponent than a 5-1 opponent. (The 'Swiss gambit', as it were.) So it's entirely reasonable to assign a sliding scale of win chance based on current record. How big a scale is the question... 2% per win? 5% per win? (This would mean a 60% deck that got lucky enough to go 11-0 would only have a 5% chance of winning the 12th game which seems absurd.) Should they have different scalings? Especially if your base win chance is high I'd expect a loss to increase it more than a win would decrease it.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 50 | 12 | 18 | 18 | 15 | 11 | 8 | 5 | 3 | 2 | 1 | 0 | 0 | 0 |
| 60 | 6 | 11 | 13 | 13 | 12 | 10 | 8 | 6 | 4 | 3 | 2 | 1 | 3 |
| 70 | 2 | 5 | 7 | 9 | 9 | 9 | 8 | 8 | 7 | 5 | 5 | 4 | 16 |
| 55 | 9 | 15 | 16 | 15 | 12 | 9 | 7 | 4 | 3 | 2 | 1 | 0 | 1 |
| 45 | 16 | 22 | 20 | 15 | 10 | 6 | 3 | 2 | 1 | 0 | 0 | 0 | 0 |
| 40 | 21 | 25 | 20 | 13 | 8 | 4 | 2 | 1 | 0 | 0 | 0 | 0 | 0 |
| 35 | 27 | 28 | 20 | 11 | 6 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 30 | 34 | 30 | 18 | 9 | 4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 50/2/2 | 11 | 18 | 20 | 17 | 13 | 8 | 5 | 2 | 1 | 0 | 0 | 0 | 0 |
| 55/2/2 | 7 | 14 | 17 | 17 | 14 | 10 | 7 | 4 | 2 | 1 | 0 | 0 | 0 |
| 60/2/2 | 5 | 11 | 14 | 15 | 14 | 12 | 9 | 6 | 4 | 2 | 1 | 0 | 0 |
| 65/2/2 | 3 | 8 | 11 | 13 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 1 | 1 |
| 45/2/2 | 14 | 22 | 21 | 16 | 11 | 6 | 3 | 1 | 0 | 0 | 0 | 0 | 0 |
| 40/2/2 | 19 | 26 | 22 | 15 | 8 | 4 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 35/2/2 | 24 | 29 | 21 | 12 | 6 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 50/2/5 | 9 | 16 | 18 | 17 | 13 | 9 | 6 | 3 | 2 | 1 | 0 | 0 | 0 |
| 60/2/5 | 4 | 9 | 12 | 14 | 14 | 12 | 10 | 7 | 5 | 3 | 2 | 1 | 1 |
| 70/2/5 | 1 | 3 | 6 | 9 | 11 | 11 | 11 | 10 | 9 | 7 | 5 | 4 | 7 |
Anyway, here's a not terribly well formatted table with some of the values I tried. The top 8 rows are for a flat winning percentage. The next 7 are when I adjusted the winning percentage by 2% per win or loss. The final 3 are when I adjusted the winning percentage by 2% per win and 5% per loss.
I'm not really sure what to conclude from this, but it looks somewhat interesting and I did it so I figured it should be included. A flat 70% win chance seems pretty absurd. Initially I thought something had to be wrong since all my 11s with visible differences were smaller than my 12s but it does make sense once you think about it. There's only one final path to an 11 (go 11-2 and then lose) but there are three final paths to a 12 (go 11-0 and win, 11-1 and win, or 11-2 and win). Unless that 12th win is configured to be rather hard the second just has to be bigger. (At an even win chance at 11-2 you're guaranteed at least as big a 11-2->win as 11-2->loss!) The fixed 40% and worse are more likely to hit 11 than 12 but they're not very likely to hit either one.
Looking at it my gut feeling for the line that best represents what I think I've been doing is the 45/2/2 line. But again, small sample size, and not even really a sample size at all since I have no data, just a gut feeling.
There's also the problem that the table is for overall expected value in the long run while individual samples are played using very different decks. So really it's probably completely useless. Oh well! It was fun to do, and that's good enough for me!
Anyway, I happen to have 200 gold on my account... I think that means I should fire up OBS and stream a draft!
3 comments:
I think you must be doing better than 45/2/2. 45% wins would only give you a 1/400 chance of getting 12 wins. Last month you posted about getting a good draft and winning the max 12 wins.
I've watched Trump, Hafu and Massan do a lot of arenas, and 8-3 would be a pretty bad finish for them, so I'm convinced that playskill actually makes up a big component of success in limited.
When Trump drafts after making his deck he'll switch his stream name to his prediction for how many wins he thinks he'll get. The lowest prediction I've ever seen from him is 10, and his predictions seem pretty good (again, very small sample size).
When I was doing some arenas, the biggest thing that helped me was reading Massan's arena guide and trying to follow his mana curve suggestion. I didn't worry so much about his card rankings, just tried to get the mana curve right and I started winning a lot more (small sample size). But basically even though I think Hearthstone is pretty easy (Trump can't count and he wins at it) I'm still not very good at it. I have a tendency to do things like fill out my board against a mage on turn six and whatnot.
I think it is a plain fact that you could be averaging 10 wins per arena and never having to stop to do quests if you put some practice in. Also, if you started streaming that you could get 10,000 viewers (though you might have to work on being a jerk to achieve that)!
I haven't played since before the last expansion, so the meta may have changed.
My experience has been that the average opponents are pretty easy in the 0-3 win bracket (I get really grumpy when I hit monster decks in that area), then the decks tighten up a fair bit in the 4-5 win area.
At 6 wins I experienced a real hump, and I would often stall there or at 7 wins.
I think the general thing is the matching algorithm tries to match you against similar win rates. So at 0 wins you play vs people who haven't won a match yet. Up around 6 wins people tend to be running out of losses and dropping out. So you're usually playing someone good enough to hit 6+ wins, with a strong possibility of facing a monster deck that deserves 9+ wins.
I'd say up at the 7+ range you're probably looking at close to 50/50 odds unless you're seriously pro-level.
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