Hearthstone

[WilliamLP]

The win-loss system they have for arena is good for strong players, but must be painful for bad players. Something that might not be immediately obvious is that the median record is (with good matchmaking) 2.5 wins and 3 losses. Literally half the runs people play never reach a 3rd win. (Suppose after four rounds, some number of people are 2-2. Some did worse and are out, and an equal number did better and are at 3+ wins. In their fifth game, half the players lose and are out. In total, 50% get 2 wins or worse, while the other 50% get 3 or more.)

Interesting! Similar to your reasoning, the binomial distribution of 5 games gives ratios of 1-5-10-10-5-1 puts exactly half at 3 wins or higher. (0-5 and 1-4 can't happen but it doesn't change things to shift those into different buckets.) Is it true that exactly half of all runs end with 3 or more wins, even if the matchmaker pairs people with unlike records?

I don't think the matchmaker pairs people with like records together. Someone on Reddit messaged a lot of arena opponents to compare records and it was all over the map.

My conspiracy theory is that the matchmaker really wants to stop you at 5 or 6 wins and you get your toughest opponents at that break point. Or it sure feels like a disproportionate number of runs end at 5 or 6 for me. That's also just short of 7 which is a guaranteed refund where you can go infinite. (That's the conspiracy... it's to optimize income.) It feels like decks get easier again after the 6th and 7th win. Of course, this could be just because those decks are really good in the first place. But an idea is that maybe once you start doing really well, the matchmaker doesn't try to make you lose anymore, but tries to use you as a spoiler, to attempt to end 5 and 6 win runs.

Am I totally nuts? Is the simplest explanation actually the correct one? Probably yes to both.

[T-hawk]

Interesting! Similar to your reasoning, the binomial distribution of 5 games gives ratios of 1-5-10-10-5-1 puts exactly half at 3 wins or higher. (0-5 and 1-4 can't happen but it doesn't change things to shift those into different buckets.)

I know nothing about Hearthstone, but do know something about binomials. If a certain number of losses eliminates a player, then the median won't follow the binomial distribution, since some paths to the median are impossible. You can't reach 2-3 by going 0-3 then 2-0 for example, but the binomial distribution thinks you can.

0-5 and 1-4 are impossible, but don't shift into another of the binomial buckets, instead they get cut off sooner and lumped into 0-3 or 1-3 buckets earlier on the binomial tree.

[Gustaran]

But an idea is that maybe once you start doing really well, the matchmaker doesn't try to make you lose anymore, but tries to use you as a spoiler, to attempt to end 5 and 6 win runs.

Am I totally nuts? Is the simplest explanation actually the correct one? Probably yes to both.

I think the most likely reason is that at a certain point matching you against a player with exactly the same record becomes much more difficult and maybe less strict. For example: At 3-1 it is easy to macth you witt another player, but I am not sure about that with 9-2. Maybe the waiting time would go up, and who wants to wait 10 minutes to start the next Arena game?

In addition I think your whole point is flawed: I don't think there is any advantage for Blizzard to stop players at a certain point.
First of all, it's advantageous for Blizzard if many people put lots of hours into Hearthstone since this will raise the popularity of the game.
So they probably couldn't care less if you start another Arena run right away or have to wait another day, it also doesn't change the fact that the total number of wins and losses in the system stays the same.

[WilliamLP]

(0-5 and 1-4 can't happen but it doesn't change things to shift those into different buckets.)

0-5 and 1-4 are impossible ... they get cut off sooner and lumped into 0-3 or 1-3 buckets ...

I completely disagree with you. [Edit, sorry for snarkiness... the 2-3 case does deserve explanation in addition to 1-4 and 0-5, though the conclusion that 1/2 of the tree (prematurely truncated or not) ends at 2 or lower still doesn't change.]

In addition I think your whole point is flawed: I don't think there is any advantage for Blizzard to stop players at a certain point.

The theory is probably bonkers. But the plausible advantage is to increase the percentage of arena players who have to pay money per arena run instead of being able to go infinite. This includes players like me who can be infinite at one run a day with daily quests but maybe not without daily quests... we're tempted to pay for just one more run that day. (The Trump / Kripp / Hafu crowd is going infinite anyway... let them pile up thousands of gold.) I don't know if it's a good business decision or not but it's not obviously implausible.

[SevenSpirits]

Interesting! Similar to your reasoning, the binomial distribution of 5 games gives ratios of 1-5-10-10-5-1 puts exactly half at 3 wins or higher. (0-5 and 1-4 can't happen but it doesn't change things to shift those into different buckets.) Is it true that exactly half of all runs end with 3 or more wins, even if the matchmaker pairs people with unlike records?

I'm just waking up and haven't done any math, but maybe, but.... the mean number of wins is 3. So I'm having a hard time seeing how matchmaking is going to pull the median past that. It's not like they can find below-average players at 3-2 or 4-2 to pair with poor saps at 0-2 or 1-2 or 2-2. The former are still going to be favored. But like I said I haven't done the math on that. It does seem like matchmaking could even things out a little bit, but it could also make things even more extreme. I mean, most likely result of pairing up a 5-1 and a 1-1 is a 6-1 and a 1-2, which isn't exactly helping to create a situation where most people are clustered around the mean. I also don't think blizzard have a matchmaking algorithm set up to make some people go 0-3 to boost the average of the others.

[Molach]

I also don't think blizzard have a matchmaking algorithm set up to make some people go 0-3 to boost the average of the others.

Indeed, I think quite a few people are perfectly capable of ensuring a 0-3 run...

With 50% win odds every match you have 50% odds of getting at least 3 wins. So half 3-3 or worse, half better.
(with 71% win chance every match the 50% occurs at 7 wins. So half your matches 7-3 or worse, half better...)
(poor players with say 30% win chance every match will only manage 7+ 1 in 100 runs)

(Above does not consider any matchmaking, all matches have same win_chance)

[Jowy]

Feels good man

[WilliamLP]

I'm just waking up and haven't done any math, but maybe, but.... the mean number of wins is 3. So I'm having a hard time seeing how matchmaking is going to pull the median past that. It's not like they can find below-average players at 3-2 or 4-2 to pair with poor saps at 0-2 or 1-2 or 2-2. The former are still going to be favored. But like I said I haven't done the math on that. It does seem like matchmaking could even things out a little bit, but it could also make things even more extreme. I mean, most likely result of pairing up a 5-1 and a 1-1 is a 6-1 and a 1-2, which isn't exactly helping to create a situation where most people are clustered around the mean. I also don't think blizzard have a matchmaking algorithm set up to make some people go 0-3 to boost the average of the others.

This is just math curiosity territory, but the mean number of wins has to be slightly less than 3, right? This is because mean wins must equal mean losses, and mean losses is less than 3 (because of 12-2, 12-1, and 12-0 runs).

In terms of invariants, sum of wins must be the sum of losses (obviously) and so the sum of every run's score against par (wins - losses) must also be 0.

I'm probably imagining that opponents and decks seem to be best at 5 wins playing for 6, but it sure feels like this!

[Sir Bruce]

Pagle is getting balanced and Tinkmaster is getting nerfed to oblivion: http://us.battle.net/hearthstone/en/foru...85288985#1. I guess maybe Tink will be playable in a Pally-token deck or something.

Aggro decks will switch in owls (if they weren't running them already) for taunt removal. Druids lose the most since Tink was huge removal for them. It's also a decent buff to big legendaries so crafting Cairne, etc is even better now.

[Gustaran]

Not a big fan of these changes. Ok, Tinkmaster was probably too strong in some decks, but now he went from mandatory to useless. If he would at least turn the minion into another one with fixed values he would make sense in Paladin or Shaman decks to possibly buff a 1/1 token or a totem.

As for Pagle, I think the problem is not so much if you have one more turn to remove him (which certainly is a nerf), but the randomness which can make him either a game winning card or a waste. I wish they would have included something like "draws a card on every other turn".