Arena Doesn't Pay For Itself: The Math

Arena Discussion
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Yes, ignoring all other rewards made a lot of these maths invalid.

I'm eager to do something but there there hasn't been much discussion on how to value dust at the moment.

For an estimation of rewards at arenas, check this other thread and contribute when you can.
http://us.battle.net/hearthstone/en/forum/topic/9792719412
Seems like the simple solution to this would be to up the rewards so that 4 wins pays for itself plus a small bonus, 7 wins pays for two more arenas plus bonuses, and 9 wins pays for 3 arenas plus bonuses.

People might complain that doing it that way makes arenas more cost effective than buying packs for winners, but that makes sense since you're also putting skill into it. In other words there are going to be a majority of people who don't break even, meaning they get less benefit from the arena than from buying a pack. So their loss is essentially the winner's gain, the way buy-in competitions with pots should be.
I'm not opposed to giving higher rewards, but...
From what I've seen, most people with 4-5 wins break even (that's including the 100 gold of a pack.)

Average would be 3-3, in which case it makes sense to be a bit short of breaking even. If you're an above avverage player (or get a bit luckier), you'll usually at least break even, but also had fun in the process.
Makes sense to me, else most of the time you'd be gaining from the arena, which I don't think is the point.

I think if they'd raise gold for regular play, someone could at least play the arena a bit more often, even if it'd still be slow at 5 gold per win. Then the arena is the fun trial where you at least get a pack and fun, as well as chance to get good rewards.

I did enjoy the numbers that Kithros put up, it gives a nice gander at how many get what:

(Out of a sample of 2048 people..)
256/2048 people go 0-3
384/2048 1-3
384/2048 2-3
320/2048 3-3
240/2048 4-3
168/2048 5-3
112/2048 6-3
72/2048 7-3
45/2048 8-3

4/2048 9-0
18/2048 9-1
45/2048 9-2


That makes 705 out of 2058 that usually break even or Better.
That's 34.4%.
The arena is fine, can be worked a little, but its fine. Normal matches are the ones who doesn't reward. Considering all arena rewards going 3-3 it already gold efficient.
stop treating this !@#$ like statistics class.

if you played lebron james 1 on 1 basketball, 1st to 20, 10 games...

your win % isnt going to be 50%. if you're wanting to win out in arena, maybe you have to play better than opponents, have a better understanding of deck types, know about pick orders etc etc etc.

do things that will increase your win% to above 50%, its pretty simple.

Except this is statistics and we can assume that the average player with an average arena deck will lose to 50% of players and beat 50% of players. Why because that's how that works (ignoring the double loss scenario).

Yes, if you go against a really good player your probability of winning is significantly lower (not 0% though as this isn't basketball...there is chance involved). But for the AVERAGE player there is an equal chance of going against someone significantly worse than you.

And skill levels don't even need to be average or high or low for those numbers to work. As long as you ignore the double loss scenario and if you were doing an arena with a closed pool of players that's the EXACT distribution of win/losses. If you turned on the server 2048 players started an arena and for some reason no one else started until it was over (and no one tied) that's EXACTLY how it will turn out.

Moreover for a random set or arena runs I'd place good money that the records are similar to those results (close enough to fit a chi-squared best fit test).

Yes to you there are a lot of really good players who will get 9 wins BUT those are the people streaming, and especially once this game has the large player base it will have that difference in skill between random players will shrink dramatically.
The real interesting math would be, how can you, say, do a daily free arena, accounting for the 40g of your daily and, to bne generous, the 5G you earned by getting 2 more wins while you were at it. Those are 45g you don't need to earn in the arena, which therefore lower the barrier of entry for people who do not take 4 hours to get their wins.

So in the end the number of people who can do arena daily without paying is more than 9%. Numbers are still valid for people doing arena only though.
Lmao, I love this post(I'm only being a little sarcastic)! Obviously ya tried to put a some thought into "the math" of it all, which I'm All for the Details, But it's actually a Lot more simpler to explain, Especially to those who didn't want to read through your Extremely Long post!

And that's by simply saying EVERY GAME HAS A WINNER AND A LOSER! So on "Average", over the whole community, the Average arena record is and will always equal out to be 50%! Meaning 3 wins and 3 losses!!

So No it doesn't pay for it's self overall, and it's looking more and more like that's the way Blizzard wants it :(!! Especially since right now Arena is the "funnest" way to play!! Do you really think they didn't give it a gold earning reward system for ranking up and didn't give it a tournament system on accident??? lmao Don't be stupid! They planned it, so they could call it a free to play game but make it "funnest" when the Average player Has to spend money on it!!

Honestly that's why I have a hard time truly considering this game a "free to play" game!! Because the normal games don't give crap for rewards and you'll Never win ranked games without Buying cards(and they still don't reward better)!! You Have to Buy multiple packs to even start standing a chance in ranked games so really they're not even worth playing! Or yes you can waste a few months of your life Grinding out literally Thousands of WINS(since loses are Worthless!!) and Pray the RNG's are on your side when you finally can spend your gold for packs, which again is only giving you a chance at a higher, yet honestly unrewarding, rank!!! Which to me is Not a "free to play" game, because NO ONE continues to play a game without worthy rewards, especially games they usually(<--casual players) lose!! So Sadly it's more of a "pay to win" game!!
Just to add to your math a bit, let's assume you get one hour of Arena free each day, accounting for daily quests and such. It probably isn't quite this much, but just to be nice to the ignorant "Arena isn't expensive" crowd, let's assume that. Let's also assume you play 4 hours of Arena a day. That's a bit much, but it's comparable to how much time you'd spend raiding a day in WOW.

Since you only get 1 hour free a day, you have to pay for the other 3. At $2 per Arena bout, which we'll guess are about an hour long for the average person, and assuming that 10% of the time you get a refund on your entrance fee, that comes to $2000 per year to play Arena for 4 hours per day.

To repeat:

IT COSTS ROUGHLY $2000 PER YEAR TO PLAY ARENA FOR 4 HOURS PER DAY.
OP statistically speaking your accurate. But there is a problem, you're applying coin flip logic to a game involving person interaction. Skill does come into play. A person with X amount of skill can have a Y% better chance of winning than Player Z with 0 skill.

As far as your post goes, I think you tried to make an argument that the payout doesn't match the pay-in. My question to you is - how many arena matches have you played to estimate payouts? My experience is that even if you go 0-3 you still get a card pack. So netting 50 gold (which based on my experience can be hit at 3 wins [your magical 50% ratio]) so you break even. This doesn't even account for the gold value of arcane dust, which currently can't be quantified.

Always look at the whole story :)

FYI: I do appreciate the knowledge on statistics though, unfortunately the logic can't be applied to something that isn't random.
TL;DR - I do understand the effects of having too much time on one's hands and being fed-up with watching streams...

But, really, who cares? They never said it is supposed to pay for itself!
Arena and pack buying is where they'll get some cash back! Good for them and good for US!

1) If you don't want to spend cash, you spend your gold earned elsewhere (quests/dailys/other arenas) - it will be the in-game gold-sink (every game with virtual currency needs one);

2) If you do want to spend cash, it's no difference to spending monthly fees on other games, like WoW, or buying mounts or battle pets with real money;

3) There's SO much randomness in arena deck building (remember that you can have 3/4/+ equal cards, unlike when building your deck), that arena games, from the streams I watched so far, depend, not JUST on how good you are at deckbuilding AND the luck of the draw for each individual match, it ALSO depends on how LUCKY you were with the subset of cards shown to you to choose from;

4) Also, don't forget that you also get something else back, be it packs, dust, gold, and that adding all that up, which depends on how far you got, tends to lower your losses, should you not break even - it's not a WIN/LOSE scenario but a win more/less;

5) Above all: IT SURE AS HELL LOOKS LIKE A LOT OF FUN! And since you ALWAYS get a guaranteed pack, you should really look at it as a more expensive pack purchase with benefits, in that you get to play cards you still don't have and try stuff and get some dusts/gold, etc...

So, just sit back, relax, and play.
09/02/2013 07:51 PMPosted by Reaper
So No it doesn't pay for it's self overall, and it's looking more and more like that's the way Blizzard wants it :(!!


First, read my post above... the payout is closer than what most people will speculate if not over.

Second, do you think a tournament that has $100,000 in prizes only makes $100,000 exactly off ticket costs, advertisement, etc? Or do you think the businesses throwing the tournament pocket some and call it profit? Blizzard is a business :)

If they paid out more gold than what was paid in (they help alleviate the issue by offering a card pack instead of raw gold), eventually gold would be so abundant that you couldn't expect people to pay for card packs EVER, which is NOT in Blizzard's best interest.
09/02/2013 08:12 PMPosted by Fever
5) Above all: IT SURE AS HELL LOOKS LIKE A LOT OF FUN! And since you ALWAYS get a guaranteed pack, you should really look at it as a more expensive pack purchase with benefits, in that you get to play cards you still don't have and try stuff and get some dusts/gold, etc...


The number crunchers only look at value as something you put a number on =\ Glad some people understand this.
09/02/2013 08:12 PMPosted by Fever
2) If you do want to spend cash, it's no difference to spending monthly fees on other games, like WoW, or buying mounts or battle pets with real money;


Yes, it is a difference. A full order of magnitude.

Imagine, instead, if the WoW subscription were 150 bucks per month instead of 15. You think people would still play it?
Yes, it is a difference. A full order of magnitude.

Imagine, instead, if the WoW subscription were 150 bucks per month instead of 15. You think people would still play it?


Well, I could more easily imagine a WoW daily pass at 1.50, for example, even if it would end up more at the end of the month, should I play the whole month, because now, if I want to play 1 day, I have to pay 1 month, 2 months if using the pre-paid coupons. And believe me, these days I only charge my WoW sub for when my daughter wants to play a bit. And it "hurts" a bit too, spending 13 euros so that she will get to play maybe 3 or 4 hours over the course of a month. Didn't hurt so much when I spent 3/4/+ hours per day, because I felt I was getting good value for money.

I like HS's model better: if I want to buy 1 pack or 1 arena entry, I don't have to pre-buy a ton (although they sell 40 packs at a discount, but I can either take that or ignore) - I'll buy accordingly to what I feel like / can afford; and if I can't afford with real money, I'll have to make do with gold earned elsewhere (dailies/whatever)

So, you'll only spend 150 bucks on HS per month if you BOTH WANT and HAVE them, so I see no problem with that. But then again, I'm not even playing beta right now, so I can't say if this game will last on me when I get to play it, or if I'll get bored quickly... Currently, I like the fact that I can leave and comeback a day/week/month later and continue where I was, not paying any monthly fees, so if I have a few hours to spare, I can pour them over, but I can also do something with 10~15 mins here, another 10~15 there, which I like.
Didn't really bother reading this whole thread, because arena does pay for itself IF you're good enough.

Yes there are going to be lots of people losing, and those people that lose help the minority that consistently win. Not everyone can be a winner, some people are meant to be fodder that are farmed, that's life.
you are looking at this wrong. arena DOES pay for itself.

you are guaranteed a pack for each arena, meaning 100g of your entry fee is a guaranteed return of at least that pack you could have paid for.

and as long as you get at least 3 wins, the dust and gold you get as the extra reward should be at least 50g worth when you translate the dust into the expected value of disenchanting packs.

so will everyone get to endlessly play arena for free... of course not although some will. however at three wins you are approximately breaking even gold wise, and anything 4+ wins you are actually profiting.
Arena does pay for itself. You spend 150 gold and are guaranteed 100 gold worth of a pack and more. Last time I went it I got my pack and ~150 arcane dust. That is way more than worth it.
Captain Obvious says that arena shouldn't pay for itself for every player. You don't need math do understand this. Simple logic.

If you are pretty skillful, smart and lucky then you can play the arena without any additional payings.
But if you're an average player be ready to give up some money and play as good as you can so it wouldn't be a waste.
If you go 7-3, that means other people had to go 3-7 for those games.

How do people not understand this, still?
I did the math on this in a previous post:

256/2048 people go 0-3
384/2048 1-3
384/2048 2-3
320/2048 3-3
240/2048 4-3
168/2048 5-3
112/2048 6-3
72/2048 7-3
45/2048 8-3

4/2048 9-0
18/2048 9-1
45/2048 9-2

Some extra math for people who are curious, though it's largely guesswork as I don't have the actual numbers to work wtih.

Of the 5 chests, 1 of them is of course going to be a pack. Of the other 4, up until 7 wins they have an approximately 50% chance of being gold and 50% chance of being dust (there is also a probability of getting a gold card or another pack, but these seem fairly rare so I will be ignoring them for the purposes of this). After 7 wins there will be 1 chest with 150 gold, and the other 3 seem to be random with about 50/50 of being gold and dust again.

Just going by observation, and admittedly not off of much actual statistics, it seems that when you get a random amount of gold or dust it's approximately something like:

Number of wins*5 + 5 + (RNG between -# of wins and +# of wins)*5
This is definitely not the exact way it's calculated, since this formula will always yield 5 gold at 0 wins when I've empirically seen it give10 gold before - but nonetheless it's roughly accurate when watching streams in my experience. This number will average out to being # of wins*5+5.

If you assume that's a decent approximation of the amount of gold given per box (when you get gold), then you'll get on average this amount of gold for each amount of wins:
0: 10
1: 20
2: 30
3: 40
4: 50
5: 60
6: 70
7: 210 (150 + 40*3/2, since there are only 3 random boxes now instead of 4 random boxes)
8: 217.5
9: 225

If you multiply these values by the probability of getting each number of wins above, the total amount of gold on average will be approximately 51. If you consider the pack to be worth 100 gold, then arenas will roughly break even in terms of gold spent (compared to spending the gold directly on packs), but also give you some amount of extra dust.

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