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# [Mathematics] Why The AH Is The Main Problem

Discussion in 'Diablo 3 General Discussion' started by Punkonjunk, Jul 25, 2012.

1. ### PunkonjunkIncGamers Member

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This is NOT my original work, AT ALL. this is from nargaque on BNET forums, and it is amazing, and I'm pasting it here, and with how slow news has been, this should be on top of the list on our frontpage, because it's an amazing self-check of how we're all thinking about gear right now. Following is the paste-in:

Many people ask, "Why am I not finding upgrades?" and "Why am I forced to use the AH to progress?"

These are both valid questions, and the answer in both cases is the existence of the AH. Let me explain.

This blue post by Wyatt Cheng should provide a background for what I am about to delve into:
http://us.battle.net/d3/en/blog/6317360/6317360#misc

If you don't want to read through the math and want to skip to the conclusion, scroll down to the part where there are two bulleted lists and start from there.

The Item Scale

First we need a mathematical scale to assign items. By convention, I am going to use a 0 to 100 scale. Let us only consider rare quality (yellow) items.

A 0 is the worst possible rare item you can find in Inferno. E.g., a level 51 chest piece that rolled 10 dex, 46 thorns, 200 health globe healing bonus, and 6 gold pickup radius. You can probably imagine worse, but that item is well under a 1 on the 0 to 100 scale.

A 100 is the absolute best-in-slot item for some slot, with perfect rolls on the stats you want. E.g., Archon Armor chest piece with 200 str, 300 vit, 3 sockets, 80 resist all, and perfect rolls on base armor and bonus armor. This item is a 100.

Everything in between works in percentiles. An item of scale level 99 is better than 99% of Inferno rares. A 10 item is only better than 10% of Inferno rares.

When we talk about "good" items, we only care about items near the 100 end of the scale.

10% More Stats Is NOT 10% More Rare.

I'm going to give two examples of chest pieces to demonstrate relative rarity, which is key to the argument. Say both are ilvl 63:

Chest A:
70 str
70 int
70 vit
70 resist all

Chest B:
77 str
77 int
77 vit
77 resist all

The common but false conclusion to jump to is that Chest B is 10% more rare than Chest A because it has 10% more of every stat. The conclusion is false because several 77's are much harder to roll than several 70s. The math is below. We conclude that Chest B is in fact 5 times rarer than Chest A.

Say the roll range for Str and Int are 20-100. It's possible to roll more due to also rolling an affix that has 2 stats, but let's not worry about that. Say these chest pieces rolled the same types of affixes. Similarly, say that the vit roll is 20-200, and the Resist All roll is 20-80. I know these exact ranges may be off but the fundamental result is the same for my demonstration.

Supposing you rolled a chest that had Str, Int, Vit, and Resist All, what is the chance that it will be strictly better than or equal to Chest A?

The chance is (31/81)*(31/81)*(131/181)*(11/61) = 1.91%

Is the chance to roll strictly better than or equal to Chest B only 10% lower than that? No, it is actually a lot lower!

The chance is (24/81)*(24/81)*(124/181)*(4/61) = 0.39%

Chest B is almost 5 times rarer than Chest A.

And to make it worse, the percentages above are only of the items that rolled Str, Int, Vit, and Resist All, which is a fairly desirable combo despite having only 4 properties. Even having a terrible roll with these 4 properties is still better than any 4-prop chest with Health Globe Healing Bonus, Gold Pickup Radius, Thorns, and say Dex.

Most of Your Items Are In the Top 1%

But wait, you probably don't just have such 4-prop items. You probably have 5- or 6-prop rares that are much better. But what we have shown above is that even Chest B is in the top 0.39% of ilvl 63 chests that roll those relatively desirable stats.

So Chest A might be around 95 on the 0-100 scale, and Chest B, being 5 times rarer, is a 99. But what about 5 and 6 prop gear? Consider Chest C and Chest D below:

Chest C:
77 str
77 int
77 vit
77 resist all
3 sockets

Chest D:
77 str
77 int
77 vit
77 resist all
3 sockets
597 life regeneration

Chest C is clearly much better than Chest B, and Chest D is much better than Chest C!

How much rarer is Chest C than Chest B? There are 3 factors at play: rarity of 5-prop versus 4-prop, rarity of the +sockets affix, and rarity of 3 sockets within the +sockets affix.

With these combined together, Chest C is likely 30 or more times rarer than Chest B, but just to keep numbers simple, say it is only 10 times rarer. Thus Chest C would have the value 99.9.

Chest D adds a 6th affix as well as an extremely high roll of a nice affix. It's probably at least 100 times rarer than C, putting Chest D at the very least 99.999.

The RNG

Now say you are poor and can only afford something of Chest B quality. The middle class probably has gear more like Chest C, while the rich have Chest D quality or better. This might not exactly match, but the relative quality is what I am getting at.

Now, a Random Number Generator (RNG) is generating random decimal numbers between 0 and 100. You play Diablo 3. Every time you find a chest armor piece, you take a number from the RNG.

Say you're poor and you have only bought Chest B. The RNG must give you a number higher than 99 for it to be an upgrade. Statistically, it is very unlikely.

Say you're a bit wealthier and you have Chest C. The RNG would have to give you a number higher than 99.9 for it to be an upgrade. Extremely unlikely. You'd have to farm for a long, long time.

Say you are even wealthier and have Chest D. Well, good luck beating a 99.999.

The Top 1% Is Your Starter Set

The problem is, most people didn't find Chest B themselves. They bought it from the AH. This is why it is extremely rare for people to find upgrades. They already have Chest B, something better than 99% of other chest pieces. The next chest they identify has only a 1% chance to be an upgrade. Those of you with Chest C have only a 0.1% chance of finding an upgrade. And those with Chest D have a measly 0.001%. To find something better than D, the chance would be akin to drawing a royal flush. It doesn't matter if you have 300% MF, it's still a gamble.

The Blizzard Internal Testers Did Not Have Top 1% Gear

They didn't even have top 5% gear, because they did not have an Auction House. Even Chest A, while laughable to many of us, would probably have been considered a great item when they were testing the game.

Of course, to get to Inferno they had to have had at least semi-decent gear, say in the top 50%. That translates to their gear level being around 50.

This is why in the article linked at the beginning of this post, Wyatt Cheng claimed that upon entering Inferno, a player might find an upgrade in 30 minutes. After all, if you start with your gear at 50 on the 0-100 scale, then any rare chest piece you pick up has a 50% chance of being an upgrade. Picking up 2 chest pieces sounds reasonable in 30 minutes.

However, using the AH screws things up because it makes you jump from 50 to 99.

Here is a comparison of what happens:

Blizzard Testers/No-AH Players
* At item scale level 50 upon entering Inferno.
* The first chest armor they find is a 37, so it isn't an upgrade. But the next is a 64, which is an upgrade.
* To upgrade again, they must roll better than a 64.
* They roll a 28, 61 (which would have been an upgrade if they didn't already have the 64), 12, and finally a 73, an upgrade.
* To upgrade again, they must roll better than a 73.
* Etc. Each time they get an upgrade, the amount of time to the next upgrade goes up gradually (at least on average). Nonetheless, they are steadily finding upgrades. This is what it felt like in Diablo 2, because there was no AH.

AH Players
* At item scale level 99 upon entering Inferno.
* The first chest armor they find is a 37, so it isn't an upgrade. Neither is the next piece, which is a 64.
* Neither is the 28, or the 61, or the 12, or the 73.
* Or the 91, 8, 29, 67, 62, 72, 84, etc.
* Or the 95, 93, 22, 60, 71, 89, or 96.
* Since seemingly nothing they find is an upgrade, they are drawn to the conclusion that the only way to find a better item is to scour the AH for a 99.9.
* Thus they feel they cannot upgrade on their own. They feel forced to use the AH, which leads to a vicious cycle. Once you use the AH, you are enslaved to it.

The AH is the problem! Of course, another issue that can be seen from the numbers above is the "Doubled It" fiasco. Before they doubled it, it was probably possible to beat the game with 98/99 gear. So it might take a few days to farm the top 1%/2% gear, but you can beat it without much sweat. But once they "doubled it," instead of being able to beat the game with 98/99 gear, you must do it with 99.99 or 99.999 gear, the top 0.01% or 0.001% gear. This doesn't take a few days of farming. This takes months of farming and/or blind luck. This exacerbates the RNG and turns the game into a lottery rather than something that resembles Diablo 2. Although, even with "Doubled It," the Auction House is still the worse issue.

Solution: Release Ladder, with no RMAH and no GAH. The bartering system, while primitive, seems to avoid all the problems of the AH system.

If you are TL;DR'ing this, at least read the bulleted comparison between non-AH and AH player experiences just above. I hope they adequately explain why the AH is so problematic.

Last edited: Jul 25, 2012
2. ### floobleIncGamers Member

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I read that, it has some merit but it still doesnt explain the utter trash we see dropping. I remember a certain other game I used to play :scratchchin: and even stuff I got there which was useless for the current character would be very good for an alternate or for trading.

In D3 I see very, very little which would be of even use to an alt and nothing of real trade value either

I also believe the current "gear is quite literally everything" stance it has is a more fundamental issue. You have the gear, or you will die horribly, there is no other option right now. If people didnt HAVE to have the gear to progress then there would be much less frustration about drops.

In an attempt to maximise RMAH income* they turned gear from the carrot, into the stick.

*I can't fault this as an objective, they are a business, but they got it wrong here imo.

Edit to add this quote from someone in the same threat I forgotten about that's pretty accurate (thought slightly overstated/rose tinted about D2):

Last edited: Jul 25, 2012
3. ### mrmudIncGamers Member

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Yes it does.
I play HC without the AH and there are plenty of upgrades dropping for me.

4. ### floobleIncGamers Member

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I wasn't and I didnt have the funds to make excessive AH purchases (I'd foolishly been levelling and using the craftsmen in town). Only after unloading a bunch of crafting materials on the AH could I make some AH purchases for my WD. By the time I'd cleared act 1 inferno, I had a level 2x hat on and a level 4x belt on for example. The rest was all pretty low level for my progress point, I was basically undergeared, technically speaking anyway as I still got there. Furthermore, very little had dropped that was worth selling either (see my lack of funds issue).

The entirety of NM/Hell/Act 1 inferno didnt offer upgrades for those two items (there were others, but those pair were the most marked in my mind, pretty sure my shoulders/bracers were level 5x 'junk' too). I'll try and check my achievement dates if I remember tonight just to confirm my memory isn't faulty.

Basically I used the AH a bit, but not much and I was still SoL in terms of decent drops.

That was still SC though, HC is a different beast in approaches.

Edit: This was back in the pre-AS nerf so that may have been a mitigating factor as I was stacking it hard and low level IAS items were better than higher level items in terms of DPS gains and glass cannon was perfectly good at that stage.

Edit2: Its coming back better now. I had a pair of low level 50's rings and ammu too. The reason I hit the AH was actually the IAS nerf - I switched spec/build philosophy a few days before it hit so I used the AH to fund/find the gear swaps required for that. Not to excess though.

I'd say there's certainly an affect been had by the godliness of the IAS items, but that doesn't change the fact there's still TONS of slots I could have upgraded but didnt or that I found naff all worth selling/handing down to an alt.

That being said, none of that would matter so much if the game wasn't one epic gear check right now.

Edit 3: Perhaps should make a new post for this. I wonder...if the blacksmith could shuffle item stats around/reroll it for a fee if that might help. You know, like an item with three sat boosts, nullify one and spread it to the others.

Last edited: Jul 25, 2012
5. ### Sky TanIncGamers Member

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the poker analogy still revolves around the RNG.

In D3 your hand will be always at least a straight beocs AH is used. All my character now is using crap gear so i actually keep almost 2 pages of mule items or lvl 60 relevant stuff to use for my other character to lvl up.

Will only visit AH one awhile for 2500 buys when the i didnt have the odd pieces.

6. ### floobleIncGamers Member

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As I said, I barely used it as I didnt have the money. I was using a level 26 helm and never saw a single upgrade from normal>>act 2 inferno. Ditto a level 4x rare belt. Now, I'm don't think I'm being unrealistic to expect an upgrade to that helm covering that span of gameplay. Or am I?

Furthermore, there is no sufficient explanation for my distinct lack of gear to sell on the AH. The stuff I'm finding isn't just "not an upgrade" to my character, it's just plain trash fit only for salvage.

Of course, it could be I simply have unfathomably bad luck, however since I went through all of hell passed Magda with pretty much a 5 stack of NV....I think there may be more too it.

7. ### Sky TanIncGamers Member

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Patience Pal, if you could find my thread which i got lucky.

=P

8. ### floobleIncGamers Member

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I should perhaps clarify that loot rareness in isolation is not an issue for me. The problem comes from the fact you're slamming into a brick wall without it. Without other means to progress (out levelling content/levelling in general) and them having done their best to mitigate anything other than gear allowing progress it limits the 'fun' value.

Like I said it's like a carrot & stick, just gone a bit wonky.

9. ### AxamasIncGamers Member

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IMHO, the problem has no solution.
The more you have a good item, the longer it will take to find an upgrade. Ever.
The reason is that stuff is based on "rare" items with random stats and affix where only the statistic laws rule.
The problem is not the AH, the problem is that stuffing is based on "rare" items.

When leveling, 99,99% of the time, drops are far below the player level. After many hours of play I only remember dropping once an item of a level I could not already use...this means that I always walk undergeared...this means also that I'm always undergeared for the monsters I encounter.
This is well known, it pushes me towards the (RM)AH or toward twinking my character with a higher level char.
If I wanted to do it the "proper" way, I'll have to farm for a long time to get the appropriate lvl stuff or to go beyond my fighting lvl to farm more quickly (the later solution being a bad tactic in HC).
If monsters' drops were of a higher level, this would solve a part of the problem, i.e. when people are leveling. Thus, this can be improved.
Now considering lvl 60 char and progress through Inferno, the problem is only about "setting the drop rate accordingly to the time you want people spend to achieve Inferno". It seems there is a lack of understanding between gamers and Blizzard : Blizzard set the game to be long -several weeks or months-, players want it to be shorter)

The difference with another game, D2 to name it, is that in D2 you didn't rely (for trade or stuffing) on rare items but on uniques and runewords and runes. Once you get the appropriate unique or RW you were stuffed, and this was humanly achievable, and this was enough to finish the game (UT included).
Of course, there were people looking for "perfect" uniques or RW, but "perfect" items were not mandatory to finish the game.

Last edited: Jul 25, 2012
10. ### floobleIncGamers Member

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Indeed but the 'problem' only exists because of the necessity of very high level gear to progress. Fix that and the problem ceases to be

There are various, viable ways to correct that imo. However, as I've said elsewhere, that carries a risk (perceived or real) to RMAH income....so it may be disallowed by the 'suits' over in activision/blizzard.

11. ### Steven HazaniIncGamers Member

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If there were no AH, trading would do the same thing.

How likely are you to find a Shako? I keep mentioning this item, but that's because it's a staple mid range item and everyone knows it.

How likely are you to find other things you can sell or trade for a Shako?

Exactly.

On one hand I've played for dozens of hours, don't have that good gear and that character has three of his items found himself, the rest were AHed. On the other hand while two of those were only small upgrades over the stuff I bought, one is head and shoulders over ANYTHING on EITHER AH.

So I'm really not sure what to make of this.

12. ### buddahIncGamers Member

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You are very, very likely to find a shako

13. ### TenetIncGamers Member

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One really quick fix that would help the problem a little is to remove ilvl 51ish from the Inferno loot table entirely. It's absolutely ridiculous and quite frustrating to bust your hump killing a pack of elites in Act 3 Inferno and have some hot garbage Balor Fist drop as a reward. This happens all too frequently, unfortunately.

The other issue with the AH is that drop rates must be tuned around it. The drop rates of good items (by this I mean items that you could use to complete Inferno) must be low, otherwise the AH would be flooded with cheap items that were of high enough quality to beat Inferno. I hate to see the comparison between the AH of D3 and trading in D2 because the two are quite different. Trading wasn't required to progress in D2. You could build your own set and farm on your own if you liked. In D3 however, the AH is nearly mandatory if you want to progress Inferno without melting your brains doing the same Warden/Butcher runs five months straight. This game has many glaring problems, and it's going to take fixing most/all of them before it gets any better but the AH is definitely one of the biggest.

14. ### TheDestructorIncGamers Member

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Diablo 2 also didn't have Inferno difficulty. Progressing to Baal in Hell wasn't really hard, it was more a foregone conclusion, with the end result you trying to find ways to maximize your item farming runs.

I think Blizz figured players enjoy the hunt for items, so they created a difficulty where the hunt is emphasized, the problem is that people get discouraged when they don't get upgrades fast enough, and with how crushingly difficult Inferno can be at times, it's a lethal combination.

I have bought only a handful of items off the AH, and have self-found some really good items, not godly, but enough to push on into Act 2. That's in about erm... 30 hours played of Inferno? Dunno, if that's bad or good, I enjoyed it so. :/

I wish recipes dropped more, it would give players more opportunity to be self-sufficient when you could at least craft some nicer ilvl62 stuff. I found an ilvl 62 recipe with 5 affixes, and it really helped me out.

15. ### Steven HazaniIncGamers Member

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80% no drop chance, then whatever chance that drop is something good, then whatever chance it is that specific item.

Very, very likely indeed. As in thousands of kills just to get the right base item.

16. ### buddahIncGamers Member

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Likely as in some moderate farming and you are wondering what you'll do with all these Shakos. I always found my own Shakos in D2 since it was so easy

17. ### MagisterLudiIncGamers Member

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Very well said OP. And to further all of what you said, tack on the fact that finding a unique (with random mods) can lead to more frustration. (i.e. my Skycutter Legendary Sword with +Discipline mod.) So each unique is only capable of being good one out of hundreds and thousands of times. In D2, you knew what you were getting.

18. ### konfetaIncGamers Member

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Interesting analysis, stupid solution. Stupid, stupid, incredibly stupid solution that doesn't address any of the problems with the item system in favor of masking them.

Also, the "bartering system avoids all the problems of the AH" only if you never put any effort into trading.

19. ### PunkonjunkIncGamers Member

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I've thought about the same thing, actually: Put in 2 items, or 3 items of the same type, and reroll with an amalgam of the stats, maybe like Yahtzee: say it's 2 6 stat ilvl 63 rares, you can select 1 stat from each you want to see on the new one, and the re-roll will pick randomly from the rest, allowing us to occasionally reroll almost amazing items into amazing items.

I think the big problem here is that 99.99 items just aren't cutting it for clearing the game. What I think could be very beneficial is to move the scale out: make 150 the next cap, expand the maximums.... but maybe that's what 104 will do with the unique fix. I 'unno.

20. ### sifueditionIncGamers Member

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I agree that the solution is not viable, however, please avoid personal attacks in your reply. Too much of that derailing what otherwise might be interesting threads.

Reasons it's not viable:
1) RMAH. Sorry, it's here to stay like it or not. As long as people have paid real \$ for something, Blizz will go to extremes to not alter those "somethings". Therefore, ladder can't happen in reference to item resets.

2) Additionally, consider WHY we had ladder in D2. Bots and dupes were apparently unstoppable (and still are so it seems =/). Those lead to the over-proliferation of items. Ladder was not meant to be an end-game. It was an unbelievably popular side-effect of trying to moderate the economy. Pure stroke of luck (or maybe brilliance?) on a positive unintended consequence instead of a negative one. They balance the economy now with drop rates since they actually feel "responsible" for the economy vs D2 where the economy was driven by third party sites. Bear in mind, I am not using the conspiracy version of this comment. I mean the multiple layers of rng and the effect it has on the probabilites of usable items that are the base rates for drops.

My personal opinion is that ladder is not really what people are wanting. They want an ever moving goal for end-game. Since ladder gave them that in the past, it keeps coming up in suggestions now. Just remember, this is not the only way to have that ever moving goal. This is one of the areas that I think Blizz will have to be innovative in a solution. Innovation is hard. I expect mistakes in this kind of endevor. I just wish they hadn't repeated some of the forseeable mistakes from D2 launch.