1.0.7 Crafting: Amulet Roll Probabilities

Re-posted from Reddit, and note that my values are different than in the original post, so check them over again. Overall, I give a big thumbs up to amulet crafting!

The basic TL;DR is:

Tries needed to craft:

• 3 valuable stats: 25
• Trifecta: 833
• Really good Trifecta: 6667
• 3 valuable stats with "top half" rolls (in the upper half of their range): 197 -- projected cost of this craft: 39.4 million
• 4 valuable stats: 359
• 4 valuable stats with top half rolls: 5751 -- projected cost: 1.51 billion
• 5 valuable stats: 14 out of 1 million

Ok folks, here it is. For those of you that have been following these posts over the last week or two, I've implemented my theory about how affix rolls work and written a program which simulates items being rolled according to these rules. This is much faster and less prone to error than doing it by hand, and--as long as the sample size is large enough--it should give pretty good approximations.

Earlier today the devs actually responded to one of my questions (Mandlebarb#1598)--the first one under the "Crafting" section. Though they were thorough and explanatory in their response, they did not offer any hard numbers or additional insight into how random affixes get applied to items. So, time for me to step in!

Here are examples of previous work so that anyone new can follow the process:

• How affixes get rolled: http://www.reddit.com/r/Diablo/comments/17s0fc/affix_rolls_explained_with_very_large/
• Examples of multiple affix legendaries being rolled and the unid values being calcualted: http://dd.reddit.com/r/Diablo/comments/17zf3m/affix_rolls_explained_v4_unid_value_of_zunis_pox/

Now I've applied these principles to crafting in 1.0.7. I simulated 10,000,000 crafted amulets and used the results to approximate the probability of getting certain valuable combinations of affixes. It is, as always, important to note the following:

• This is only an approximation of how rolls work, with no official knowledge obtained from Blizzard or any other inside source. I may be wrong, but I have done testing which indicates that these numbers are pretty accurate.
• Some crafted items in 1.0.7 have the chance to be standalone BiS, meaning that their ceiling is higher than anything you can find from farming. This alone will make them pretty appealing to high level players.
• Time actually becomes a pretty big issue now. It takes a really long time to craft enough amulets to expect elite rolls. That being said, it would take a really really long time to expect to farm these same elite items.
• The whole right-hand side with the projected costs and rolls needed to hit are for DPS stats and AR. Thereare other valuable stats that aren't included (Life %, Vit, LoH, and Regen and Armor to a lesser degree), which means that the chance of getting a good amulet isn't quite as bad as I calculated. However, most people are looking for beefy DPS stats out of their ammies, so that's what I focused on.
• Remember that you need to add 200-230 of a primary stat to those rolls! That makes them much more valuable than they seem when you first look at the list.

Without further ado, here's the spreadsheet:

https://docs.google.com/spreadsheet/pub?key=0ArooAQ_ASbpjdHRpWnowSTNNcm41ZFVsS09ZUkpwc2c&output=html

The Price of Brimstones in North America

If you invested in Brimstones prior to the 1.0.7 patch looking to make a nice rake after the patch got deployed on Tuesday, you may be scratching your head over their lackluster trading value on the AH. As of checking last night, they were trading for around 27k per stone, down from about 36k leading up to the patch, and as high as about 60k following the announcement that they'd be used in the new amulet recipe. Does this signify that low prices are here to stay? Well, that's obviously a complicated question, but it helps to consider the larger context.

Since Blizz deployed the 1.0.4 patch to buff legendary items and increase their drop rates there has been a significant increase in Brimstones entering the economy. This has been coupled, conversely, with a negligible amount leaving the economy. For about the last 5 months there has been an almost unmitigated growth in the number of Brimstones that exist within the D3 economy. I'll attempt a back-of-the-envelope calculation that might give us an idea of how many we might expect there to be (on the US server):

Recent reports quoted that about 12 million copies of D3 were sold worldwide. I'll assume about 1/3 of these were sold in NA. That leaves 4 million copies, of which I'll guess that about 1 million are currently active. That guess may be a little high, but better to be high rather than low in this case, I think. Depending on you gear level and farming efficiency, the number of Brimstones you farm in a month probably varies quite widely. Again, better to be high than low, so I'll say the average player farms about 100 Brimstones per month. This number has probably increased as average gear level has increased, more efficient runs have been discovered, and average paragon level (so MF and/or run speed) has increased. Putting these numbers together, we can get a rough estimate of the total number of Brimstones in circulation:

(1 million players)*(5 months)*(100 Brimstones/month) = 500 million Brimstones.

That's quite a few, clearly. I actually think it's a bit lower, maybe in the one-hundred million range, but I want this estimate to be an upper bound, so 500 million is fine.

Now, for the first time, we have an enticing Brimstone sink in the economy: amulet crafting. Forums are awash with peoples' successful amulet crafts, as they appear to be a worthwhile investment. It's notoriously hard to predict peoples' behavior, as it is often irrational, but let's assume some level of rationality here. Amulets and gloves are the two big items worth crafting (and bracers to a lesser degree), so I'll group everything else in its own category and assume that 1/3 of all crafts are being done on amulets currently. Thus, the current level of Brimstones leaving the economy is dictated by 1/3 of the rate at which Demonic Essences are entering the economy. We'll assume an average rate of 20% of the total elite packs being killed by all players, at about 50 packs/hour. If every player spends 3 hours a day playing, this means the following:

(1 million players)*(50 packs/hour)*(3 hours)*(1/3)*(.2) = 10 million Demonic Essences per day being used on amulets.

So, how long before we burn through the current stock of Brimstones? Well, according to these really rough estimates, about 50 days. So, as a really rough general rule, in 1.5 months we could expect the price of Brimstones to begin rising as the current supply gets eaten up. But there's (much) more to the story, of course, namely:

• Brimstones will continue to enter the economy over this period at (roughly) the same rate as before, so the time to run through them all should be extended so somewhere around 80 days, summing the infinite series pretty roughly.
• The rate at which people craft amulets will likely decrease over time as they find upgrades. However, if people are rational, they'll realize that they need to craft thousands of amulets to expect one with epic rolls, and that rolling that many is actually a worthwhile investment.
• Finally, and most importantly, the issue of storage and liquidity. This is probably the toughest of all things to account for--how many Brimstones are locked up in storage, and at what price will people "unlock" (i.e. sell) them? Probably well less than 10% of all Brimstones are either currently on the market or bound for the market before any significant price increases. Most people who knew they'd be crafting amulets probably have hundreds or thousands saved up, which means those stones aren't on the market--but it also means that those people aren't buyers (again) yet.

The takeaway, however, should be that so long as there is a net outflow of Brimstones from the economy (which I believe there is), prices should eventually rise. That's why the absence of an immediate post-patch increase isn't concerning me, and why I'll continue to buy Brimstones at their current prices. Will you be doing likewise?