Looting Ancient Items: A Statistical Analysis of GR 90+ Runs

General Discussion
1

Hi folks,

I have long wondered whether farming higher GRs is more beneficial for getting Ancients and Primals. Due to the lack of official word on the matter from Blizzard, as well as opposing opinions from different players on the forums, I decided to document all the drops from my GR runs to see whether higher runs are beneficial for someone farming better gear (assuming they can clear them equally fast). I started off recording GR 75+, but stopped running everything below GR 90 as this is where the item drop cap is hit. This means that at GR 90, the Rift Guardian is guaranteed to drop a total of 12 items. At GR 85, you get 11 items each time, at GR 75 ten items, and so on.

[METHODS]
I ran 15 non-consecutive runs of GRs 90, 95, 98, 100, and 105. Data on total drops, number of legendaries, set items, ancients of both, and primals of both, were recorded. In addition, gem drops were also recorded. Mean values of legendary items and ancient items per run were compared. Potions cannot be ancient and were considered regular legendaries. Ramaladniā€™s Gift becomes very common by the time one clears GR 90, and this was also considered a regular legendary drop. Statistical significance was computed using a simple Paired T-test. Both one-tail and two-tail used where appropriate. A P-value of 0.05 was used as the cutoff for statistical significance.

[RESULTS]
For legendary/set drop rate

  • GR 090 = 161 of 180 total drops (95% CI +/- 0.36) = 89.44%
    • Mean 10.7 per run (95% CI 10.4 to 11.1)
  • GR 095 = 165 of 180 total drops (95% CI +/- 0.33) = 91.67%
    • Mean 11.0 per run (95% CI 10.7 to 11.3)
  • GR 098 = 172 of 180 total drops (95% CI +/- 0.32) = 95.56%
    • Mean 11.5 per run (95% CI 11.1 to 11.8)
  • GR 100 = 179 of 180 total drops (95% CI +/- 0.13) = 99.44%
    • Mean 11.9 per run (95% CI 11.8 to 12.1)
  • GR 105 = 177 of 180 total drops (95% CI +/- 0.21) = 98.33%
    • Mean 11.8 per run (95% CI 11.6 to 12.0)

There was no statistically significant difference between GR 90 and GR 95 with respect to legendary+ drop rate (P = 0.15). As compared to GR 90, GR 98, 100, and 105 produce a significantly greater total legendary drop rate, with P-values of 0.01, <0.0001, and <0.0002, respectively.

As compared to GR 98, GR 100 and 105 yield more legendary drops per run (P = 0.015 and 0.028, respectively), but there is no difference between GR 100 and 105 (P = 0.17).

For Ancient+ Drop Rate

Conveniently, albeit disappointingly, I did not see any Primals drop during my data collecting. As such I am unable to comment on whether higher GRs increase the likelihood of seeing Primals. As such, all of the data below pertains to Legendaries and Set items that were Ancient.

  • GR 090 = 20 of 180 total drops (1.33 / run), or 12.42% of Legendary Drops
    • Mean 1.33 per run (95% CI 0.97 to 1.7)
  • GR 095 = 21 of 180 total drops (1.40 / run), or 12.73% of Legendary Drops
    • Mean 1.40 per run (95% CI 0.8 to 2.0)
  • GR 098 = 16 of 180 total drops (1.07 / run), or 9.30% of Legendary Drops
    • Mean 1.07 per run (95% CI 0.62 to 1.51)
  • GR 100 = 15 of 180 total drops (1.00 / run), or 8.38% of Legendary Drops
    • Mean 1.00 per run (95% CI 0.40 to 1.60)
  • GR 105 = 15 of 180 total drops (1.00 / run), or 8.47% of Legendary Drops
    • Mean 1.00 per run (95% CI 0.49 to 1.51)

There was no statistically significant difference between the either of the above groups, with P = 0.133 for GR 90 vs GR 105.

Because Ramaladniā€™s Gift and Potions were lumped in with Legendaries and they take up a drop slot (but canā€™t be Ancient), I wanted to see if a difference existed at the level of Set items alone. Comparing only GR 90 with GR 100 we have:

  • Set Items / Run = 2.1 vs 3.2, P = 0.0499
  • Ancient Set Items / Run = 0.1 vs 0.5, P = 0.087

In order to increase statistical power, I lumped together the data from GR 90 with GR 95, and compared these to GR 100 + GR 105. N=30 for each. Pooled analysis shows:

  • Set Items / Run = 1.97 vs 2.90, P = 0.008
  • Ancient Set Items / Run = 0.23 vs 0.47, P = 0.055

[CONCLUSION AND DISCUSSION]
Based on an analysis of 15 runs each of different GRs 90+, you are more likely to see a larger amount of total legendary/set drops, and this seems to cap out at GR 100 as the drop rate approaches 100%. This contrasts with some opinions on these forums, where I have read the cap to be somewhere around 94 to 97.

What was very surprising was that, doing higher GRs does not increase the probability that you will see Ancient items overall. I suspected that this might be due to an observation I made that higher GRs drop more potions and Ramaladniā€™s Gifts, which I have automatically considered to be normal legendary. These items seem to take up legendary drop slots but can not be ancient. To see whether this was true, I looked at Set Items alone, and pooled data from 90+95 with 100+105 to increase statistical power. This showed that higher GRs yield significantly more Set drops (Set Items / Run = 1.97 vs 2.90, P = 0.008). There was also a trend towards significance with respect to ancient set item drops, where I saw almost twice as many Ancient Set Items at GR 100-105 than at GR 90-95, but with a P-value of 0.055. More data is required to see whether this relationship remains true. If it does, recording data for even higher GRs will be the next step.

I canā€™t comment on Primals as I did not see any so far. This probably also means that, unless a large group of data-hungry individuals pool our data together, we would not have the statistical power to detect any differences.

In conclusion, if you are running GRs for the loot (ancient items), farming GR 90 is not statistically worse than farming GR 105 or anything in between overall. If you are looking for Ancient Set Items specifically, you may see more of these at higher GRs, though more data is needed to know for sure.

If anyone is interested in collecting data and pooling this all together, I would love to collaborate!

12 Likes
2

How about a statistical analysis on speed runs? If possible trying to complete GRs all in the same time frame ( < 2minutes ). See if that nets any better loot.

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3

This is an interesting thought! Do we have any reason to believe clear times would affect drops?

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4

While the data is nice to have, was there any doubt about this? Blizzard stated that, as long as you play above T1, any legendary has a 10% chance to be ancient. As long as youā€™ve unlocked primals and play above T1, then any legendary has a really small chance to be primal. Higher difficulty levels increase the drop rate of items, but not increase those chances nor improve the quality of items.

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5

You will get more in the long run as you also obtain more Blood Shards and, if Solo, can carry more of them. So, add the possible drops from Kadala in there as ā€œlootā€ and youā€™ll get maybe 2-3 more.

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6

After reading numerous conflicting opinions on these forums and elsewhere, I would say yes! However, even if this werenā€™t the case, having evidence that corroborates what we are toldā€“and take to be trueā€“is of great value.

This may or may not actually be represented by the data. The overall rate seems to be 9.3% after looking at 1,124 drops. But this isnā€™t evenly distributed, with the rate actually hovering around 7% in GRs 75-89 based on 200 observations. Of course, more data would always help. The one crucial problem here is the ā€˜Potions and Ramaladniā€™s Giftā€™ taking up legendary slots, so the number may actually be around 10% when accounting for those.

However, this is why I looked at Set items (Legendary equivalents) separately, and for these I found Ancient rates to be ~11.5% for GR 90-95, and 16.1% for GR 100-105. These results are very different from the 10% rate, and also statistically significant. This is why data is important.

I canā€™t comment on Primals as I donā€™t have the data.

7

A 10% chance of an ancient doesnā€™t mean that every 10th legendary will be ancient, though. Over a large number of items, it will likely even out to be around 10%, but in a smaller sample, you may not achieve exactly 10% ancients. And why would you count items that cannot be ancient or primal in the totals? That makes no sense.

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8

You are capped at 12 drops, and these ā€œun-Ancientableā€ items take up legendary/set drop slots. Itā€™s important you take them into account if the point of your analysis is to determine an optimal farm strategy.

Iā€™d like to refer your to my section on Set Items drops, as that may address your confusion.

2 Likes
9

So what exactly are you trying to measure? If you are trying to determine the rate of ancient and primal drops, why would you included items that cannot be either of those. It doesnā€™t matter whether it takes up a ā€œspotā€ in the items dropped. I still get the odd yellow and blue item even on GR115+. I certainly wouldnā€™t include those when trying to work out drop rates for ancients.

10

Im left with whats the point of all this. Everyone who has played for a bit already knows all this.
You soon notice you get on average 24 legendary items every double key run from drops & bloods combined.

If you are after primals then farm 90+ at what ever you can do around 2min mark or aim at 20 GRs per hour.
Primals are 0.2% chance I find. so 1/500 legendary drops.
Key count then craft. ie note your number of keys after u drop a primal. then take 35-40 keys off this number(12leggy per key x 35keys = 420legendary). Go speed GR90+ till you hit your number. Then craft/cube as the odds are now more in your favor of getting the item you are after.
Yes its still RNG based. but you are playing odds. Still rng is rng. You are often more likely to get a primal to drop than get to your number.
every time a primal drops reset key count.
i expect to see a primal every 2 - 2.5 hours of farm.

-Edit -
15 runs aint much. thats under an hour per GR grouping. make it 50 or better yet 100 runs. this way you should get more reliable data and primals.

1 Like
11

15 runs is anecdotal evidence, isnā€™t it? You probably need 1000 times more for a valid conclusion. But anecdotally, I think most people would agree with your findings.

The trick is not doing really high GRs, but doing lots of them, at least that is what I have found.

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12

Thank you very much, thatā€™s exactly what I was looking for. Going to test it myself.

15 runs of each, thatā€™s 75 runs in total. Sure, more data is always better, but judging by the confidence intervals and p-values, thatā€™s already solid enough. Enough to make one thinking, at least.

The only problem with this kind of analysis, as I understand it, is that D3 seems to be having clustering effects on its RNG (much like Lineage 2 had, or most of mmorpgs for that matter). Basically, the second set of results obtained 1-2 weeks after the initial test might differ considerably from the first one. Iā€™m no statistician, and have no idea how that could be accounted for.

13

The first sentence of my post:

If you are capped at 12 items per run, and you can clear a range of different GR levels, itā€™s important to know whether, OVERALL, you will get any extra ancient loot by clearing higher GRs.

Removing the potions and gifts from the equation would just give you the probability of a legendary turning into an ancient, which is not what this post is about. I encourage you to actually read my post in itā€™s entirety.

2 Likes
14

When you say craft/cube are you referring to upgrading rares to legendary or rerolling legendary values or both? The latter one requires bounty mats obviously.

15

Why should you get more Ancients on higher Grifts ?
The Chances that a legendary Item can get Ancient or even Primal are fix.

The only thing that is important, is that you cant get more Drops after GR 100
Everything above this LvL is only to increase the XP-Points, while farming.


or do you belive, everyone who runs higher are getting flooded with primals, while you cant get any , because you only run lower grifts ?

16

Many times Iā€™ve seen better drops on 2 min or less gr as the monster groups get vaporized.
Faster kill does mean better drops in my book.
Tho, Iā€™m not going to spend the time collecting data to prove one way or another the point.

17

Iā€™m afraid Iā€™m going to have to see numbers before I believe this. I have seen zero evidence of it myself

18

Please take a moment to actually read my original post, as this answers all of your questions and then some.

2 Likes
19

Your fantastic analysis underscores what I believe to be the largest flaw in D3 design: the lack of proper reward scaling. It is bad enough that items themselves are not rare, but rather only well rolled versions of those items. But as you sagely showed, the quality of items does not rise with difficulty. Therefore, the number of legendaries per hour is all that matters.

This game is built around efficient play rather than ambitious play, and that runs counter to the very spirit of the ARPG genre, in my book, or tome.

3 Likes
20

Iā€™ve also played Borderlands where making fast work of an elite enemy can net you better loot. That game series also has a similar legendary, epic, rare, etc loot system and Blizzard is the one that pioneered such loot systems (I think). So, Iā€™m assuming Blizzard games may follow a similar pattern? Or at least maybe D3.

Iā€™m not saying getting data for fast GRs is a must, but if youā€™re in the hobby of generating statistics, that is one possible area for you to look into.