Have you documented the number of tries?
Also should you use the prediction like that?
Not trying to be a besserwisser but at a 60% success rate, you a 60/40 chance for success/ failure.
Trying 5 times in a row may yield weird results.
Like I said earlier I no statistician so I won’t press the matter too hard, I might be all wrong but you might need to look at your model again.
Kudos to your work though.
That is an analogy, but it’s not exactly valid for my assertion. Certainly as a character becomes more developed the gear that qualifies as an “upgrade” becomes far more rare, and thus most items are likely to get salvaged, that’s not what I’m talking about.
What I’m saying is this; take 100 Ancient versions of an item, and 100 Legendary versions of an item, and look at the statistical mean, median, and mode of the value of the Legendary power.
For example, the Fortress Ballista has a Legendary power that ranges from 2.0% to 3.0%.
My assertion that Legendary items roll like crap means specifically that Blizzard weighted the Legendary power of Ancient items to roll toward the lower end of the available range, or when a low value is desirable, toward the higher end of that range, whichever is least desirable.
In my observation, the Legendary power of 100 Ancient Fortress Ballistas would tend toward 2.3 or 2.4%, while the Legendary power of 100 Legendary Fortress Ballistas would tend toward 2.8 or 2.9%.
I’ve seen this in tens of thousands of rolls: an Ancient Holy Point Shot with 87% out of 100% (75-100). An Ancient The Ninth Cirri Satchel with 465% out of 600% (450-600). A Dead Man’s Legacy with 154% of 200% (150-200).
I throw out 9 out of 10 Ancient items because the Legendary power is worthless, and 9 out of 10 regular Legendary items have a Legendary power that rolls in the top 85% of its range.
This observation may not be supported by statistical calculation, but it’s what I see day after day.
Well you started this thread by saying that you just wanted to to get some screams to get some augments now that the season is close to ending. That’s an indication that you only play sporadically - and that you even spread your playing time over several accounts. All this will give you a lower “efficiency” in good drops. As we all agree that most drops are sub par, it then takes a lot of drops to get really good gear. On the other hand if you don’t play intensely and strive to get to the top of any leaderboard, personal og official, it doesn’t really matter if you don’t have top notch gear on your heroes.
I’m not sure what you’re getting at. Perhaps if you articulated what is bugging you, I could answer. Meanwhile:
Yes, I kept track of all my tries for a season. The number was, as I recall, around 300 (at 60%).
Yes, at a 60% success rate, it’s 60%/40% for each try. At the end of a GR, you ask Urshi to do that 5 times. IF the tries are independent of each other, as they would be with a truly random RNG, the number of successes you get out of 5 tries forms a binomial distribution. That’s a well-known distribution, so nothing weird there. The percents for that, shown in my previous post, are easy to calculate. So, yes, those are the right percents for comparison.
We know the game uses a pseudo-random number generator (PRNG), so the numbers aren’t really random and thus the tries aren’t really independent. The “goodness” of a PRNG can be measured by how indistinguishable its results are from a truly random RNG. On the plus side, 60% of my tries at 60% were successes, so I conclude the stated 60% is accurate. We can also compare the observed 5-try results to the predicted 5-try results with a chi-squared analysis. That confirmed the difference between the two was significant. (And yes, chi-squared takes the sample size into account.) So, over a few hundred tries, the PRNG was measurably different from truly random, but that’s not surprising. When your game server needs to do a gazillion PRNG calculations a second, you go for “quick and dirty”, not “slow and make a statistician happy”. It’s possible even this difference would disappear over a few thousand tries.
I started all that because I felt I was getting too many 5-fail streaks, which made me question the 60%. In the end, I am convinced the 60% is accurate, and the extra streaks are a PRNG artifact.
Finally, in case it isn’t now obvious, I’ve been teaching statistics in university for the last 20 years. Before that, I was a programmer/sysadmin.
Inspired by this thread I decided to go on an extended run and throw some stats into the hat for you, which may turn into a bit of a Kulle story…
50 GR110’s on HC Valor Crusader, my first HC char. Created for the 45 no set, can’t stop playing it!
5 Primal Screams, as I think of them now
10 Angelic Crucibles
3 Ramaladni’s Gifts
27 Holiday Gifts (no wings, still hoping for Cosmic)
2 Puzzle Rings
1 Primal, sigh, a Nutcracker. Well ain’t that a kick in the…
The vaults gave me 1 more Holiday gift
The ENs were fun, managed a 151 kind of by mistake. Probably not very wise but I can’t resist those Goblins!
Salvaging the Angelic 8 remaining upgrades, no screams
All those bounty mats let me finally get a semi-decent lightning/10/71 Traveller’s Pledge, non-ancient, but at least it let me switch to CoE so I can push a bit higher. Running a Holy primal one with SoJ before, which topped out at GR127. So that’s a 128 at 9ish minutes done (106, EU), will push into top 100 before season end!
Oh and in that GR, Kormac got some new Primal shoulders 
Best of luck finding those Screams!
Rank 49 Hardcore Season 27 GoD striving enough? Rank 112 UE? 636 (666 Overall) Shadow (GR124)? And that’s with doing the Season Journey to Guardian 12 times during the Season.
Yes, that’s an assertion. Do you have any data to back that up though?
Remember, we’ve been through similar things before. For example, in a thread a couple of years ago now, you asserted that crafted bows / crossbows / one-handed crossbows rarely ended up with DEX and/or VIT on them. In that thread, I crafted hundreds of them, and posted the results. The results contradicted your assertion and you were forced to admit that the assertion was wrong.
Go make 100 Fortress Ballistae. Record the values of the legendary power. Post the results.
No, I made hundreds of them and posted the results, and happily admitted that the assertion was wrong.
lol
You made 90, …I made 450.
-------------------------------------------------------------------
Craft DEX VIT Craft DEX VIT Craft DEX VIT
01 x x 31 x 61 x
02 x x 32 x 62 x
03 x x 33 x 63 x
04 x 34 x x 64 x
05 x x 35 x 65 x x
06 x 36 66 x
07 x x 37 x 67 x
08 x 38 x x 68 x x
09 x x 39 x x 69 x x
10 x x 40 70 x
-------------------------------------------------------------------
11 x 41 71 x x
12 x x 42 x 72 x x
13 43 x 73 x
14 x x 44 x 74 x x
15 x 45 x 75 x
16 46 x x 76 x x
17 x 47 x 77 x
18 x 48 x 78 x
19 49 x 79 x
20 x x 50 x 80 x
-------------------------------------------------------------------
21 51 x x 81 x
22 x 52 x 82 x x
23 x 53 x 83 x
24 x 54 x 84 x x
25 x x 55 x 85 x x
26 x 56 x 86 x x
27 x 57 x x 87 x
28 x 58 x 88 x x
29 x 59 x 89 x x
30 60 x 90 x
-------------------------------------------------------------------
DEX Only = 27/90 = 30%
VIT Only = 23/90 = 25.56%
DEX and VIT = 26/90 = 28.89%
DEX Present = 53/90 = 58.89%
VIT Present = 49/90 = 54.44%You claimed there is a 1:8 ratio of main stat to vitality on crafted items.
If that was true, 10/90 items should have had DEX but there were 53.
If that was true, 80/90 items should have had VIT but there were 49.
Okay, so I crafted 90 Blitzbolter hand crossbows…
-------------------------------------------------------------------
Craft DEX VIT Craft DEX VIT Craft DEX VIT
01 x 31 x x 61 x
02 x 32 x x 62 x
03 x 33 x x 63 x
04 x 34 x x 64 x
05 x 35 x 65 x x
06 x x 36 x 66 x x
07 x 37 x 67 x
08 38 x 68 x
09 x 39 x x 69 x x
10 x x 40 x x 70 x x
-------------------------------------------------------------------
11 x 41 x 71 x x
12 x x 42 x x 72 x
13 x 43 x 73 x
14 x 44 x 74
15 x 45 x x 75 x
16 46 76 x
17 x x 47 x x 77 x x
18 x 48 x 78 x x
19 x 49 x x 79 x
20 x 50 x 80 x
-------------------------------------------------------------------
21 x x 51 x 81 x
22 x 52 x 82 x
23 x 53 x 83 x x
24 x 54 84 x x
25 55 x x 85 x x
26 x 56 x x 86 x x
27 x x 57 x 87
28 x x 58 x x 88 x
29 x 59 x x 89
30 x x 60 x 90 x
-------------------------------------------------------------------
DEX Only = 24/90 = 26.67%
VIT Only = 23/90 = 25.56%
DEX and VIT = 32/90 = 35.56%
DEX Present = 56/90 = 62.22%
VIT Present = 55/90 = 61.11%You claimed there is a 1:8 ratio of main stat to vitality on crafted items.
If that was true, 10/90 items should have had DEX but there were 56.
If that was true, 80/90 items should have had VIT but there were 55.
Compare that to the results of crafting level 70 rare bows…
I’d say this pretty much blows your claim of a 1:8 ratio out of the water.
I still have my spreadsheets, BTW…
https://docs.google.com/spreadsheets/d/177BtrYpUDUTq75sAo8TGXTJEGhoWJxxIOyljQAaeru0/edit?usp=sharing
But look at the Sydyru Crust, Ancient. Three in the group, all had Vit, none had Dex.
Here is an example of what Marhault is trying to get at:
You flip a coin 1000 times.
You document the results in 5 flip intervals.
The first 5 are all heads.
The second 5 are all tails.
This continues for the 1000 flips.
At the end, it is 50% for heads and 50% for tails which is what you would get statistically. This set of data, however, is not random as there is a definite pattern to it. For it to be random, you should get a small amount of all heads or all tails, a larger amount of 1 head/4 tails and the reverse, and a even larger amount of times it was 3 heads/2tails and the reverse.
It tested Urshi several seasons ago. I did all my upgrades at 60% to 90%. My results were very close to 60%, 70%, 80%, 90%, but I did notice there were a lot of groupings were there were high amount of strings of fails and successes. I didn’t analyze them any further as I saw Urshi was giving me the long term rate she is supposed to.
On a side note, I hope they do not have this 
in D4. If I pass a GR XXX, I should be able to level my gems up to that level without a potential penalty. Nothing is more discouraging than doing a GR138 for the first time, then having your gem at 137 fail 5 times to upgrade.
What is this?
My results are bigger than your results?
LMAO
Who cares?
Items drop weird in this game all the time. You either get garbage and you salvage or you get an upgrade. Its not rocket science. lol
You know what upset me most about this argument over the bows? Very few people commented how beautiful my spreadsheet was…lol
You felt that something was one way. You asserted it was that way. I didn’t think it was that way. So, we tested it and it turned out that it wasn’t the way you felt and asserted.
That’s the point. How you felt about stuff got disproved by data and now you’re making similar claims about legendary affixes, i.e. feelings / assertions with no data to back it up.
Go make 100 Fortress Ballistae. Record the legendary affix values for them all. Make a spreadsheet if you like, and make a graph showing the distribution curve. My hunch is that it’ll look a lot like a Poisson Distribution.
I suspected as much!
If I am not mistaken you presented the expected outcomes with a 90% accuracy gaussian distribution. That was the biggest clue 
No I am not trying to lecture you, by all means.
Out of curiosity and awe I asked if you had documented all this, both to get a picture of the sample size and a scope of your commitment.
That is what my last comment
Finally it indeed feels weird when things like that happens in game.
Peace Stedia
That doesn’t disprove my argument (which is more than the few lines you quoted). The way you play can easily affect how many drops you go through in a season, compared to other players who just play on one account.
It also shows that even with “crappy drops and rolls” the results you can get with them (getting on the HC leaderboard etc) can still be fine.
I think stat roll ranges probably follow a discrete uniform distribution.
Could be a (shifted) Poisson I suppose, although it can’t be a true Poisson because stat rolls are bounded on the upper end and a true Poisson distribution has an infinite upper tail.
I just tested with 200 all res rolls on Enchantress Focus. If you get one with the right secondaries, you can have it where all res is the only roll option and you get 2x all res rolls per reroll, makes the process faster. Only had to do 100 rerolls to get 200 data points.
The results after 200:
| Value | Roll count |
|---|---|
| 86 | 38 |
| 87 | 45 |
| 88 | 37 |
| 89 | 44 |
| 90 | 36 |
Seems to be roughly uniform with some noise. It appears like a roughly symmetric distribution, it’s not heavily skewed towards lower values in the range, so it doesn’t appear to be a low rate parameter Poisson.
I deliberately picked a stat with a low number of discrete values, so I don’t know if this trend would hold for stats with a wider range too. I suppose I could do int ,vit, or life on hit instead on an Enchantress Focus (can also get those as the only possible reroll option) to see what the distribution looks like for a stat with a larger range of possible values.
My gut just from observation over the years I’ve been playing is that stat rolls follow a discrete uniform distribution over the range of possible values. That does seem to be supported by the (admittedly limited) bit of data I did tabulate here.
Okay, I did 200 for int as well. Range is 525-625 on a rare Enchantress Focus.
559 570 552 547 556
610 613 607 611 612
564 528 581 612 609
564 527 625 600 591
528 582 621 561 606
620 554 618 569 528
595 553 617 593 571
582 609 538 595 530
552 555 584 559 525
544 585 587 563 547
542 528 538 595 539
588 568 623 617 591
543 528 617 611 581
541 543 602 574 610
540 554 580 601 587
562 606 601 583 583
537 528 555 604 576
567 598 549 536 553
574 557 536 546 587
555 615 625 622 593
618 602 570 620 580
595 623 569 592 588
609 606 565 613 552
622 541 550 622 571
605 606 551 543 585
564 570 583 617 574
593 541 620 618 573
583 536 585 553 612
528 606 555 548 623
604 537 579 546 608
528 534 534 569 592
560 551 528 622 589
602 532 607 557 608
617 559 625 588 624
624 624 593 620 585
574 550 576 531 536
575 622 572 536 528
540 607 619 590 550
529 600 541 609 588
580 559 558 568 585
Again, looks fairly uniform to me (with a bit of noise):
I wish I could upvote this more than once. It’ll always be the fish distribution in my mind.
So, Stone’s conspiracy theory of low end values being too prevalent doesn’t seem to be the case based on hundreds of data points?
I just got 2 primals in 3 T16 rifts. First, a super bad sunkwuko shoulders, the other band of rue chambers. That’s math for ya!
I have like 20 Petrified Screams and I played the season for like the first 6 weeks and have a grand total of 279 hours of playtime for the entire season. I ran maybe a total of 20 Echoing Nightmares with clanmates with keys that weren’t mine. I’ve fully augmented 3 different characters and 6 different builds (roughly 65-70 whispers of atonement used)
it has been 173 days, 4,148 hours since Season 27 began. If you didn’t find the time to push during those 6 months and waited until the last week of the season? That’s on you, nobody else. Quit pretending it’s RNG’s fault. It’s your own.