Guild Wars 2

[KING], in addition to posting a comprehensive guide to high-level fractals also publishes data on their drops from the tiered rewards, i.e. those 1-4 bouncy chests we get for completion of one of the three daily fractals (as opposed to the scaled rewards, which are for a particular island/level).

Their original data collates by each type of chest: master, expert, adept, & initiate. However, I thought it would be more interesting to pivot by tier, since there’s no way to obtain a master chest, without also obtaining all the others.

Accordingly, as of today, their data on 414 runs looks like this:
Ascended Boxes (weapon or armor)

• Tier 4: 8.9%
• Tier 3: 4.3%
• Tier 2: 1.4%
• Tier 1: 0.24%

Accessories or Infused Rings

• Tier 4: 15.6%
• Tier 3: 8.8%
• Tier 2: 2.4%
• Tier 1: 0%

Gold Fractal Weapons

• Tier 4: 2.5%
• Tier 3: 0.8%
• Tier 2: 0%
• Tier 1: 0%

Here’s my personal summary of these results:

• In terms of reward-per-time spent, get yourself to T4 as soon as you can. A single T4 is more likely to net you ascended armor/weaps than any combination of lesser tiers (except all three T3). Similarly, a single T3 is as good as three T2s.
• Gold skins don’t drop for T1 or T2.
• The rates are seemingly worse than for [KING]’s data from 2015, until you take into account time spent: a single T4 reward of four chests requires completion of one island now; the equivalent champion reward (14.8% chance of armor/weap) required completion of 3. Moreover, you can get three T4 rewards (of four chests) per day now; you could only get one champion chest per day before 19 April.

edit: as per Jahoots, the summary odds are correctly calculated by opening four individual boxes, which is not the same as summing all the drops from each. Instead, it’s calculated by determining the chance that none of the boxes drop ascended and subtracting that from 100%. This makes a small (downward) change for the T4 summary, but has little impact on T3 or below, because the odds are so low to start with. It obviously has no impact on the odds for T1, since that is always just one chance.)

This seems a bit misleading. The data in its original format more accurately represents their findings.

At T4 you do not have an almost 10% chance of getting an ascended box, you have four individual chances, with the greatest being 3.4% and the least being 0%.

Wait, wasn’t the champion chest the one you get after three random and one of the boss islands? So it’s technically 4 islands.

Agree to Jahroots; you cannot collapse the data that way. The probability to get ascended armor or weapons at all from playing tier 4 fractals daily is about (20+12+6+1)/ (414×4)= 2.3%.

You forgot to include drop rates for the endless fractal tonic. ~69 kappas~

Jahroots.6791:

This seems a bit misleading. The data in its original format more accurately represents their findings.

At T4 you do not have an almost 10% chance of getting an ascended box, you have four individual chances, with the greatest being 3.4% and the least being 0%.

Assuming the math is correct, I actually like the way OP presented the percentages. It’s a usable shorthand for “if I do a t__ fractal, then I have an X% to get an ascended.”

Jahroots.6791:

This seems a bit misleading. The data in its original format more accurately represents their findings.

At T4 you do not have an almost 10% chance of getting an ascended box, you have four individual chances, with the greatest being 3.4% and the least being 0%.

The data in the original format is also misleading — we can’t possibly obtain a master chest without also obtaining the other 3; accordingly, there is no circumstance in which you have only that single chance, which is what their summary table shows.

On the other hand, you’re also correct: it’s four individual chances (the least of which, according to their data, is 0.24%) and technically the summation would be additive inverse of the chance that none of the chests have ascended armor/weapons.

Master’s: 95.2% for none, Expert: 97.1% for none; Adept: 98.6%; Initiate: 99.8%
(.952 * .971 * .988 * .998) = ~91% of getting neither ascended weapons or armor from any of the four chests, or a ~9% chance of getting an ascended box of some sort. Similarly, it’s 5% for T3.

Thanks for pointing that out — I’ll update the numbers accordingly.

Absurdo.8309:

Jahroots.6791:

This seems a bit misleading. The data in its original format more accurately represents their findings.

At T4 you do not have an almost 10% chance of getting an ascended box, you have four individual chances, with the greatest being 3.4% and the least being 0%.

Assuming the math is correct, I actually like the way OP presented the percentages. It’s a usable shorthand for “if I do a t__ fractal, then I have an X% to get an ascended.”

Unfortunately, Jahoots is correct: I goofed the initial math. (It’s not quite additive.) I’ll fix it shortly.

Wow, those drop rate are pretty low :S no wonder I haven’t been getting ascended box. I don’t really mind as someone with tons of armor and weapon already, but 90% chance to get nothing is very high.

But that’s not how percentages work, is it? If you have a 10% chance of getting something from a chest, opening ten of that chest doesn’t mean you have a 100% chance.

There’s a reason [KING] presented their findings in a different format. Let’s say you’re grinding fractals hoping to gear up for raiding and you complete one T4 daily. You’ll receive four chests – The best one has a 3.4% chance for armour and 1.4% chance for weapon, and the worst will not drop anything at all. This is not the same as a 9.2% chance at getting an ascended box.

Jahroots.6791:

But that’s not how percentages work, is it? If you have a 10% chance of getting something from a chest, opening ten of that chest doesn’t mean you have a 100% chance.

There’s a reason [KING] presented their findings in a different format. Let’s say you’re grinding fractals hoping to gear up for raiding and you complete one T4 daily. You’ll receive four chests – The best one has a 3.4% chance for armour and 1.4% chance for weapon, and the worst will not drop anything at all. This is not the same as a 9.2% chance at getting an ascended box.

3 chest each having 3,33% chance of getting you a drop is indeed not the same as 1 chest having a 10% chance of getting you a drop. But on average it will give you the same amount of drop.

Openning 10 chest won’t give you 100% chance of getting 1 drop. But the chance of dropping 1 item in 1 of those chest is pretty high.

Trice.4598:

Wow, those drop rate are pretty low :S no wonder I haven’t been getting ascended box. I don’t really mind as someone with tons of armor and weapon already, but 90% chance to get nothing is very high.

It’s not a 90% chance to get nothing though as there’s other things that can drop too.

Man those are disgustingly high rates for end game gear. Here people were worried loot got nerfed. Old daily chest pale in comparison. I am however annoyed by the lack of any actual gold value bar T7 mats and matrices.

thanks for the list, dude

Apparently I’ve just been really unlucky. After doing all three t4 dailies 11 times, the odds of getting at least one ascended chest is 95.4%. but I still haven’t gotten any since the change.

To OP, please learn how to use statistics before posting. 8,9% chance to have an ascended box (armour or weapon) in T4+T3 +T2 chests is totally wrong.

You cant add percentages….

Edit : In this case and just for armour and weapons :
Master : 3,4% for armour and 1,4% for weapon
Expert : 2,4% for armour and 0,5% for weapon
Adept : 1,2% for armour and 0,2% for weapon

Gives for armour : 3,4+2,4+1,2 = 7 : 3 = 2,3333% chance to get an armour chest from doing a T4 fractal (3 chests)

For weapon : 1,4+0,5+0,2 = 2,1 : 3 = 0,7% chance to get a weapon chest from doing a T4 fractal (3 chests).

KickzNGigglez.4958:

Man those are disgustingly high rates for end game gear. Here people were worried loot got nerfed. Old daily chest pale in comparison. I am however annoyed by the lack of any actual gold value bar T7 mats and matrices.

Well, you get gold from the other reward. You get at least 4 gold in encryption + some rare, etc.

Red Daing.7804:

To OP, please learn how to use statistics before posting. 8,9% chance to have an ascended box (armour or weapon) in T4+T3 +T2 chests is totally wrong.

Actually, you’re the one who’s wrong here.

reikken.4961:

Actually, you’re the one who’s wrong here.

Please elaborate

Red Daing.7804:

To OP, please learn how to use statistics before posting. 8,9% chance to have an ascended box (armour or weapon) in T4+T3 +T2 chests is totally wrong.

You cant add percentages….

Edit : In this case and just for armour and weapons :
Master : 3,4% for armour and 1,4% for weapon
Expert : 2,4% for armour and 0,5% for weapon
Adept : 1,2% for armour and 0,2% for weapon

Gives for armour : 3,4+2,4+1,2 = 7 : 3 = 2,3333% chance to get an armour chest from doing a T4 fractal (3 chests)

For weapon : 1,4+0,5+0,2 = 2,1 : 3 = 0,7% chance to get a weapon chest from doing a T4 fractal (3 chests).

Now I know why you were ranting about asc boxes some days ago. Wrong math added to a bad rng is the problem on your side.

OK, let’s not turn this valuable and important data into an open forum to discuss statistics. The OP’s original method of adding the chances of getting X together to arrive at a single number is, statistically speaking, incorrect. However, it achieves the desired goal of roughly determining probabilities and I appreciate the OP’s time and effort involved in collecting the data.

To those of you who argue the math is wrong, you are correct. Obviously, you can’t add up probabilities. If you have a 50% of getting heads every time you flip a coin, you don’t have a 100% of getting heads every other flip. However, if you flip that coin 1000 times, you will get heads around 500 times, more or less.

I’m revising the post as I had a chance to sit down and actually go through it. Since I was rushed doing the calculations, I had originally over-complicated it.

You can find the probability of getting a specific drop by multiplying the probability of not getting it for each chest and then subtracting that result from 1. So the probability of getting an ascended chest from doing just one Tier 4 fractal is:

1-[(420-14)/420] * [(420-10)/420] * [(420-5)/420] * [(420-1)/420] = 7.0%

The probability of getting an ascended chest from doing all 3 daily fractals is:

1-(1-7%)^3 = 19.51%

Of course, please double-check and make sure I didn’t forget something. I’m a little iffy on the probabilities of getting nothing for the bottom tables.

Red Daing.7804:

To OP, please learn how to use statistics before posting. 8,9% chance to have an ascended box (armour or weapon) in T4+T3 +T2 chests is totally wrong.

You cant add percentages….

Edit : In this case and just for armour and weapons :
Master : 3,4% for armour and 1,4% for weapon
Expert : 2,4% for armour and 0,5% for weapon
Adept : 1,2% for armour and 0,2% for weapon

Gives for armour : 3,4+2,4+1,2 = 7 : 3 = 2,3333% chance to get an armour chest from doing a T4 fractal (3 chests)

For weapon : 1,4+0,5+0,2 = 2,1 : 3 = 0,7% chance to get a weapon chest from doing a T4 fractal (3 chests).

According to your maths, the chance to get a weapon/armor would be higher if you opened only the t4 chest (3.4%) instead of all chests. I hope you realize that this does not make any sense.

Osu.6307:

The OP’s original method of adding the chances of getting X together to arrive at a single number is, statistically speaking, incorrect.

and it has since been revised to be correct

Ayrilana.1396:

I’m revising the post as I had a chance to sit down and actually go through it. Since I was rushed doing the calculations, I had originally over-complicated it.

You can find the probability of getting a specific drop by multiplying the probability of not getting it for each chest and then subtracting that result from 1. So the probability of getting an ascended chest from doing just one Tier 4 fractal is:

1-[(420-14)/420] * [(420-10)/420] * [(420-5)/420] * [(420-1)/420] = 7.0%

The probability of getting an ascended chest from doing all 3 daily fractals is:

1-(1-7%)^3 = 19.51%

Of course, please double-check and make sure I didn’t forget something. I’m a little iffy on the probabilities of getting nothing for the bottom tables.

Make sense: but your number only applies to Ascended Armor, not Weapon. Still, calculation makes sense.

Iris Ng.9845:

Ayrilana.1396:

I’m revising the post as I had a chance to sit down and actually go through it. Since I was rushed doing the calculations, I had originally over-complicated it.

You can find the probability of getting a specific drop by multiplying the probability of not getting it for each chest and then subtracting that result from 1. So the probability of getting an ascended chest from doing just one Tier 4 fractal is:

1-[(420-14)/420] * [(420-10)/420] * [(420-5)/420] * [(420-1)/420] = 7.0%

The probability of getting an ascended chest from doing all 3 daily fractals is:

1-(1-7%)^3 = 19.51%

Of course, please double-check and make sure I didn’t forget something. I’m a little iffy on the probabilities of getting nothing for the bottom tables.

Make sense: but your number only applies to Ascended Armor, not Weapon. Still, calculation makes sense.

Yeah. I didn’t see the point in lumping armor and weapon chests together.

Good thing these things are tracked. Leaving ascended mats totally out however feels a bit wrong imo. Those things are worth about 10g each.

So, was the fractal tonic lost in all the loot table swaps? I tried really hard to get one but never was so lucky and now it seems like they’ve been totally forgotten. :/

Illconceived Was Na.9781:

• Gold skins don’t drop for T1 or T2.

420 isn’t a huge sample size for something that could be very rare, especially considering the small number for T3 as well I think it’s likely T1/T2 drop them just very rarely; unless Anet have said otherwise.

I’ve received a gold skin since the revamp and before I was doing T3 fractals – but I can’t remember what chest it came from unfortunately (mostly because I spam open them), it may have come from one of the recommended dailies rather than a T1/T2 chest.

rfdarko.4639:

So, was the fractal tonic lost in all the loot table swaps? I tried really hard to get one but never was so lucky and now it seems like they’ve been totally forgotten. :/

No. People are still getting them. It’s just very rare.

Since people are getting hung up on the theory, I went ahead and ran Monte Carlo simulations on the data. The only controversial assumption I made was that a single master/expert/adept/initiate chest could not drop both an ascended weapon and an ascended chest.

I created a random number for each chest in each T4 run (returning 4 chests). I used the KING data to determine the cut off points for each potential drop. I then ran simulations of 10,000 runs (40,000 total chests) and added up all the results. As a validation check, I compared the individual chest rates to that of KING’s data.

The results (of opening four reward chests in the simulation):

• The chance of getting an ascended weapon or chest was as low as 8.4% and as high as 9.9%.
• The chance of getting nothing on KING’s list was 63%.
• About 2% of of the time, there were streaks of 42+ runs without an ascended gear box, equivalent to two weeks of running all three tiered dailies.
• It’s very uncommon (~20 chances per 10,000) to get more than one ascended gear box in a single run (e.g. from both master and expert chests). (Some 10k runs had triple drops, but the max was usually 2.)

Again, the the controversial assumption made was that a chest won’t drop both a weapon and an armor box. I feel confident that’s reasonable, since the results are consistent KING’s rates (within 0.1% absolute each run, well within a 95% confidence interval).

I welcome others to try the same thing, whether to replicate or refute my results. I used Excel and I’m sure an adept programmer can set something up more quickly. I’m happy to help you get setup in Excel, if you’re not sure where to start. (Hint: formulas use RNDBETWEEN, ROUND, CHOOSE, COUNTIF.

tl;dr simulation of 10,000 runs confirms the numbers listed in the (edited) original post (which were validation-checked by comparing to the KING data). The chances were 8.4-9.9% that a Tier 4 run yields at least one box of ascended gear.

I would say that the expected return is a more interesting number than the chance to get something. Expected return (additive) tells how much stuff you get in the long run. Chance to get something (multiplicative) tells the chance to get anything in a single run. Expected return is a bit higher because you can get multiple drops.

Also drops probably overlap with each other so combining different drops isn’t simple.

Wethospu.6437:

I would say that the expected return is a more interesting number than the chance to get something. Expected return (additive) tells how much stuff you get in the long run. Chance to get something (multiplicative) tells the chance to get anything in a single run. Expected return is a bit higher because you can get multiple drops.

Good idea. I added a rolling 21-run accumulative loot to the simulation — that covers a week’s worth of full dailies (or three weeks of 1/day).
--————————————
For 21 runs, using just under 10k trials (since we can’t count the first 20):

• The median is 2 runs with at least one chest; the average is about the same.
• 0 chests is common; about 10-15% of people doing 21 runs will get no ascended chests.
• Getting the median (2) occurs about 25% of the time, i.e. slightly more than 1/3 of people will get less than 2 chests per 21 runs, a third get more than 2, and a quarter get exactly 2.

That’s vaguely consistent with the anecdotal results most of us post (“I’ve gone X weeks without an ascended chest!”)
——————————————

Also drops probably overlap with each other so combining different drops isn’t simple.

Yes, that’s why I went with a simulation instead, since that doesn’t rely on everyone agreeing on the ‘proper’ way to tabulate the odds. (Of course, the disadvantage is that folks have to run their own simulation to compare results and most people won’t be willing to do that.)
——————————————
reminder: this assumes (1) the KING data is representative; (2) my simulation is accurate; (3) a single reward chest can drop only one ascended box, i.e. a weapon or armor, not both; (4) I counted a run that had a drop from both master & expert as ‘one’, since most of us are interested in how bad our luck might be, not how good.

I’m confident in my results, since the validation checks mirror KING’s data, but I urge skeptics to run their own tests to confirm.

Eh, it’s pretty obvious by now they will never undermine their precious trading post as the most efficient means to obtain high end items.

If people can circumvent the ridiculous 400+ gold price tag on full ascended crafting (not including the cost of leveling the professions themselves), their beloved goldsinks would suffer.

As usual, if you’re doing anything but Trading Post Baron, you’re doing raids/fractals not because they have good rewards but because they’re fun. GW2 will never have good/optimal in-game rewards so long as John Smith’s tenure endures.

Zenith.7301:

Eh, it’s pretty obvious by now they will never undermine their precious trading post as the most efficient means to obtain high end items.

If people can circumvent the ridiculous 400+ gold price tag on full ascended crafting (not including the cost of leveling the professions themselves), their beloved goldsinks would suffer.

As usual, if you’re doing anything but Trading Post Baron, you’re doing raids/fractals not because they have good rewards but because they’re fun. GW2 will never have good/optimal in-game rewards so long as John Smith’s tenure endures.

I’m not sure if using the Trading Post is more efficient (unless you can play the market). It’s just that farming gold can be done continuously while fractal/raid farms are capped at once per day/week. If one would calculate the actual time spent (in minutes/hours not rounded up to days as most people do) it could be that running fractals for weeks to get a set of ascended armor is actually less time spent than farming gold/mats for days. On the other hand, once you have your ascended equip you can keep farming mats/gold, while ascended armor boxed will just fill your bank (see screenshot, additionally i have at least 6 full asc heavy, 3 full asc med, 4 full asc light, i’m too lazy to swap my equip all the time).

And now back to the main topic:

I’m missing the “Chest of Black Lion Goods” in KINGs data, got 3 of those so far (no key of them though).

Illconceived Was Na.9781:
I would be interested in the number of runs needed so that 50% / 90% have at least gotten 1 chest. Especially the 90% number could be used to say “about 1 chest every x runs”.

Bohantopa : The 90% number if the chance of asc box is 8.9% is at 25 trials. This gives a 90.27 % chance to get >= 1 ascended box (CMIIW).