Understanding crit percentages

[robbie1435]

I crafted 10 things this evening with a 75% crit chance... NOTHING critted

[Amwedhil]

Well, you could've been very unlucky

[cdq1958]

A 75% success chance implies a 25% failure chance, so 10 failures consecutively should happen about once per million trials on average. You hit the unlucky jackpot.

[Giseldah]

I've been so unlucky while using Scroll of the Ages. I think I never critted anything (horselord recipes) with it except one time for a kinship member.. Think it was maybe 7 times and then I started to use those 100% scrolls.

[q945]

I failed to crit on two of the fanghorn recipes with 73% chance (inc scroll of ages). There is no way I will be grinding for another 30 days to get 400 more tokens for another chance. I wouldn't even grind for a recipe for the other head/shoulder slot even though a teal non-crit is an upgrade..

[asimon]

honestly - crafting crits is working fine for me.
You must really have had an unusual bad luck streak.

and IMHO you're kinda overkilling with that headline

[LethalLethality]

I've had just as bad runs on crits with a 73% chance to crit (have yet to get the newest/best craft tools).

When I was working to make a set of light Malledhrim armor for my RK a couple of days ago. I critted a pair of shoes after the seventh attempt, a set of armor after the third attempt, and a couple other failures. All in all, I chewed through about 300 Magnificent Leathers to make one set of armor.

[Leixy]

I went 4 for 4 crits on Onodrim 95 armour with 73% crit chance, so it's pure crit chance per item, not overall chance to crit in bulk.

Like someone said, you just got extremely unlucky many times in a row.

However, if I'm doing a lot of items and I notice a bunch of non-crits in a row, I do stop, walk far enough away from the crafting facility to clear the buff, then re-enter & re-click the crafting facility, just in case there is indeed a crafting bug. lol.

[mjk47]

It really is pretty random. Sometimes you need to stop flogging the dead horse and step away from the crafting chamber.

Did you equip the horseshoe?

[Feraxks]

It really is pretty random. Sometimes you need to stop flogging the dead horse and step away from the crafting chamber.

Did you equip the horseshoe?

Would that be the horseshoe you took from the dead horse?

[robbie1435]

Friend of mine had a 23% chance for the gold fangorn recipe and it critted first try. Almost seems backwards, tbh. Odd though, that with a 75% chance to get a non crit.

[Neumi]

Chances are chances ... one can also crit with a 5% chance - or not crit with a 90% chance.

It's normal. Frustrating? Yes, but normal anyway.

The chance to get no crit in 7 tries with 75% crit chance is ~0.006% btw, that's 1/16384 = 1/(2^14)
Edit: Due to a mistake I had the wrong numbers here. Fixed it now.

[Leixy]

The chance to get no crit in 7 tries with 75% crit chance is ~0.00153% btw, that's 1/65536 = 1/(2^16)

that's incorrect. each crit is determined by each item crafted, not a bulk chance like your formula is representing.
if you craft 3 items for 75%, that's 75% for item 1, 75% for item 2, 75% for item 3. the crit roll is determined for each item, not all together.

It is not the probability of 0.25^7.

[Vulcwen]

that's incorrect. each crit is determined by each item crafted, not a bulk chance like your formula is representing.
if you craft 3 items for 75%, that's 75% for item 1, 75% for item 2, 75% for item 3. the crit roll is determined for each item, not all together.

It is not the probability of 0.25^7.

Actually, it is the probability of 0.25^7 (but definitely not 2^-16).
Each successive roll has the same 75% or 25% chance, but the chance of getting a specific sequence is the product of the chance of each element in the sequence. So the chance to get no crit with a 75% chance 3 times in a row = 0.25 * 0.25 * 0.25 = 0.25 ^3
The chance to get 1 crit than 1 non-crit and than a crit again = 0.75 * 0.25 * 0.75 = 0,140625.

The sum of the products from each possible sequence of the specific length always ends up as 1.

length = 1:
0.75 + 0.25 = 1
length = 2:
0.75 * 0.75 + 0.25 * 0.25 + 0.25 * 0.75 + 0.75 * 0.25 = 0,5625 + 0,0625 + 0,1875 + 0,1875 = 1

Ok it gets really long with 3 or more, but you get the point.

So @OP, the chance to get 10 non-crits in a row with 75% crit chance = 0.25^10 which is around 0.95/million. So around once in a million as cdq1958 said.

[Neumi]

that's incorrect. each crit is determined by each item crafted, not a bulk chance like your formula is representing.
if you craft 3 items for 75%, that's 75% for item 1, 75% for item 2, 75% for item 3. the crit roll is determined for each item, not all together.

It is not the probability of 0.25^7.

Oh, it is ... you are right, the events are independent from each other, but we are not observing the single tries, but the bunch of tries a a whole. The calculation must not be if a crit happens or not, the calculation is about the chances for NO crit in 7 tries.
Here's a simple Rule. If you connect 2 events with AND, you need to multiply the chances. If you connect them with OR, then you ADD the chances, but only if they come from the same event. If you say "at least one crit" ... you have a very long calculation ... except if you go the other way and say "chance of at least one crit" = 1 - "chance of no crit".

If you try 2 times, there are 4 possible results, that can happen. NONE can crit, ONE of them can crit (either one) or BOTH can crit.
(!a && !b) || (!a && b) || (a && !b) || (a && b)
The sum of the chances for all possible results = 1
Let's say a is the chance for the first crit to happen, then !a is the opposit, meaning that !a = 1-a The same goes for b.
((1-a) * (1-b)) + ((1-a) * b)+ (a * (1-b)) + (a * b) = 1

Actually, it is the probability of 0.25^7 (but definitely not 2^-16).
...
So @OP, the chance to get 10 non-crits in a row with 75% crit chance = 0.25^10 which is around 0.95/million. So around once in a million as cdq1958 said.

My bad, I mistyped on my calc. I accidently did it with 8 tries instead of 7. With 7 tries it would have been 2^-14
2^-16 would have been the chance to fail 8 times in a row (and trying 8 times).
For 10 tries the chances are 2^-20 (=0.00000095367431640625, like you said)
(0.25 is a very convenient number to calculate)

[elianidd2]

I crafted 10 things this evening with a 75% crit chance... NOTHING critted

I think this is an issue of late. Specially with higher-end materials the crit ratings just don't seem to add up, and I remember quite well when they did (like two months ago). I'm going to submit a bug report for it myself. I also had the problem of it straight up eating ingots every once in a while if I used crit materials. It would say that it gave me the ingot on the chat window and eat the materials but the number on the stack would not go up.

[HaleElven]

It would say that it gave me the ingot on the chat window and eat the materials but the number on the stack would not go up.

Out of curiosity... Is it possible that you had more than one not-full stack of materials in your inventory?

Because, if you're using processing, the new ingot may be going into the first stack and not the second stack that you're watching.

[gelleg]

while I can't prove it. I believe the current time possibly seconds is used as part or all of the seed value. I find if I get a fail and craft another item immediately after it, I am likely to fail again. Also I believe they use a very streaky RNG. I tend to wait 5-10 seconds or more after a crit failure before resuming crafting. I find it gives you more even results and fewer failures. Ultimately if you craft 100 items at 75% crit, most times I see 3/4 crit, but I will often see several fails in a row and several successes in a row. The RNG as they say does work, but it works in streaks in my experience. A good example is the c runtime RNG function. If you input two near seeds (ie 4,5) you are very likely to get the same result when the RNG value is divided by the number of possible outcomes. For example 75% chance would be done as rnd()%100 < 75 so they take the random number from rnd() and get the remainder when divided by 100 and see if its less then 75. So if the result of rnd with a seed of 4 and the result with a seed of 5 result in two values only separate by 1 or 2 numbers the result of the division by 100 will be similar enough to cause the same result. This is how the streaks happen. If you wait enough time after a failure you may get a very different result.

[Grimdi]

Usual RNG failure. Unfortunately impossible to proove that it's flawed.

[Michaleo]

I haven't seen the software, but because it would require more work, I assume that you don't get your own personal random number generator and that it retains no history to be biased for or against you. Given how many "random" events are happening on a server each second, you would never see the streakiness in the RNG, to the extent there is any. (I wonder how many random numbers ARE generated each second on average.)

Unless the displayed percentage doesn't match the percentage used by the game, there is no easy way for the game to discriminate. RNG-based operations are so fundamental and pervasive in the game, it is hard to imagine how they could be unfair to a particular person or in a particular situation. It would take thousands of trials to demonstrate that the actual crit rate differs significantly from the displayed rate.

Human intuition leads to many fallacies regarding random (or pseudo-random) events. People buy billions of lottery tickets despite the fact that on average over the long run they are losing about half their money. On the other hand, despite astronomical odds for any individual, there are regular lotto winners. Lotteries make money because people ignore the former and pay attention to the latter.

No one complains when they get more crits than they "deserve". (OK, some did when they kept getting interrupted by the inscription prompt when they were levelling crafters, but that's been remedied. lol)

Feel free to believe in luck, Karma or the Law of Attraction if you like, but you're probably just seeing a pattern in random occurrences.

[idontcare789]

Or it could just be Craft item>check tools>check scrolls>check crit item=%to crit>rng 1-100(75% crit)>you rolled a 1.......Next craft item>check tools>check scrolls>check crit item=%to crit>rng 1-100(75% crit)>you rolled a 4. Maybe it just does a check on the beginning of every item and you just seriously hit bad luck, 75% chances to win but still 25 to lose. Why is this so hard to grasp?