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#18 Added by Bitttymacod 9 years ago Report | Quote [en]

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You clearly have not used q60 and q70 scrolls. The reuse time on those is significantly longer than the use time.

Were you still getting the xp for a 50 level difference in your case of a 50 level difference and a q40 scroll? If so, that's a bug. :D

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#19 Added by Placio 9 years ago Report | Quote [en]

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why on Atys would it be a bug? And i dont understand your claim that success is less than what is dispalyed, I just checked and success rate goes up by about 1.6% at those low levels, so if using a q50 and it adds 8 levels than it actually should increase the success by 13% :(

Edited 2 times | Last edited by Placio (9 years ago)

#20 Added by Bitttymacod 9 years ago Report | Quote [en]

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It would be a bug because XP is supposed to be based on the level of the the person vs. the level of the operation. It should not matter if the level is a base level or an enhanced level.

(A q50 scroll adds 10 levels.)

Last edited by Bitttymacod (9 years ago)

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#21 Added by Placio 9 years ago Report | Quote [en]

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Yes i has a q40 in my bag :( but an increase of 10 levels still produces an additional 16%. XP is your lvl vs final product, I checked that also, it did not change even with a scroll boost. So I still stand by my advice to use scrolls when overcrafting by the already established 50 lvls. And I still dont know why you think the scrolls give levels- that would result in more success rate than the 8% or 10% etc. that the product states.

#22 Added by Bitttymacod 9 years ago Report | Quote [en]

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I state that scrolls give levels because of analysis of the use of scrolls at high level. The success rates are within experimental error of the result for boosting levels and well away from the percent increase reported by the crafting window.

And I maintain that using them to grind overcrafting is a waste of resources that could be used to decrease your chance of a degrade when making something useful. It just is not that difficult to harvest more grind mats than you can shake a stick at. Minor improvements in xp gain per hour are just that, minor.

This, however is philosophical. Use of scrolls certainly will not strongly affect how rapidly you advance from journeyman (level 200) to master, but if you want to do it, feel free.

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#23 Added by Placio 9 years ago Report | Quote [en]

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I'm not sure what analysis you did, but the craft actions are independent. In essence if your success rate is 5% than you have a 95% degrade chance on every item, even if you make a million, and because the actions are independent you will have much lower than 5% on average.

I'm not sure you analysis of high levels should be applied to overcrafting; if overcrafting you gain 1.6% for every skill level you get closer to your action level- under your levels hypothesis this would give 1.6x the amount of points stated by the scrolls and craft window. However if the crafter's level is above their action level they only get 0.5% for every level above- this might explain you lower observations, or it was just random.

Finally, scrolls are not some rare thing. they are pretty easy to replace. and the 'minor' xp improvements can add up, because a boost of 8 or 10% might not get you your full action q but will increase the q of the majority of degrades.

#24 Added by Bitttymacod 9 years ago Report | Quote [en]

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Placio (atys)

I'm not sure what analysis you did, but the craft actions are independent. In essence if your success rate is 5% than you have a 95% degrade chance on every item, even if you make a million, and because the actions are independent you will have much lower than 5% on average.

I'm not sure you analysis of high levels should be applied to overcrafting; if overcrafting you gain 1.6% for every skill level you get closer to your action level- under your levels hypothesis this would give 1.6x the amount of points stated by the scrolls and craft window. However if the crafter's level is above their action level they only get 0.5% for every level above- this might explain you lower observations, or it was just random.

Finally, scrolls are not some rare thing. they are pretty easy to replace. and the 'minor' xp improvements can add up, because a boost of 8 or 10% might not get you your full action q but will increase the q of the majority of degrades.

The analysis on my part involved several thousand crafts using q60 scrolls, the highest level that is "easy" to get. Daomei's analysis involved a similar number of crafting actions using q70 scrolls, because she is even more bloody-minded than I am. The percentages matched the 0.5% per level figure that you note.

Your analysis of the statistics, however, is flawed. The actions are indeed independent, but a 5% success chance means that *on the average* one crafting action in 20 will be a complete success. This will be true whether you craft a thousand times or ten thousand times. There is no reduction in percentages for large numbers of actions; on the contrary there is a closer and closer approach to the 5% value as random variations even themselves out.

In addition there is no indication that the potential frequency of a certain amount of degrade if there is not success is affected by the level of crafting skill. As a master I have only a 15% chance of degrade when crafting at q250. However, I seem to have just as much chance of producing a q200 as I have of producing a q245 if I do fail, and this does not change even when I am using scrolls.

Without looking at the code I cannot be certain, but it very much looks as if the calculation is :

xx=rand(1,100)
if xx<=success_threshold
then q_result = q_attempt ; (success!)
else
yy = rand(1,100) * 0.20
q_result = q_attempt * (1 - yy) ; (degrade by random amount up to 20%)
endif

Whether or not there are extra decimals involved in the calculation is a detail.

The real question in my mind is whether or not the increase in success factor will produce a decrease in time to master that is significant in terms of requiring significantly fewer bags of materials or hours on line. Obviously it will have some effect, but I doubt very much that it is a large one.

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#25 Added by Placio 9 years ago Report | Quote [en]

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No Bittty, independent means action 1 is 5% chance, action 2 is 5% chance, etc. Even if you get 999,999 fails in a row the next action still only has a 5% chance of success. So if your success is lower than 50% you will tend to fail more than each action failure rate, and if the rate is above 50% you will tend to succeed more than the rate would suggest.

I finally found Dao's post, and she concluded that scrolls are working properly now. You levels hypothesis is accepted by a few the know the game code better than me, so I'll go with it. But that would make scrolls even more valuable to over crafters because it is 1.6 percent additional success for each skill level approaching the action level.

#26 Added by Bitttymacod 9 years ago Report | Quote [en]

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Placio (atys)

No Bittty, independent means action 1 is 5% chance, action 2 is 5% chance, etc. Even if you get 999,999 fails in a row the next action still only has a 5% chance of success.

True, as far as it goes. However, it assumes that we know the ideal chance of success. (e.g. we know that it is a totally unbiased d20 that we are watching for a 3 to appear). While your example is correct if we know that, the probability of that occurrence is very very low.

If we were attempting to evaluate what the true chance of success was by measuring data and we had that result, our best estimate would be that the chance of success was one in a million.

Placio (atys)

So if your success is lower than 50% you will tend to fail more than each action failure rate, and if the rate is above 50% you will tend to succeed more than the rate would suggest.

False, because if it were true it would mean that the measurements were not independent.

What you are saying is equivalent to saying that since I get an 85% chance (as reported) to successfully make a single jewel, that my overall rate of creating jewels should be *more* than 85%.

Placio (atys)

I finally found Dao's post, and she concluded that scrolls are working properly now. You levels hypothesis is accepted by a few the know the game code better than me, so I'll go with it. But that would make scrolls even more valuable to over crafters because it is 1.6 percent additional success for each skill level approaching the action level.

In fact, hers was a very conservative statement. There is no solid evidence to suggest that the scrolls were actually ever broken.

Once again, you assert "value". I once again assert that if the "value" is decreased time and mats to master rank, that the value is there, but that it is small.

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#27 Added by Placio 9 years ago Report | Quote [en]

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Bitttymacod (atys)

If we were attempting to evaluate what the true chance of success was by measuring data and we had that result, our best estimate would be that the chance of success was one in a million.

In my example you might have observed 1 in a million, but the chance of each action is still 5%. As they are independent they do not have to average out so that our sample has a success rate similar to each individual action. If you did another million crafts the rate would almost certainly be different each time. No matter how many times you observe the only thing that matters is the individual craft's success rate; Its like playing Roulette and saying my number *must* come up once every 37 spins, well it could come up 3 times in 37 spins or not once in 10,000 spins...

Bitttymacod (atys)

Placio (atys)
So if your success is lower than 50% you will tend to fail more than each action failure rate, and if the rate is above 50% you will tend to succeed more than the rate would suggest.
False, because if it were true it would mean that the measurements were not independent.

What you are saying is equivalent to saying that since I get an 85% chance (as reported) to successfully make a single jewel, that my overall rate of creating jewels should be *more* than 85%.

I said *tend* in your example you have an 85% success rate, so every time you craft there is a better chance that you will succeed than fail (15% failure rate per action). In the case of an over crafter where success is only 10% this time, there is a better chance of failure each action. If you failure rate is 90% each time it would *tend* to give you less than 10% success because each time you have a great risk of failing. But as you point out they are independent, so they do not have to trend that way, you might get lucky one day or really unlucky the next.

Bitttymacod (atys)

Once again, you assert "value". I once again assert that if the "value" is decreased time and mats to master rank, that the value is there, but that it is small.

Based on your levels hypothesis I argued that scrolls provide more benefit to over crafters, because when a master uses them they only get .5% for each level over their skill, but over crafters get 1.6% for each level that they get closer to the action level. So a master getting 10 point boost from a scroll only gets an additional 5%, but an over crafter getting the same 10 point boost will get an additional 16% success.

#28 Added by Rubiksmomo 9 years ago Report | Quote [en]

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It's true that individual actions are very random, but I think Bitty is right about the larger data having average closer to the chance.

You can try this out in a spreadsheet. Add a small amount of random numbers between 0-1. The average is probably not very close to 0.5 (the middle point). Now start adding more random numbers and you will see the average getting closer to 0.5 more often.

So I think you can calculate the chance if you have enough data. What is enough data? Depends on the chance, if the chance is smaller you need more data.

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#29 Added by Gidget 9 years ago Report | Quote [en]

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Rubiksmomo (atys)

It's true that individual actions are very random, but I think Bitty is right about the larger data having average closer to the chance.
You can try this out in a spreadsheet. Add a small amount of random numbers between 0-1. The average is probably not very close to 0.5 (the middle point). Now start adding more random numbers and you will see the average getting closer to 0.5 more often.
[p]So I think you can calculate the chance if you have enough data. What is enough data? Depends on the chance, if the chance is smaller you need more data.

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How much data you need also depends on how the Random Number Generator works. For instance, taking one regular six-sided die, the RNG most people are familar with, will give you numbers between 1 and 6 with a pretty even distribution that gets closer to 16.66...% as you add more data points.

However, taking two six-sided dice to get random numbers between 2 and 12 will yield a V-shaped curve with the odds of getting a sum of 7 being equal to the combined odd of getting 2,3,11 and 12 combined; of the thirty-six possibilities, six yield a 7 while 2 and 12 only have one possibility each while 3 and 11 each have two, and (1+2+2+1)=6.

So how many data points are needed kind of depends on how many "dice" are used. One gives a linear distribution with equal chances of each result, two results in a V-curve, using three or more is a bell curve. In the event of a curve (V or bell), the center will be halfway between the high end low limits of the range.

Usually rolling a number of times equal to twice the number of possible outcomes will tell you whether it's a single "die" or multiple "dice", but to get a reasonably accurate curve you need a number of samples at least three times the total number of possibilities, an number which increases exponentially as teh number of "dice" increases. For 2d6 with thirty-six possible outcomes, about a hundred data points will be pretty accurate since (3*36)=108, but 3d6 has two-hundred-and-sixteen possible outcomes, meaning over six hundred data points would be required for reasonable accuracy.

The real question then is who (if anyone) has the free time and desire to do the research to make a spreadsheet. I may be a numbers geek, but even I have limits to how much statistics I'm willing to do so it wouldn't be me! Maybe Bittty....

Last edited by Gidget (9 years ago)

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#30 Added by Bitttymacod 9 years ago Report | Quote [en]

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Yegads! All true, Gidget. Thank goodness that there is no evidence that the devs used more than one RNG to generate the probabilities in xp for crafting. The number of samples that both Daomei and I did are consistent for a single RNG to determine success and a second one to determine degree of failure.

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#31 Added by Placio 9 years ago Report | Quote [en]

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This has to be the last time I reply to this....

Rubik, I looked at your spreadsheet example and found a big problem, at least in my Excel, the random number function produces an 'evenly distributed' set of random numbers (it says so in the formula description), so this cannot represent the independent craft events that occur in game. Also at 50% odds either way, like the flip of a coin, it will at times appear as if the average/overall probability is 50% but it does not have to stay that way.

Gidget, sample size is irrelevant. These are independent events, so their population is 1. There is an equation for determining the correct sample size of a population, but it requires the population size, standard deviation, and the z-scores that correspond to the desired confidence interval. You can't do that with independent events, no matter how much data you collect. And we don't need to because the population of an independent event is 1 and we already are given the probability for one action, it is displayed in the craft window.

Bittty, going back to my roulette example (which I have to correct since we have 38 spaces on an American roulette wheel) no matter how many observations you make and calculate the probability from, these are just curious observations. They have no analytical or predictive value. There is no overall or average success rate for a group of independent events since they are in fact independent of each other. The closest we can get would be to ask questions like: What is the probability of hitting number 7 four times in a row? We can easily calculate this by doing (1/38)^4=0.00000048 or less than 5 in a million. Applying this to an Armilo tool situation: What is the probability of no boosts in ten crafts? (9/10)^10=.03486. So even with ten crafts the probability of all failing is still almost 35%, nearly 25% more than your success rate of an individual action. It takes 22 crafts for the chance of failure to fall below the chance of success (9/10)^22=0.0984. But even multiplying the probabilities of independent events is still just an estimation, they are independent and each action is still as probable as its own success rate.

Last edited by Placio (9 years ago)

#32 Added by Mjollren 9 years ago Report | Quote [en]

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Observations on roulette can have predictive value if the physical object deviates from an ideal object - e.g. it has some slight material deformations that make it more probable for the ball to end on a certain number (or a class of numbers).

Similarly, random number generators used to be quite weak on computers. One may observe behaviour in the hope that a weak one was implemented in game :D

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