Z
Zardo Zap
Guest
Foreward
This is for you who have been following a discussion kicked off and pursued by Kylas - who noticed that runic hammers don't give bonuses the way we expect them to.
Its rather long, but since there will be a number of people who disagree with the results I thought I better set it out in detail, so that I minimise the risk of being misunderstood. To those who feel its too long winded I apoligise, you can always skip the conclusion.
Finally, if you hope to sell a high end hammer, don't let your customer read this.
Background - the problem
The first thing Kylas noticed was that... well lets explain by example take a shadow hammer (why a shadow will become clear later /php-bin/shared/images/icons/wink.gif ), shadow generates intensities in the range of 20% to 45%. Now when an intensity is generated you might expect it to generate a roll in the range of 20% to 45% - But it doesn't - this is the chop "effect". What it does is generate an intensity between 1% and 100%. If its below the hammers minimum it raises it to the minimum (in a shadow's case 20%). If its above the maximum it lowers it to the maximum (here 45%). This effect is readily apparent if you are looking for it. All runic hammers create a disproportionate number of items at either the minimum or maximum of the range (well obviously not valorite at the top of its range). I think everyone accepts the "chop" effect.
The more controversial element is the distribution. When it generates its initial intensity does it generate it straight line e.g like rolling a 100 sided dice, the same chance to roll 2% as 34% as 67% as 1% as 99% etc or is their a "distribution curve" that is, is it more likely to roll something in the range of 1-10% than it is in the range of 91% to 100%?
"Well" I thought to myself - "I think there is a distribution curve lets see."
The experimental set up
I didn't have enough bronze hammers to waste in an experiment, copper hammers were no good as they could produce either 2 or 3 enhancements and it might be difficult to work out which hammers only had one intensity apply to their enhancements. Shadow was perfect - I had lots - and they produce two intensities always.
The idea was I would use 6 hammers, produce 265 ringmail gloves (iron) [the actual idea was I would only produce 264 gloves, but I used all of one hammer by mistake]. I would then check the distribution of resists on the gloves which got one and only one resist and for which I could spot where the other enhancement went.
The reason for making sure I knew where the other enhancement went was because IF both enhancements were applied to the same resist (e.g. fire), the higher one would prevail and this would skew the results.
I would then have a number of enhanced gloves, with a single resist enhanced in the range of 20% to 45%.
So what do I mean an enhancement of 20% to 45%, resists are in the range of 1 to 15 right?
Yep, but 20% of the max (15) gives us 3 - which is what the minimum of the shadow hammer is. Curiously the resists round up, so a roll of 21% up to 26% gives us 4. The full list is here (note I have rounded to the nearest full percentage which causes a slight discrepency, but as we will see that is not significant)
For a shadow runic - remembering the "chop" effect the enhancement percentages to resist points are as follows
<ul>[*]0%-20% 3 points[*]21%-26% 4 points[*]27%-33% 5 points[*]34% to 40% 6 points[*]41% plus 7 points[/list]
Just note out of interest that the 45% max of shadow still only gives you the 7 points you would get if you get a 42% intensity.
The d100 hypothesis
Or as some might call it all the "all intensities have equal chance" hypothesis.
If this were right, then using the above calculation, of the pieces I make with one and only one resist we would find the following distribution,
20% of them would have 3 extra resist points,
6% of them 4 points
7% of them 5 points
7% of them 6 points
and 60% of them 7 points
Note - actually the 4,5 and 6 points would have the same chance this is the rounding error I alluded to earlier.
The results
I got 90 gloves (out of 265 made) with one and only one resist enhancement.
They were distributed as follows
7 resist points - 30 gloves - 33% compared with hypothesised 60%
6 resist points - 6 gloves - 7% compared with a hypothesised 7%
5 resist points - 8 gloves - 9% compared with a hypothesised 7%
4 resist points - 12 gloves - 13% compared with a hypothesised 6%
3 resist points - 34 gloves - 38% compared with a hypothesised 20%
Well! The high end and the low end is completely different from a straighline prediction.
I could do a standard deviation check, make sure I have statistically significant data, but that would bore you, bore me and is not needed.
Kylas you are vindicated, in my mind at least the d100 theory is dead.
So how are runic hammers distributed ??
A new theory
Well its OSI, lets see something used elsewhere.
When calculating the impact of luck on monster drops they use an inverse square root distribution ... lets see if that fits.
What do I mean by an "inverse square root distribution" - good question! Let me answer it in an inverse way /php-bin/shared/images/icons/smile.gif If you wanted to calculate the chance of rolling in the range of 0-10, you would go 100 minus 10 gives you 90, square 90, gives you 8100, subtract from 10000, gives you 1900 and divide by 10000, gives you a 19% chance of rolling 0-10. Or if you wanted to calculate the chance of rolling above 90 (hold on to your hats here), calculate the chance of rolling 1-90 as 100 minus 90 equals 10, square 10 to get 100, subtract 100, from 10000, to get 9900, or a 99% chance of getting 1-90, and only a 1% chance of getting above 90. [Valorite hammer owners who were hoping to get a few properties above 90% might be feeling a bit sick at this point.]
Difficult to explain, but easy to calculate especially as OSI has a square root approximater they use for luck. So generate a number between 1 and 10000, and take the square root,
and subtract it from 100, 1 becomes 99%, 100 becomes 90%, 8100 becomes 10%.
If you don't follow me, just take it for read that it really reduces your chance of rolling big.
So that's the new hypothesis lets compare it to the results...
If I am right I would expect the following percentages:
Chance of 7 resist points is 36% - experiment gives 33%
Chance of 6 resist points is 9% - experiment gives 7%
Chance of 5 resist points is 9% - experiment gives 9%
Chance of 4 resist points is 10% - experiment gives 13%
Chance of 3 resist points is 36% - experiment gives 38%.
Oh - that is quite close - you know the hypothesis could be right.
Well the only way to get a better confirmation would be to burn some bronze and see if the top end dies away as we would expect. Bronze can go up to 10 resist points. Any intensity roll above 60 will give you 10 points.
Under the (in my mind discredit) d100 theory you would expect 40% of bronze made armour with one resist to have an additional 10 points of resist. Under the Square root theory you would expect only 16% of them to have the 10 points - sadly that fits my memory of the results I got.
Just to finally spur the Agapite plus owners into action you only have a 4% chance of an intensity greater than 80 (12 points) and a 1% chance of a verite or valorite hammer getting a resist geater than 90% intensity (14 points).
Oh well at least we know, but what we don't know is - was it intentional!
-------------------------------------------------------------------------------------
New Data provided by McHuberts
McHuberts recorded all the information he made on well over 260 bronze armour pieces. From the data there were 112 items which had one and one only resist enhanced.
The "inverse square" theory predicts (rounded slightly) ...
The chance of getting 10 points = 16%
The chance of getting 9 points = 5.1%
The chance of getting 8 points = 7%
The chance of getting 7 points = 8%
The chance of getting 6 points = 9%
The chance of getting 5 points = 55%
The data provided by McHubert gave the following results (out of 112 hammers)
10 points - 15 items - 13% compare with predicted 16%
9 points - 5 items - 4% compare with predicted 5%
8 points - 5 items - 4% compare with predicted 7%
7 points - 7 items - 6% compare with predicted 8%
6 points - 15 items - 13% compare with predicted 9%
5 points - 65 items - 58% compare with predicted 55%
The differences could be down to just fluctuations, but if anything the inverse square theory over states the chances (although my gut feel is still that its right).
The predicted marked drop off for 10 points was certainly found to exist.
I would also note as an aside of the 264 items made (thats about 7.5 hammers!) he only got 3 items which had resists (or potential resists if they had been made of valorite) of 50 or over! that's 1.1% - I predicted 1.8% (with bit of guess work). They certainly seem to be in the same ballpark.
Whats important to realise is except for the fact that you have a chance of more properties applying to resist these same stinking odds apply to the bigger hammers too - and you have less strikes with them. It really is a bit pathetic.
Zardo
This is for you who have been following a discussion kicked off and pursued by Kylas - who noticed that runic hammers don't give bonuses the way we expect them to.
Its rather long, but since there will be a number of people who disagree with the results I thought I better set it out in detail, so that I minimise the risk of being misunderstood. To those who feel its too long winded I apoligise, you can always skip the conclusion.
Finally, if you hope to sell a high end hammer, don't let your customer read this.
Background - the problem
The first thing Kylas noticed was that... well lets explain by example take a shadow hammer (why a shadow will become clear later /php-bin/shared/images/icons/wink.gif ), shadow generates intensities in the range of 20% to 45%. Now when an intensity is generated you might expect it to generate a roll in the range of 20% to 45% - But it doesn't - this is the chop "effect". What it does is generate an intensity between 1% and 100%. If its below the hammers minimum it raises it to the minimum (in a shadow's case 20%). If its above the maximum it lowers it to the maximum (here 45%). This effect is readily apparent if you are looking for it. All runic hammers create a disproportionate number of items at either the minimum or maximum of the range (well obviously not valorite at the top of its range). I think everyone accepts the "chop" effect.
The more controversial element is the distribution. When it generates its initial intensity does it generate it straight line e.g like rolling a 100 sided dice, the same chance to roll 2% as 34% as 67% as 1% as 99% etc or is their a "distribution curve" that is, is it more likely to roll something in the range of 1-10% than it is in the range of 91% to 100%?
"Well" I thought to myself - "I think there is a distribution curve lets see."
The experimental set up
I didn't have enough bronze hammers to waste in an experiment, copper hammers were no good as they could produce either 2 or 3 enhancements and it might be difficult to work out which hammers only had one intensity apply to their enhancements. Shadow was perfect - I had lots - and they produce two intensities always.
The idea was I would use 6 hammers, produce 265 ringmail gloves (iron) [the actual idea was I would only produce 264 gloves, but I used all of one hammer by mistake]. I would then check the distribution of resists on the gloves which got one and only one resist and for which I could spot where the other enhancement went.
The reason for making sure I knew where the other enhancement went was because IF both enhancements were applied to the same resist (e.g. fire), the higher one would prevail and this would skew the results.
I would then have a number of enhanced gloves, with a single resist enhanced in the range of 20% to 45%.
So what do I mean an enhancement of 20% to 45%, resists are in the range of 1 to 15 right?
Yep, but 20% of the max (15) gives us 3 - which is what the minimum of the shadow hammer is. Curiously the resists round up, so a roll of 21% up to 26% gives us 4. The full list is here (note I have rounded to the nearest full percentage which causes a slight discrepency, but as we will see that is not significant)
For a shadow runic - remembering the "chop" effect the enhancement percentages to resist points are as follows
<ul>[*]0%-20% 3 points[*]21%-26% 4 points[*]27%-33% 5 points[*]34% to 40% 6 points[*]41% plus 7 points[/list]
Just note out of interest that the 45% max of shadow still only gives you the 7 points you would get if you get a 42% intensity.
The d100 hypothesis
Or as some might call it all the "all intensities have equal chance" hypothesis.
If this were right, then using the above calculation, of the pieces I make with one and only one resist we would find the following distribution,
20% of them would have 3 extra resist points,
6% of them 4 points
7% of them 5 points
7% of them 6 points
and 60% of them 7 points
Note - actually the 4,5 and 6 points would have the same chance this is the rounding error I alluded to earlier.
The results
I got 90 gloves (out of 265 made) with one and only one resist enhancement.
They were distributed as follows
7 resist points - 30 gloves - 33% compared with hypothesised 60%
6 resist points - 6 gloves - 7% compared with a hypothesised 7%
5 resist points - 8 gloves - 9% compared with a hypothesised 7%
4 resist points - 12 gloves - 13% compared with a hypothesised 6%
3 resist points - 34 gloves - 38% compared with a hypothesised 20%
Well! The high end and the low end is completely different from a straighline prediction.
I could do a standard deviation check, make sure I have statistically significant data, but that would bore you, bore me and is not needed.
Kylas you are vindicated, in my mind at least the d100 theory is dead.
So how are runic hammers distributed ??
A new theory
Well its OSI, lets see something used elsewhere.
When calculating the impact of luck on monster drops they use an inverse square root distribution ... lets see if that fits.
What do I mean by an "inverse square root distribution" - good question! Let me answer it in an inverse way /php-bin/shared/images/icons/smile.gif If you wanted to calculate the chance of rolling in the range of 0-10, you would go 100 minus 10 gives you 90, square 90, gives you 8100, subtract from 10000, gives you 1900 and divide by 10000, gives you a 19% chance of rolling 0-10. Or if you wanted to calculate the chance of rolling above 90 (hold on to your hats here), calculate the chance of rolling 1-90 as 100 minus 90 equals 10, square 10 to get 100, subtract 100, from 10000, to get 9900, or a 99% chance of getting 1-90, and only a 1% chance of getting above 90. [Valorite hammer owners who were hoping to get a few properties above 90% might be feeling a bit sick at this point.]
Difficult to explain, but easy to calculate especially as OSI has a square root approximater they use for luck. So generate a number between 1 and 10000, and take the square root,
and subtract it from 100, 1 becomes 99%, 100 becomes 90%, 8100 becomes 10%.
If you don't follow me, just take it for read that it really reduces your chance of rolling big.
So that's the new hypothesis lets compare it to the results...
If I am right I would expect the following percentages:
Chance of 7 resist points is 36% - experiment gives 33%
Chance of 6 resist points is 9% - experiment gives 7%
Chance of 5 resist points is 9% - experiment gives 9%
Chance of 4 resist points is 10% - experiment gives 13%
Chance of 3 resist points is 36% - experiment gives 38%.
Oh - that is quite close - you know the hypothesis could be right.
Well the only way to get a better confirmation would be to burn some bronze and see if the top end dies away as we would expect. Bronze can go up to 10 resist points. Any intensity roll above 60 will give you 10 points.
Under the (in my mind discredit) d100 theory you would expect 40% of bronze made armour with one resist to have an additional 10 points of resist. Under the Square root theory you would expect only 16% of them to have the 10 points - sadly that fits my memory of the results I got.
Just to finally spur the Agapite plus owners into action you only have a 4% chance of an intensity greater than 80 (12 points) and a 1% chance of a verite or valorite hammer getting a resist geater than 90% intensity (14 points).
Oh well at least we know, but what we don't know is - was it intentional!
-------------------------------------------------------------------------------------
New Data provided by McHuberts
McHuberts recorded all the information he made on well over 260 bronze armour pieces. From the data there were 112 items which had one and one only resist enhanced.
The "inverse square" theory predicts (rounded slightly) ...
The chance of getting 10 points = 16%
The chance of getting 9 points = 5.1%
The chance of getting 8 points = 7%
The chance of getting 7 points = 8%
The chance of getting 6 points = 9%
The chance of getting 5 points = 55%
The data provided by McHubert gave the following results (out of 112 hammers)
10 points - 15 items - 13% compare with predicted 16%
9 points - 5 items - 4% compare with predicted 5%
8 points - 5 items - 4% compare with predicted 7%
7 points - 7 items - 6% compare with predicted 8%
6 points - 15 items - 13% compare with predicted 9%
5 points - 65 items - 58% compare with predicted 55%
The differences could be down to just fluctuations, but if anything the inverse square theory over states the chances (although my gut feel is still that its right).
The predicted marked drop off for 10 points was certainly found to exist.
I would also note as an aside of the 264 items made (thats about 7.5 hammers!) he only got 3 items which had resists (or potential resists if they had been made of valorite) of 50 or over! that's 1.1% - I predicted 1.8% (with bit of guess work). They certainly seem to be in the same ballpark.
Whats important to realise is except for the fact that you have a chance of more properties applying to resist these same stinking odds apply to the bigger hammers too - and you have less strikes with them. It really is a bit pathetic.
Zardo