English

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.

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%.

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.

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...


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.


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.

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.

.

[/p]

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....

 

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.

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.

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

Placio -- You have consistently misunderstood the word "random" and the difference between a priori expectations and observational measurements of events directed by chance.

You seem to have the "gambler's fallacy" locked down, but you are seriously misinterpreting it. I don't know what textbooks or schooling you are taking for your interpretation but either they are wrong or your interpretation of them is. I made my living for 40+ years interpreting results that were based on the measurement of random impacts of photons on a receptor. I know the statistics.

Bittty - That simplifies matters greatly.

Placio - The reason I say large sample sizes are better is because we don't know the actual numbers behind the curtain. In the event of a roulette wheel or coin toss, we could get away with a smaller sample size simply because we already know the mechanics; they are 1d38 and 1d2.
When you don't know how the numbers are generated though, it takes a bit more data to figure out. If I rolled 2d10 about thirty times, it's entirely possible that I could roll mostly 7s and not have a single result above 12 and thus mistakenly assume that I'm rolling 2d6, but the more I roll, the more likely is is that I'll get a distribution curve that matches what 2d10 would put out.
You are correct that prior results have no impact on future results, but no matter how many times I flip a coin, I can predict with a high degree of certainty that my next toss will be either Heads or Tails with a 50% chance of either... assuming a perfect coin.

Mjollren - You mean like coin tosses generally being 51/49 affairs due to the fact that coins are not perfectly balanced?

The q30 simple writing accessories clearly state they will give 6 skill points bonus. I use them regularly when crafting and have seen these skill boosts: 6,8,10,10, and 9.


The scrolls do NOT work as intended.

its not a bug its a feature

Cathach -- what are you talking about? The skill level increase does not show -- it is just applied. All random factors involved in crafting are also applied. Screenies???

Ok, Let me copy the info of q30 Simple Writing Necessities for you: Modifies your Craft skills by 6 point(s) for 10 min and 40 sec.

Somehow, the origional intent seems to have been changed, such that the items of any level can have any value. I gave examples of greater benefits than the occupation level deserved.

These random values, of any level, obviates any need to take risk and accomplish the highest level of an occupation. This idea of "any random benefit" flys in the face of the notion of achievement. I recommend that the indicated values for this occupation be restored.

What do you mean you've *seen* these boosts? As Bittty said, your skill is simply modified behind the scenes. Have you tracked the rate of degrades and concluded it's all over the place?