Chance to learn spell % is BS
ankheg
Member Posts: 546
I am sure that it is well known but this number was never accurate. I mean come on, with 85% less than half of them are successful.
Post edited by Dee on
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Remember that it's not 85 out of every 100; it's an 85% probability with each attempt. It's sort of like the chances of rolling an 18 or higher on your attack roll; it seems improbable, but it's just as likely as rolling between 9 and 11.
(I've also edited the thread's title; a little profanity in the thread itself is one thing, but broadcasting it to the forums is another.)
Are you on normal difficulty? The game is set on normal difficulty by default, which means you never fail to copy a spell. I set mine on core difficulty, which has a chance for failure. Higher difficulties beyond that also have chances of failure.
With that kind of numbers, this sort of stuff does happen too, eventually.
My results were 56 successes out of 100. I think that is a sufficiently large sample size to statistically conclude that the success rate in the game is BS. Of the 44 failures, there were 5 times where it failed 3x in a row, and once where it failed 4x in a row.
Here is a list of each individual result of my trial, Y=success, N=failure:
YYYNYNYYNN
NYNNYYNYNY
YYYYNNNNYY
YNYNYNYYYN
NNYYYYNNNY
NNNYYYYNNN
YNNYYYYNYY
YNYYYYNYNY
YNNNYNNYYN
NYYYYYNNYN
I thought about the fact that computers are never truly random, and that I might have chanced upon a random seed that favored failure. So I repeated the experiment without reloading. It takes considerably longer because each success meant I had to go into the spell book and erase the spell.
The results were better, 67 successes out of 100, but still well short of the expected 75. I think 100 is a sufficiently large sample size to still conclude there is something wrong with the system in the game. In this trial, there were 4 times where it failed 3x in a row.
YNYYYNYYNY
YNYNYYNYYY
YNNNYNYYYY
YNYYNNYNYY
YYYYNNNYYN
YNYYYYYYYY
YNNNYYNNYY
NYYYYYYYNY
YNYYYYNNNY
YNYYYYNYYN
You are welcome to try this experiment yourselves.
You could toss a coin in the air 500 times in a row. Now, your logic says that it ought to be a 50/50 chance of landing on heads, but in reality, you could have 450 tails if you did it.
The percentage of chance is reset for every new try.
As far as your experiment, you had more successes than fails, so it's absolutely in the realm of a 75% chance.
If you did it a thousand times, you'd almost certainly wouldn't nail a precise 75% success of reading the spell.
The probability of tossing 450 tails out of 500 tosses is 7.07x10^-82, that is 1 in 1.414x10^81, that is the order of magnitude of 10 with 81 zeroes after it. You have a much higher chance of winning the powerball, good luck.
I think a sample size of 100 is very reasonable for a two-outcome test. The margin of error certainly wouldn't be greater than 8% from the results of the second test, and certainly not the 19% from the first test.
Statistical probability suggests that the likelihood of a certain outcome diminishes or increases depending on the results of previous trials. In other words, if your first toss comes up heads, then your second toss is statistically more likely to come up tails, because the statistical probability of it coming up heads twice in a row is lower than the statistical probability of it coming up heads and tails in equal turns.
Mathematical probability, on the other hand, means that with each toss of the coin there is a 50/50 chance of either outcome, regardless of how many times the coin is tossed. In other words, you might toss the coin once, and it would come up heads, and the second time you toss the coin there is the same probability of it coming up heads. Which is to say 50%, each time.
What we're dealing with is an expectation of statistical probability, which suggests that for every hundred trials there should be a direct correlation to the percent chance of success. In other words, for an 85% chance of success, there should be 85 successful results in 100 attempts. That's not what's happening.
What's happening is 100 individual attempts, each calculated on their own, using their own set of randomly generated numbers. Which means that each attempt has an 85% chance of success. This likelihood of success doesn't increase or diminish depending on the number of trials. You might have fifteen failures followed by eighty-five successes. You might have no successes at all. You might not have any failures. When it comes to randomly generated numbers, the key word is "random". The game's engine does not create results that take into account all previous results.
Anyone who has played tabletop D&D understands this. You could have a night where you roll nothing but 1's and 5's. That same night, the person to your left might roll a series of natural 20's. It doesn't mean the dice are rigged; it means you had a string of bad luck.
And sometimes you might have several strings of bad luck. Or you might find yourself rolling really well during combat but rolling terribly in social situations (such as writing spells, for instance).
-Assumes the results of the repeated experiment are independent
-Assumes the means of the repeated experiment follow a normal distribution
Hypothesis testing:
Ho: Mu = 75
Ha: Mu < 75
Using normal approximation for binomial distribution:
Mu = Population Mean = np (number of trials*prob of success)
Sigma = Population Standard Deviation = npq (number of trials*prob of success*prob of failure)
N = number of experiments
where q = 1-p, n=100 trials
Mu = 75
Sigma = 18.75
N about 30
Stat test:
Z = (Sample Avg - Mu) / (Sigma / SquareRoot( N) )
(We just need the sample avg.)
Taking our level of significance at 5%, if Z is less than -1.645, then we reject the null hypothesis that the probability of success for Neera's scribing scrolls is equal to 75%; otherwise, we fail to reject the null hypothesis and the results can be explained by random chance. IN OTHER WORDS, if we reject the null hypothesis, we are 95% confident that Neera scribe scrolls less than 75% of the time.
If there is a probability associated with an event, then the mathematical probability will approach the statistical probability (or vice versa) with each increasing trial. So with a sufficiently large sample size, they should be similar. That is more or less the essence of statistics. Obviously if you do one or two trials you're not going to be able to determine if an event has 85% chance of happening.
Statistics is a way of empirically testing mathematical probability. Is it perfect? No, but it's probably the best method of doing it, and with a sufficient sample size it does a damn good job in practice. There is no method that I know of that proves an event's mathematical probability, I don't think it's possible. I've already said this a few times in this thread; failing many times in a row with 85% chance of success is obviously possible, it's just not probable if the system is working properly.
So while you say that it's possible to get a string of bad luck is true, saying statistical probability is irrelevant is false. That is only a part of statistics, the permutation part. Combination, which deals with separate events that have no effect on previous trials is also a part of statistics. Also, your example is incorrect. Tossing two heads in a row, two tails in a row, head then tail, or tail then head all have the same statistical probability of 25%. Coin tosses are combinations, each toss doesn't affect successive tosses. However, getting a head and a tail once each (with no regard to their order) has a higher statistical probability than two heads or two tails. So if you already tossed a head, it's still equal chance that you will get either a head or a tail on the next toss, you're not statistically more likely to toss a tail.
That statement is false. Statistics never claims to have "direct correlation" to results. It suggests that with each increasing trial it will get more and more accurate to mathematical probability.
What you're describing is a combination as opposed to a permutation. Like I said before, they are both still part of statistics. If you do the trial enough times, the number of times of success should still be close to 85%. That is the whole point of the number 85%. If what you say is true, then any number from 51% to 99% would be essentially the same. They are all calculated separately, so each trial has a higher chance of success than failure, therefore there would be no difference between 51% and 99%.
If it's an integer between 1 and 100 compared with a threshold value of 85, then it's working correctly. If it's not comparing with that threshold value, or if the generated integer is between some different number range, then it's not.
Beyond that, the only thing about the mechanic that could be broken is the way the number is generated. And if it's wrong here, then it should be wrong everywhere else in the game (because the same method should be used).
However, if it's not wrong here, and if the mechanic is designed as I described above, then no amount of anecdotal evidence will convince me that what you're experiencing is anything more than a string of bad luck. Highly improbable bad luck, but bad luck nonetheless. Because if the number generator is working correctly, and the mechanic is designed correctly, then the only thing that could cause a deviation is if the numbers just happen to be turning up the same each time.
Edit: did 100 more with an 18 int mage, 92 successes.
And then INTMOD.2da has these numbers.Column 1 is your intelligence, column 2 is the % to learn the spell
LEARN_SPELL MAX_SPELL_LEVEL MAX_SPELLS_PER_LEVEL MAZE_DURATION_DICE_NUM MAZE_DURATION_DICE_SIZE
0 0 0 0 4 4
1 0 0 0 4 4
2 0 0 0 4 4
3 0 0 0 4 4
4 0 0 0 4 4
5 0 0 0 4 4
6 0 0 0 4 4
7 0 0 0 4 4
8 0 0 0 4 4
9 35 4 6 4 4
10 40 5 7 4 4
11 45 5 7 4 4
12 50 6 7 3 4
13 55 6 9 3 4
14 60 7 9 3 4
15 65 7 11 2 4
16 70 8 11 2 4
17 75 8 14 2 4
18 85 9 18 1 4
19 95 9 99 1 4
20 96 9 99 1 4
21 97 9 99 1 4
22 98 9 99 1 4
23 99 9 99 1 4
24 150 9 99 1 4
25 150 9 99 1 4
I'm going to try the Y/N chart up until mid-day (12:00-13:00), since I have nothing much to do today. I've already done two charts and it's almost 9AM. I tend to play on insane, too, so there's no problem with the rules automatically allowing the character to learn spells. I never realised just how long it takes to learn a spell, then erase, and repeat 99 more times. It really is a chore.
So, I'll get to it . For science (and curiosity, mostly curiosity)!
That kind of pokes a hole in your "Mechanics are faulty" theory.
I also don't think some of you understand statistics.
It is possible to flip 100 heads in a row. Is it probable? No, but the possibility remains..
"omg this coin flipped heads more than half the time. it most be broken."