Quote:
Originally Posted by WarpathEQ
[You must be logged in to view images. Log in or Register.]
However, if the event is performed enough times in succession the law of averages tells you that the past results do in fact influence future outcomes in that past annomolies in one direction will correct over time by compensating in the other direction and returning to the average.
|
This is way of phrasing it is absolutely incorrect. That is not how it works. I don't mean to pick on you as everyone in this thread talking about probability is either misinformed, poory educated, or very sloppy in both their phrasing and reading comprehension. What you wrote is a clear example of the gambler's fallacy and it is wrong.
To set a clear foundation, I think we're all talking about calculating the probability of independent events. The success or failure of a tradeskill combine is unrelated to the outcome of past tradeskills combine. Each tradeskill combine of a given item is an independent event with an identical probability of success. Everyone agrees with this, right?
The nuance with calculating probabilities of the outcome of a series of independent events comes with the point in time when you're making the calculation. The probability of flipping a coin 1 time is 50%. The probability of flipping a coin 10 times and having them all come up heads is 0.5^10, or about one in a thousand. I think everyone would agree with this too.
if you've already flipped a coin 9 times and they're all heads, the probability of the next coin flip being heads is still 50%.
At this point in time the probability of getting 10 heads in a row is 50%, because
nine of the flips are in the past and they're already heads. The gambler's fallacy is to think that because there's less than a 1% chance of getting 10 head flips in a row, the next flip is almost certainly going to be tails. This is not true. It's 50%. (This is disregarding the possibility that the coin is weighted or double-headed, we're assuming it's an actually fair coin).
What you're talking about with laws of averages and reversions to the mean is different from how you're applying it. You said "past anomalies in one direction will correct over time by compensating in the other direction". This is not correct. An accurate way to say it would be "past anomalies in one direction will be have their impact diluted by adding enough additional coin flips."
Image you're going to flip a coin 100 times. You expect you'll get about 50 heads, plus or minus a couple. The first 10 flips are heads. An incorrect understanding of probability is think "of the next 90 flips, its likely there will be more tails than head". That is precisely the gambler's fallacy. A correct understanding would be "the next 90 flips are likely going to be 50% outcomes with about 45 heads, so I expect the total number of heads will be about 55, more or less". The next 90 outcomes will swamp the effect of the first 10 heads. But it's not "compensating in the other direction".
Anyway, I hope you don't take this as a personal attack. You've been very helpful to me on these forums in the past, and what you wrote is broadly right in general, just wrong on the exact mechanism by how it happens.