Thread:Jkalm/@comment-24577221-20150313023719/@comment-26174729-20150313052211

Hi BunsenH,

I see where I went wrong with my edit. But the way the math is stated on the pages is also wrong.

Here's the problem. Evac156 wrote, "Your chance of 70 consecutive failures is (0.99 ^ 70) = 0.4948, so you have a 49.48% chance of failing 70 times." But that's not the way the formula works. What it should really say is, "After 69 consecutive failures, your chance for a 70th consecutive failure is (0.99 ^ 70 = 0.4948), so you have a 49.48% chance of failing on your 70th attempt."

To make things simple, let's look at a coin toss. Your chances of getting heads are 50% per toss. If you get tails on your first toss, then your chances of getting tails on your second toss is (0.50 ^ 2 = 0.25), so you have a 25% chance of failing to get heads on your second attempt. If you get tails on your first two tosses, then the your chances of getting tails on your third toss is (0.50 ^ 3 = 0.125), so you have a 12.5% chance of failing to get heads on your third attempt. If you get tails on your first three tosses, then the your chances of getting tails on your fourth toss is (0.50 ^ 4 = 0.0625), so you have a 6.25% chance of failing to get heads on your fourth attempt. If we were to report this coin tossing project the way Ghazt breeding possibilities are reported on the Ghazt page, we would say, "According to statistics, doing 2 attempts gives you a 75% chance of successfully getting at least one heads; and doing 4 attempts gives you a 93.75% chance of successfully getting at least one heads."

Now because the words "at least" are in there, the statement is true, but it's not very descriptive of what we are likely to encounter as we toss our coins. Because after four coin tosses, we would most likely have gotten 2 heads, statistically speaking. But, if we got tails on our first three tosses, and we make a fourth toss, then we will only have a 93.75% chance of getting even one heads during our four tosses. Probability always has to account for the worst case scenario, while statistics describes what is most likely. Because of this, the larger our sample size, i.e. the more attempts we make, the probabilitiy calculations become less relevant, and the statistical predictions become more relevant.

To put this back into My Singing Monsters terms, according to the exhaustive research on breeding ethereal monsters you quoted here, after 11,750 breeding attempts, you found that you had a breeding success rate of roughly 1.030%. Now lets imagine that you had suffered the misfortune of having had 11,749 consecutive failed Ghazt breeding attempts. Probability tells us that your chances of failing to breed a Ghazt on your 11,750th attempt are roughly (0.99 ^ 11,750 = a truly infinitesimal number). So the way the Ghazt page is worded right now, we would say, "According to statistics, doing 70 attempts gives you a 50% chance of successfully breeding at least one Ghazt; doing 690 attempts gives you a 99.9% chance of successfully breeding at least one Ghazt; and doing 11,750 attempts gives you a 99.999999999999999999999999999999999999999999999999999483% chance of successfully breeding at least one ghazt." But that's not what statistics really tells us. That's what probability tells us. According to statistics, doing 70 attempts ought give you 0.7 Ghazts, doing 690 attempts ought to give you 6.9 Ghazts, and doing 11,750 attempts ought to give you 117 Ghazts. In your study's case, doing 11,750 attempts actually resulted in 121 Ghazts, but that's within the margin of error. So which number is the most relevant after 690 attempts, that you ought to have 6.9 Ghazts, or that you have a 99.99% chance of having at least one Ghazt?

I suggest that we fix this confusion by making it clear that the statement is about probability rather than statistics. We could even preface it with a statement about statistics.

Here is the correction I propose:

"Although statistics predict that you will be able to breed one Ghazt successfully every 100 attempts, that is not guaranteed. According to the laws of probability, after 69 unsuccessful attempts, you a have only a 50% chance of successfully breeding a Ghazt on your 70th attempt; but after 689 unsuccessful attempts, you have a 99.9% chance of successfully breeding a Ghazt on your 690th attempt."