Site Searching Statistics Questions

Edratman · #1 November 15th, 2007, 03:07 PM

VedalkenBear - first class analysis.

What I think would be most helpful (and you have provided ample evidence of ability) would be a table showing the average number of sites per province with the settings of 10,20,.....100%. (The values higher than 75 are available using map edit.)

Thank you.

VedalkenBear · #2 November 15th, 2007, 03:14 PM

Hey, I'm an Industrial Engineering student, and probability/statistics are used in every single one of my classes. I hope I'd be good at it.

As for the expected number of sites per province, it really is just (4*p). I've verified it for several different values of p in Excel, and it follows exactly.

Now, if someone were to give me the actual terrain differences on the different types of sites, I could do some more advanced analysis.

VedalkenBear · #3 November 15th, 2007, 03:18 PM

Thejeff: Sorry, the 1-(P of not Earth) was supposed to be not Astral.

The 'if not searched' value included the probability in the Astral analysis that an Earth site could be any one of the remaining sites (that is, the probability of the site NOT being Astral was 8/9). If Earth was searched (at level 4 or 9), then the probability that the sites could be Astral would be 1/8, not 1/9. The slightly higher value takes this into account. (I had this value at hand because I initially forgot Holy sites, and therefore had done all the calculations for 1/8 instead of 1/9.)

VedalkenBear · #4 November 15th, 2007, 03:25 PM

Oh, I'm using the binomial not the hypergeometric. The binomial probabilities are simply the probabilities of a given number of sites in a province. These states are not dependent on one another. If the site placement algorithm checked for a first site, found none, and _did not check anymore_, that would be conditional probability.

Basically, for the second calculation you have:

0 sites in province (trivial case): 0
1 site in province (also trivial): 0
2 sites in province, 1 is earth, chance that the second is earth: Probability that there are two sites in province * 1-(Probability that the first is not Astral(1)*Probability that the second is not Astral(0.875) = 0.3456*(1-(1*0.875)

And so on. If the probabilities change given one state, that means the probabilities are conditional. The only way for that to happen in this case would be if the site search algorithm were to stop checking for sites if any check failed. That AFAIK does not happen.