pssvr -> RE: =AQ= Houses With Estates - Discussion (9/20/2009 9:32:04)
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On the issue of half armies versus full armies (and by extension, 8 rep versus 11 rep): quote:
ORIGINAL: SIGMUND Using completely unmathmatical language I'll try to explain. It is due to the smaller range of possible results which happens many times and gives a more stable average for smaller armies. Although over a long period of time the large armies should generate a similar average, They do not do so during the war because you can't send Large armies enough times to generate the stable average. The Captain described this as logical and seemed to approve of it. Now, translated into math, what this seems to imply is that sample mean values of half-armies have a lower standard deviation than sample mean values of full-armies, which is sensible, given that the sample size for half-armies will be twice as large as the sample size for full-armies if the resources used are the same. Since sample means like this approximately obey the rule sample mean standard deviation = population standard deviation / squareroot( sample size ), we find that the standard deviation of half-armies should be 1 / sqrt(2) times the standard deviation of full-armies. Furthermore, the post says, "over a long period of time the large armies should generate a similar average," This, if correct, implies that the true mean reward for sending armies INDEPENDENT of whether you said half or full armies. The APPARENT strength of half-armies would be a misconception due to small sample size. There is only one way (short of the Captain giving a definite answer) to clarify this issue. People who collect data on the rewards must use a sample size of at least 25 (so that a standard normal distribution approximation may be applied) and must report the standard deviation of their data as well as the mean. Then, when the means and standard deviations of both half-armies and full-armies are reported, we can test to see whether the true means are different or not. Even if we take it as a given that the number of armies sent doesn't matter, this same technique still applies to determining how reputation affects reward. I'll do my best the next time we have a war.
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