imported>Byrthnoth at 18:48, 27 July 2011

2011-07-27T18:48:38Z

New page

Many MMO events are two-state systems, also known as Binomial. Anything that either can happen or cannot ([[Zanshin]], [[Double Attack]], [[Hit Rate]], [[Magic Critical Hit]], etc.) are all binomial when framed correctly.<br>

For instance, it's widely accepted that [[Triple Attack]] [[proc]]s before [[Double Attack]]. Therefore, a [[THF]]/[[WAR]] cannot take their raw [[Double Attack]] rate and assume it's binomial. There were not two options, there were actually three (TA, DA, and single attack). However, the same player could make their [[Double Attack]] rate binomial by subtracting out rounds where [[Triple Attack]] procced. With [[Triple Attack]] removed, only two options remain ([[Double Attack]] and single attack).<br>

Though the reasoning is beyond the scope of this article, things that are binomial have very nice, simple statistics. They can be easily used to calculate a confidence interval with a normal approximation (valid when n{{math|times}}p>5 and n{{math|times}}(1-p)>5):
:'''95% Conf. Interval Width''' = 1.96*SquareRoot('''p'''{{math|times}}(1-'''p'''){{math|divide}}'''n''')
In the above equation, '''p''' is the probability of something occurring from the sample you have collected. So if you have a 15.05% [[Double Attack]] rate on your [[WAR]]/[[NIN]], '''p'''=0.1505 . Also, '''n''' is the sample size. So if your 15.05% [[Double Attack]] rate was the result of 45 Double Attacks / 299 Attack Rounds, your '''n'''=299. All told, the above equation gives you 15.05{{math|plusmin}}4.05% for your confidence interval.<br>

In a more complicated case, where you need to (for instance) filter out [[Triple Attack]], the parse would say it like this:
:[[Triple Attack]] rate = 15.05% = 45/299
:[[Double Attack]] rate = 11.7% = 35/299
::However, '''p''' = 35{{math|divide}}(299-45) = 13.78%, because [[Double Attack]] was unable to proc on 45 of the attack rounds.
This may change in a future parser version, but at the moment this is a correction that you have to make for yourself.

The above confidence interval assumes normality, which may not be valid (could underestimate the confidence interval) when near 0% or 100%. A more conservative way to estimate the confidence interval (the Clopper-Pearson method) is linked below, and should be used when you have low N or a probability near 0% or 100%.

== Other Resources ==
* [http://www.youtube.com/user/khanacademy#g/c/1328115D3D8A2566 Khan Academy Statistics Page]
* [http://statpages.org/confint.html#Binomial Javascript Binomial Distribution calculator - Clopper-Pearson Method]
* [http://www.measuringusability.com/wald.htm#wilson Binomial Distribution calculator - Variety of methods]

[[Category:Game Mechanics]]

Binomial Distribution - Revision history

imported>Byrthnoth at 18:48, 27 July 2011