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Inukchuk wrote:Do you lump all your pitchers together, or do you separate starters and relievers?
Nerfherders wrote:My projection system consists of a 3x5 photo of every player, a large cork board on the wall, and about a dozen or so darts. So far, I've never come in last place using this system.
rookies and cream wrote:Trust me, the central limit theorem does not apply to saves and stolen bases. Traits (stats) only approach a normal distribution if they are normally distributed in the population (MLB).
GotowarMissAgnes wrote:rookies and cream wrote:Trust me, the central limit theorem does not apply to saves and stolen bases. Traits (stats) only approach a normal distribution if they are normally distributed in the population (MLB).
More nerdery. Back to stats class for you. The only requirement for convergence to the normal distribution by the CLT is that the random variables be i.i.d. (independent and identically distributed). The CLT, remember, is a statement about the distribution of the sample average: "The central limit theorem states that as the sample size increases , the distribution of the sample average of these random variables approaches the normal distribution with a mean µ and variance σ2 / n irrespective of the shape of the original distribution."
So, applied here, think about each fantasy team representing a sample of 20 position players. The average steals of each team would be normally distributed according to the CLT.
rookies and cream wrote:Yeah, but does it matter that were not talking about multiple samples? I was speaking in terms of one sample (all players in MLB in one year), not teams in a fantasy league. We also discussed whether SB's would be normally distributed over the history of baseball. However, even if you consider each year as an individual sample, they would not be independent of one another due to player overlap. Does the CLT even apply to what we are discussing?
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