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Standard Deviation in Rankings

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Postby RugbyD » Mon Jan 03, 2005 1:03 pm

Cornbread Maxwell wrote:I understand thats what using SD is trying to do: 1 out from the mean, 2 out from the mean, etc... but the problem is that SD is based on a normal bell curve, and I argue that with a sample size of 15-20 of the best players at a position, there is rarely going to be a normal bell curve. Thats the whole argument. Therefore rather than using SD as a strict formula to determine tiers, I think there is probably a better way that a strict formula base would more than likely hinder.

I also want to add that a tiered approach is only based on SD - but it isnt locked into the strictness of it. Using a tiered approach and using a SD approach are not the same thing.


I would expect a lognormal distribution, which is still normal, just not symmetrical, regardless of position depth.
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Postby mbuser » Tue Jan 04, 2005 2:48 am

fallas, forgive my ignorance. while i am borderline obsessed with sports statistics, i only went as high as pre-calc in math, so a lot of talk in this thread is foreign to me.

are you saying that stdev can't really be arrived at unless there are negative values? also (but separate), would calculating standard deviation using every major league player that had at least 1 AB or IP last season skew the numbers? and (why?) would using every player be worse than just using the top players to get values? and i have no idea what T-distributon or lognormal is :-o

i hope you don't mind taking the time to break this down a little for the 'layman', shall we say. i'm trying to come up with some rankings using stdev, but i want to know if my methods are flawed.
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Postby Bloody Nipples » Tue Jan 04, 2005 3:17 am

mbuser wrote:fallas, forgive my ignorance. while i am borderline obsessed with sports statistics, i only went as high as pre-calc in math, so a lot of talk in this thread is foreign to me.

are you saying that stdev can't really be arrived at unless there are negative values? also (but separate), would calculating standard deviation using every major league player that had at least 1 AB or IP last season skew the numbers? and (why?) would using every player be worse than just using the top players to get values? and i have no idea what T-distributon or lognormal is :-o

i hope you don't mind taking the time to break this down a little for the 'layman', shall we say. i'm trying to come up with some rankings using stdev, but i want to know if my methods are flawed.


I would use only the players you think will be drafted in your analysis. If you think 20 1B will be drafted and used in your league, then take the stdev of those twenty. I have no idea t-distr or lognormal is either, but the above is the way i would handle it
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Postby RugbyD » Tue Jan 04, 2005 10:52 am

A normal distribution is a perfect shaped bell curve, where the mean, median and mode are all right in the middle, where the highest point of the curve is.

A lognormal distribution exists where there is a limit, typically when the downside cannot go below zero. The perfect example is stock prices. In this case, you can't have negative HR, K, etc. The distribution is still considered normal, but it is not symmetrical on both sides of the peak. The peak (mode) will be left of center and the mean will be right of center.

I wrote off the Quant II section of the CFA exam and I was pledging during college stats, so I'm not versed on t-values.

Here's a nice picture: http://www.riskglossary.com/articles/lo ... bution.htm

EDIT: You don't want to use the one AB guys raw stats. I try to commom-size everything to 162 games and adjust from there. I also only use guys that would be remotely draftable, which usually eliminates the low AB guys anyways, because measuring std.dev is useful as a relative measure, not an absolute one. You will need to just make up projections for some young guys who are expected to play and have to useful track record unless you're going to take the time to wade through minor league stats.[/i]
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