![]() ![]() In our case, we only have one entry outside (Carrier) so 99.5% of the data fits between 20 and 80. Still a pretty good fit compared to a normal distribution.Ī normal distribution would predict roughly 98% of the data being between the 20 and 80 bands. Still, we are relatively close as I'd say about 90% of the data lies between the 30 and 70 bands (20-25 points out of 220 are outside). This is where you can see our distribution is obviously skewed as we have about 20-25 entries above the 70 band and only one entry below the 30 band. ![]() Now 95% of our data is supposed to also be between the 30 and 70 bands. The 40-50 "bin" looks to have more frequency than 50-60 "bin" to me. We have 220 total entries and most of our data should be located between the 40 and 60 bands, and that definitely looks to be the case. In our case I think a normal distribution fits pretty well. I had this done last night, but EXCEL crashed on me so for now you'll just have to visually estimate how much data lies between each set of bands. In order to see how well the actual data fits with the normal distribution, you have to conduct what is called a frequency analysis by making a histogram based on these "bins" (I usually prefer bins of half standard deviations to be able to visualize a bit better) and then overlaying the ideal normal distribution curve over the top of those histograms. About 95% of the data will lie between the 30 and 70 range and 98% will lie within the 20-80 bands. In a normal distribution you will have 68% of the data points within the 40-60 range. Typically we find in that a normal distribution fit is a pretty good representation of this type of sports data. For those of you familiar with how the 20-80 scale works, each 10 points away from 50 is supposed to represent one standard deviation away from the average player. Overlayed on top of the data are data bands representing the Mean (Roughly 1.5 WAR) and bands representing 3 standard deviations in either direction from the mean. Below I've pasted an image showing a slightly incomplete WAR analysis for the 2048 WBL.
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