draft capital

The cycle of regressions for the draft capital variable was done differently than fantasy_value_per_game. We originally hypothesized that a player's draft age was a covariate, but in the end this was found to be a case of overfitting. The process was instead simplified to loop only thru the n⁺ variable. In other words, the only other factor considered in addition to draft_capital, was NFL experience.

One complication came up, that draft_capital didn't fit with a straight line. Upon scrolling thru the following images, you can see what I mean. The larger circles in the following scatter plots reperesent bin averages of each 10th percentile; these percentiles were added to make the trends easier to see.

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The next group of images shows the same thing except with a trend of best fit included. In the top right corner you'll find each trend's formula from the completed regression.

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The graphs only show n+ 0-5, but the regressions were completed up to 14, just in case was needed. The following table displays all the regression parameters for each position. You can see R² ranges anywhere from 0.000-0.400, but mostly hovers around 0.200.

The next group of images below graphically displays the parameters of slope and y-intercept from the previous table.

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Similar to how these parameters needed to be adjusted for the fvpg predictor variable, the same goes for the variable ln(draft_capital). Slopes, and intercepts adhere to a general trend, and as such should follow a smooth transition instead of bouncing around. On one hand it's a bit easier for ln(draft_capital) because there's only one controlling variable, n⁺; on the other, there's no simple way to apply a function to the trend. As such, a variation of the moving average technique to smooth the parameters. The black line in the following images represents the adjusted values.

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