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FIP Regression Question


If you postulate a linear model of:

Earned Runs Allowed = A * HR + B * BB + C * K

And fit an ordinary least-squares regression to that model using historical data from ~1965 to present (pick any years, really)...

How close do the estimated Earned Runs Allowed (ERA hat?) multiplied by 9 and then divided by Innings Pitched come to FIP?

Are there heteroskedasticity issues? I would think there would be in this model since I'd expect RA to vary more with higher HR and BB amounts with the idea that higher HR and BB amounts would imply higher chances for multi-run HRs while lower HR/BB amounts would imply fewer multi-run HRs, thus resulting in higher variances with more HRs/BBs allowed. Alternatively, I would think Ks would have a decreasing effect on variance as a high-K pitcher would reduce balls in play resulting in fewer base hits and potentially fewer "normal" runs as well as fewer potential base-runners for HRs.

What about differences among eras?

Sorry for the rambling, but I'm curious about the estimation procedure for FIP and, particularly, whether stuff like heteroskedasticity has been addressed in the linear weights and what kind of variance assumptions were used to adjust for it.

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