If you follow sabermetric baseball analysis you probably read about pitchers over or underperforming their peripherals on a daily basis; typically, by way of a reference to a pitcher's ERA relative to their FIP. The former gives an account of what has happened in terms of actual earned runs allowed, while we believe the latter to tell us more about the role the pitcher played independent of his defense. FIP does this by taking into account the events over which the defense has the least impact -- strikeouts, walks/hit batters, and homeruns -- and also lays out a reasonable expectation of the performance to come.

Take FIP from ERA (E-F) and you have a measure of the pitcher's earned run results relative to the performance we might expect if his defense nabbed an average number of batted balls. While this handy metric acts as a proxy for the divergence between individual performance and observed outcome, we're left to account for the variance between pitchers. It should be noted that neither metric is a perfect reflection of the latent concept it seeks to measure, but they are two widely used metrics worthy of study. While FIP isn't perfect, FIP is *pretty good*, and understanding how and why a pitcher's ERA would be higher or lower is the aim of this effort.

At the end of the 2014 season, Neil Weinberg did a case study in which he provided an explanation for the largest positive (Clay Buchholz) and negative (Doug Fister) E-F values that season. I've followed his lead here, but I've also added a couple new indicators -- some of which are proxies -- which I hypothesize will also account for some of the variance of E-F. Feel free to disagree with these variables or to suggest new ones.

- BABIP -- luck (though not exclusively luck)
- Percentage of runners left on base -- a proxy for sequencing of events
- Ground ball rate -- type of contact induced
- Average exit velocity of batted balls -- quality of contact induced
- Rate of stolen base attempts -- ability to control the running game (click here for an explanation of how that's calculated)
- Expected runs allowed per nine innings (RE24/9) minus park adjusted runs scored per nine (pRA9) -- a proxy for bullpen influence on runs allowed

There's a very simple way to evaluate this [bullpen support] effect. If you leave a runner on first base every time you get pulled, but the bullpen allows them to score every time, all of those runs aren't really your fault. You should really only be charged for the expected number of runs, which we can approximate using RE24 on a per 9 inning scale. We'll also have to park adjust their RA9.

**WARNING: MATH AHEAD, POTENTIALLY GORY**

### E-F ~ BABIP + LOB% + GB% + SBA% + AverageExitVelo + (RE24/9)/(pRA/9) + ε

Estimate | Std. Error | t value | Pr(>|t|) | p-value less than | |
---|---|---|---|---|---|

(Intercept) | 6.82 | 2.33 | 2.93 | 0.00 | 0.0010 |

BABIP | 12.25 | 1.38 | 8.85 | 0.00 | 0.0001 |

LOB | -6.23 | 0.74 | -8.45 | 0.00 | 0.0001 |

GB | -0.84 | 0.49 | -1.73 | 0.09 | 0.1000 |

SBA | 0.068 | 0.87 | 0.08 | 0.94 | 1.0000 |

AverageExitVelo | -0.062 | 0.03 | -2.37 | 0.02 | 0.0500 |

RE249RS9 | 0.078 | 0.15 | 0.50 | 0.62 | 1.0000 |

FIP = ((13*HR)+(3*(BB+HBP))-(2*K))/IP + constant

Mean Sq | % Variance | F value | Pr(>F) | p-value less than | |
---|---|---|---|---|---|

BABIP | 23.61 | 70.9% | 235.53 | 0.00 | 0.0001 |

LOB | 8.83 | 26.5% | 88.08 | 0.00 | 0.0001 |

GB | 0.17 | 0.5% | 1.72 | 0.19 | 1.0000 |

SBA | 0.00 | 0.0% | 0.02 | 0.89 | 1.0000 |

AverageExitVelo | 0.56 | 1.7% | 5.60 | 0.02 | 0.0500 |

RE249RS9 | 0.03 | 0.1% | 0.25 | 0.62 | 1.0000 |

Residuals | 0.10 | 0.3% |

**THE MATH IS OVER, COME BACK!**

*Thanks to Neil Weinberg and Russell Carleton for their helpful comments (and extreme patience). All modeling was done using*R

*. You can find a copy of the data*here

*and the syntax I used*here

*. Please feel free to take issue with my analysis and/or interpretations in the comments section below.*

**. . .**

*Matt Jackson is a featured writer for Beyond the Box Score and a staff writer for **Royals Review**. You can follow him on Twitter at @jacksontaigu.*