Since I talked about Darvish and Napoli at the beginning of this article, let me feature the duo to illustrate the point. Darvish faces Mike Trout with Napoli behind the plate and Bod Davidson... - Oh! the Nemesis of all Japanese fans! - calling the game, and Darvish throws 93 mph fastball a bit far and away to Trout, that Trout kept the stick on his shoulder and Bob called the pitch 'Ball!'. In 2012, that 1-0 pitch to a right-handed batter is estimated to be judged strike 87.0% of the time according to naive model, and this probability functions as a reference point. Then, the estimated probability of called strike on that pitch is adjusted by the hitter, pitcher, and umpire's own rate. Net called strike rate for Yu Darvish is -0.1%, meaning every pitch Darvish throws is less likely to be called strike, on a very slight amount. Likewise, Trout's net called strike rate is -0.5% and Bob's 1.7%, so the 87.0% probability naive model spitted is adjusted that exactly the same pitch to the same-handed hitter in the same hitting count for the same year, is now estimated to be called strike 88.1% of the time. Since Bob is a pitcher-friendly umpire, that pitching combo could benefit from his wider zone. Nonetheless, that pitch is called ball, so Napoli is debuted -.09 runs (-.881 times 0.102 runs, the run value in 1-0 count) for this result. The same procedure is conducted through all called pitches for all years. The count-based run value is via my own calculation, that I figured out linear weights through the count for 2008 to 2012, weeding out all intentional walks, bunts, and pitchers as batters. I did some slight correction for the distribution of the quality of hitters in each specific count, since lots of Pujols, Fielder, Mauer, et al. see themselves in 3-0 count. Here's run values chart for all counts permutation.

Ball |
Strike |
Run Values |

0 |
0 |
0.071 |

0 |
1 |
0.079 |

0 |
2 |
0.195 |

1 |
0 |
0.102 |

1 |
1 |
0.107 |

1 |
2 |
0.231 |

2 |
0 |
0.152 |

2 |
1 |
0.165 |

2 |
2 |
0.319 |

3 |
0 |
0.179 |

3 |
1 |
0.256 |

3 |
2 |
0.575 |