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# Benefit of the Doubt: A Tale of Two Hernandezes

So we all know that veteran RHP Livan Hernandez gets the benefit of the doubt when it comes to balls and called strikes. At the very least, those of you who follow this column or watched Game 5 of the 1997 NLCS know this. He gets the pitches outside against LHB and he gets the pitches way inside against RHB (see heat maps above).

On the other side of the strike zone spectrum we find Felix Hernandez. As you can see below, his strike zone is far tighter than Livan's. King Felix does not get the benefit of the doubt.

Heavy hangs the head that wears the crown.

But how much of an effect to pitchers' personal zones have on the actual game? In order to answer this question, we have to apply a run value to every miscalled ball or strike.

For every count, we can expect certain number of runs to score between the moment of the pitch and the end of the inning. Saberists call these run expectancies "linear weights." As one would expect, the linear weights are heavier in hitters' counts and lighter in pitchers' counts.

Several analysts--including but not limited to Tom Tango, Mike Fast, Phil Birnbaum, Joe Sheehan, John Walsh, Jeremy Greenhouse, Harry Pavlidis and Craig Burley--have crunched the numbers. We'll be using Tom Tango's, in part because his sample is the largest and presumably most stable, but also because I've used his numbers in my earlier work on the relationship between run expectancy and zone advantage.

Once we know what the run expectancy is for each of the 12 count states, and the change in run expectancy of a strike or ball in any given count, we can determine what the linear weights are for a blown call in any count. The table below presents these numbers, which I refer to as the "linear weights differential," or LWD:

 B S Errant Ball LWD Errant Strike LWD 3 2 0.630 -0.630 2 2 0.361 -0.361 3 1 0.269 -0.269 1 2 0.263 -0.263 0 2 0.218 -0.218 3 0 0.193 -0.193 2 1 0.174 -0.174 2 0 0.172 -0.172 1 1 0.117 -0.117 1 0 0.113 -0.113 0 1 0.089 -0.089 0 0 0.077 -0.077

Here's how you read the final entry on the table above: when the count is empty, the hitting team can expect to score 0.077 more runs through the end of the inning if the umpire calls a ball instead of a strike; conversely, the hitting team can expect to score 0.077 fewer runs through the end of the inning if the umpire calls a strike instead of a ball.

Note that the effect of a blown call is far greater for a full count than an empty one. Note also that these numbers apply to the average game state: they do not account for outs, bases occupied, inning or run differential.

So now we know that not all blown calls are equal. By adding up all these LW credits and debits, we can now establish a run value for every pitcher's individual zone. The chart below presents the top ten aggregate LWD leaders over the last three regular seasons, followed by the bottom ten laggards.

 Pitcher Called Pitches LWD LWD/Year LWD/75 Hernandez, Livan 4877 -67.49 -22.50 -1.04 Lowe, Derek 4965 -54.63 -18.21 -0.83 Halladay, Roy 4985 -43.49 -14.50 -0.65 Moyer, Jamie 4055 -38.96 -12.99 -0.72 Buehrle, Mark 4766 -38.52 -12.84 -0.61 Arroyo, Bronson 5207 -33.67 -11.22 -0.48 Garza, Matt 4761 -31.27 -10.42 -0.49 Rivera, Mariano 1404 -30.19 -10.06 -1.61 Johnson, Josh 3710 -28.79 -9.60 -0.58 Billingsley, Chad 4693 -28.33 -9.44 -0.45 ~ ~ ~ ~ ~ Jackson, Edwin 4658 8.82 2.94 0.14 Parra, Manny 3756 8.95 2.98 0.18 Duke, Zach 4147 9.96 3.32 0.18 Kershaw, Clayton 4215 10.67 3.56 0.19 Perez, Oliver 2971 12.44 4.15 0.31 Maholm, Paul 4708 12.63 4.21 0.20 Robertson, Nate 2718 14.35 4.78 0.40 Ohlendorf, Ross 2618 14.41 4.80 0.41 Miller, Andrew 2110 14.55 4.85 0.52 Hernandez, Felix 5054 20.06 6.69 0.30

Sample note: Only pitchers who threw at least 250 called pitches in each of the last three seasons qualified for this list.

As you can see, there was a reason why I picked Livan and King Felix for this example. Livan's personal strike zone has been the most pitcher-friendly, costing opposing teams 67 runs since the beginning of the 2008 season. On the other hand, Felix's personal strike zone has been the most hitter friendly, charitably awarding opponents 20 runs during the same time period.

These aren't trivial numbers. In game states prior to the ninth inning or earlier, these run values would translate into 2.47 extra wins per season for Livan's teams and 0.74 fewer wins per season for Felix's.*

*That said, we cannot just assume 9.1 runs per win (the average game run environment from 2008-2010), because run expectancy does always translate directly into win expectancy. This is especially true for relievers, which we'll spotlight in next week's episode. No matter, as those of you following the Mariners or the Nationals in recent years probably haven't noticed anyway.

You may have noticed that Mariano Rivera is the only reliever to make his home in the LWD Top 10. You may also have noticed that Mo's thrown about 1/3 as many called pitches as his peers. That should tell you something about who will lead all pitchers when we look at standardized LWD (LWD/150 pitches) (LWD/75 pitches), next week.

PitchF/X data originate from Darrell Zimmerman's SQL-based PitchFX database, run expectancy data by Tom Tango at Inside the Book. Photos courtesy of Wikimedia Commons and licensed under Creative Commons terms.

Previous episodes in the Benefit of the Doubt series: