A very quick look at the Reds/Pirates game tonight.
Reds starter Johnny Cueto, this season, had a .207 eqa against left-handed hitters and a .234 eqa against righties. He is himself a RH.
Russell Martin, the Pirates catcher, is right-handed, and hit for a .275 eqa against right-handed pitchers.
Now, if a hitter with a .275 eqa goes against a pitcher who allows a .234 eqa, the expected eqa of the result should be roughly (275*234 / 260), or .248. This value is consistent with converting each of the eqas into winning percentages, letting them go head to head with the log5 method, and converting back into an eqa.
Repeating for the whole Pirate roster
C Martin (R) .275v234 = .248
1b Morneau (L) .297v207 = .236
2B Walker (S) .296v207 = .236
SS Mercer (R) .247×234 = .222
3B Alvarez(L) .299v.207 = .238
LF Marte (R) .278v234 = .250
CF McCutcheon (R) .322v234 = .290
RF Byrd (R) .291v234 = .262
The average value, for the whole Pirate team, is .249; eqas don’t sum linearly, they sum by the 2.5 power. That’s not a big deal here (a straight mean is .248), but will be for the opposite calculation.
Doing the same thing for the Reds against Francisco Liriano is trickier, because his EQA against lefties is so low as to be below zero. The eqa is low enough that a lineup of average hitters would be better off without that hitter in it, even if they got fewer chances as a result. Using an alternate form of the eqr equation, one that can’t go sub-zero, yields an eqa of .132. Against righties , he’s got a decidedly pedestrian .265 eqa allowed.
C Hanigan (R) 225v265 = 229
1b Votto (L) 303v132 = 154
2b Phillips (R) 271v265 = 276
SS Cozart (R) 245v265 = 250
3B Frazier (R) 278v265 = 283
LF Ludwick (R) 278v265 = 283
CF Choo (L) 243v132 = 123
RF Bruce (L) 262v132 = 133
The average value here works out to a .230 eqa when using the 2.5 power rule, quite a bit higher than the .216 you’d get from a straight average.
The win chance of a .249 eqa team (the Pirates) against a .230 team (the Reds) is .598.
Extending this into bullpens would probably only help the Pirates more. They had a composite .240 eqa from their bullpen in 2013, compared to the Reds .245; their likely top 4 dominate the Reds top 4, in a game theory sense:
Melancon 190 v Chapman 207
Watson 207 v Hoover 231
Wilson 217 v LeCure 232
Grilli 225 v Simon 225
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