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Do sinker-ballers pitch better on short rest?

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Suffering from listening to Joe Buck and Tim McCarver (is there a worse announcing tandem?) as they call the NLCS, McCarver said that ground-ball pitchers are better on short rest. This is a long held axiom in baseball, but is it actually true? (This is partly motivated by the fact that I hope he's wrong.)

The following are stats of some of the top ground-ball pitchers in the game. Short rest is three or fewer days between starts. Normal is four days. Extra is five or more days.

 

Chien Ming-Wang:

Short rest: 1.29 ERA (7 ip)

Normal rest: 3.99 ERA (390 ip)

Extra rest: 3.54 ERA (226.1 ip)

He's done slightly better on extra rest. The one start on short rest is too small a sample to draw any conclusions on.

Brandon Webb:

Short rest: never

Normal rest: 3.19 ERA (800.1 ip)

Extra rest: 3.31 ERA (514.1 ip)

Extra rest slight hurts his ERA, but nothing to write home about.

Fausto Carmona:

Short rest: never

Normal rest: 3.64 ERA (234.2 ip)

Extra rest: 4.96 ERA (138 ip)

The first sinker-baller that does pitch significantly better on less rest - or rather, he pitches worse on extra rest.

Derek Lowe:

Short rest: 4.78 ERA (32 ip)

Normal rest: 3.69 ERA (948.1 ip)

Extra rest: 4.32 (579 ip)

Lowe is the only pitcher who we can draw some kind of conclusion from based on his relief pitching (381 relief innings in his career) as well as his starting. The others' relief innings are negligible (all under 50 ip).

Back-to-back days: 4.22 ERA (70.1 ip)

1-2 days of rest: 2.94 ERA (204.2 ip)

3-4 days: 1.78 ERA (80.2 ip)

5+ days: 3.20 ERA (25.1 ip)

Inconclusive overall. If anything, he pitches worse on short rest.

Roy Halladay:

Short rest: 3.47 ERA (48.2 ip)

Normal rest: 3.74 ERA (1108.1 ip)

Extra rest: 2.97 ERA (596 ip)

Halladay pitches nearly a run better on extra rest. Nothing conclusive regarding short rest, but he's another sinker-baller that pitches better on extra rest, with which the old axiom would seem to disagree.

Tim Hudson:

Short rest: 2.61 ERA (20.2 ip)

Normal rest: 3.66 ERA (1310.1 ip)

Extra rest: 3.18 ERA (685.1 ip)

Read Halladay's conclusion.

 

So it seems that McCarver's axiom is false. Sinker-ballers, who would seem to benefit from a tired arm, do not pitch better on short rest. If anything, they pitch better on extra rest. Four of the six pitchers actually pitch better on extra rest. Only two pitched best on short rest (Wang and Hudson), but that was just 27.2 ip combined.

The next step is to compare sinker-ballers to other types of pitchers. Since sinker-ballers don't pitch any better (in general) on short rest, what about relative to fly-ball pitchers? But that's a study for another day.