Last night, the Rockies, pushing for a playoff spot and just out of the lead in the National League West, suffered a tough loss to the Arizona Diamondbacks, a team that’s been “playing for pride” for months. The loss dropped Colorado to 2.5 games back in the divisional race with only 12 games left to play. In the top of the ninth inning, down 3-1, the Rockies’ batters due up were the red-hot Troy Tulowitzki, veteran Melvin Mora, and Rockie (Rocky?) for Life Todd Helton. Wait, what? Melvin Mora? Surely the right-handed hitting Mora wouldn’t bat against the right-handed pitcher Juan Gutierrez? Maybe the Rockies’ bench is a bit thin due to injuries, but while Helton has had a down season, he has the platoon advantage… Mora is only playing because of Ian Stewart‘s injury. Colorado manager Jim Tracy wouldn’t let Mora bat, not with this being the Rockies’ last chance in a key game, right? After Tulowitzki struck out, Mora did indeed go up to bat and struck out swinging; then Helton fouled out to end the game. Did Tracy make a mistake in not pinch-hitting for Mora in such a crucial game?
Mora has actually been fairly useful for the Rockies this season, offsetting his poor fielding with slightly above-average hitting (104 wRC+), which is pretty decent for a somewhat cheap bench player. Of course, for this situation we need more than current performance; we want “true talent.” For that, I’ll refer to CHONE’s August 29 updated projections, which I’ve translated to wOBA (using last season’s weights and leaving out SB/CS as they aren’t relevant for potential PH/platoon situations). Mora is currently a .330 wOBA hitter according to CHONE. Mora’s career (well, 2002-present) platoon split is not that big — .354 wOBA vs. LHP, .351 wOBA vs. RHP. When estimating his platoon skill with reference to his .330 wOBA CHONE projection, his expected wOBA vs. RHP is .326, and vs. LHP .339. Tracy would want to pick a batter expected to have a better than .326 wOBA in this situation, obviously.
On the Rockies bench at the time were two obvious candidates (the others all being either right-handed and/or terrible, and Ryan Spilboroughs having already been in the game): Jason Giambi and Seth Smith. I say “maybe three” because one could make a case for Chris Iannetta, as he’s a pretty good hitter, but a) he’s right handed, b) I’m not sure he was available given recent injury problems, and c) the pinch-hitting penalty eliminates his chances of likely being helpful in this situation anyway.
The key is c): the pinch-hitting penalty. Research has shown that hitters typically have a much more difficult time hitting off the bench than normal, so we expect their wOBA to be about 10% lower in these situations.
So in Giambi’s case, while CHONE projects a .357 wOBA, off the bench, we’d expect him to be a .321 hitter. After estimating his platoon skill, we’d expect him to be about a .328 hitter versus RHP. CHONE projects Smith projects at .368 wOBA, which is .331 after the PH penalty, and after adjusting for the platoon advantage, comes out to .333.
While the “penalty” means that pinch-hitting for the platoon advantage is rarely as beneficial as fans think it is, in this case, it does appear that the Rockies would have had a better chance by having Smith or Giambi hit for Mora. But let’s not got crazy — over 700 PA, a .328 wOBA is worth less than two runs over a .326, or barely a thousandth (~0.0017) of a run per PA. Given the margin of error in projections, not pinch-hitting Giambi for Mora is hardly a ridiculus decision. There is a bigger gap between Smith and Mora: over 700 PA, a .333 wOBA is worth about 4 runs than a .326, but that’s still less than a hundreth of a run (~0.0058).
It is fair to say that given the game and season situation that Tracy should have pinch hit Seth Smith for Melvin Mora. Once we take a closer look at the numbers, however, the advantage gained wouldn’t have been as big as one might think.
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