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## One-Third of an Inning Pitched, 6 or More Earned RunsJune 1, 2011

Posted by tomflesher in Baseball.
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Carlos Marmol came in last night to close a fine performance by Carlos Zambrano, who had pitched 8 innings and allowed one earned run on 7 hits, no walks, and 7 strikeouts for a game score of 71. (Zambrano went 0-2, dropping his batting average to a paltry .346.) Marmol had allowed 3 runs in 23 innings pitched prior to last night, with 10 saves, two blown saves, and a record of 1-1.

Then came last night.

On one third of an inning pitched, facing the 6-7-8 part of the Astros’ lineup, Marmol first allowed Brett Wallace to single, followed by Chris Johnson doubling and sending Wallace to third. Matt Downs hit for catcher Robinson Cancel and doubled, sending both Wallace and Johnson home. (Two earned runs.)

At this point, I’d have been willing to let pitcher Fernando Rodriguez hit for himself, but Angel Sanchez came in and sacrifice bunted Downs to third base. Credit Marmol with one-third of an inning pitched. Michael Bourne singled to bring Downs home from third (three earned runs), then stole second to put the winning run in scoring position. Clint Barmes walked, followed by Hunter Pence homering (six earned runs). Mercifully, Sean Marshall came in to finish off the inning, allowing one more single but getting the two outs to end the inning.

It’s surprisingly common to have at least 6 earned runs in one-third or less of an inning pitched. Ryan Dempster even managed to allow seven earned runs in .1 IP to start the game and his team bravely held on for the loss, and Jason Marquis once allowed seven earned runs in NO innings pitched (although in Marquis’ defense he left the bases loaded and Miguel Batista allowed all three inherited runners to score).

So, buck up, Marmol, and buy Mr. Zambrano a steak dinner.

## Zambrano Back on the HorseMay 27, 2011

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Last night, Carlos Zambrano pitched on one day’s rest after pinch-hitting against the hapless Mets for two RBIs on Tuesday. We’ve talked about Zambrano’s pinch-hitting prowess before, but last night he was an awesome 3 for 3 from the plate, including a double. In fact, in 26 plate appearances, Zambrano’s got 9 hits for a .375 batting average and, since he has no walks, a .375 on-base percentage. Not only is that impressive, but I hear he can pitch, too.

I figured that was pretty impressive. It can’t be often that a pitcher gets three at-bats and hits for all of them, can it? It’s happened 450 times since 1919, including, surprisingly, once already this year. The Mets’ Chris Young managed a 3-for-3 night while notching the win against the Phillies back on April 5.

In recent memory, the most at-bats by a pitcher who hit each time was Dan Haren, who grabbed a 4-for-4 as a Diamondback against the Cardinals last year (also as the winning pitcher). Haren also gave up a whopping 7 runs, so he’s lucky he was hitting.

Micah Owings has had two games where he pitched and hit in all of at least 3 plate appearances, including a 4-for-4 from 2007 in which three of his 4 hits were doubles.

Finally, Mel Stottlemyre (in 1964) and two pitchers from the 1920s had 5-for-5 games. Stottlemyre’s two-hit gem included him hitting a double and pitching to a game score of 83.

## Utility Pitchers II: Alternate DefinitionJanuary 3, 2011

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In the previous post, I discussed utility pitchers, which I defined as players who primarily play a defensive position who are called on to pitch. It never occurred to me that Bleacher Report had previously defined it otherwise – as a pitcher who can perform well in any role.

How can I quantify that? Well, it seems to me that a sign of quality as a starter is the vaunted quality start (game score above 50, or six innings with three or fewer runs allowed, depending who you ask), and a sign of quality as a reliever is the save. Thus, a good utility pitcher is one who can muster at least one quality start and at least one save in a given season. It’s not perfect, since it relies on the manager being willing to insert a primary starter at the right point in a game to earn a save (or starting a primary reliever, as Joe Girardi did with Brian Bruney back in 2008). Nonetheless, eight pitchers managed that feat this year.

By far the most versatile was Hisanori Takahashi of the Mets. Tak managed six quality starts, a handful of appearances as a left-handed specialist, and eight saves when he stepped in as the Mets’ closer after Francisco Rodriguez became unavailable.

Mike Pelfrey also represented for the Mets, although he made only one relief appearance (in the crazy 20-inning game against the Cardinals).

Matt Garza of the Rays made some news this July when he showed his versatility by starting and saving games in the same series.

The other five pitchers were Bruce Chen, Nelson Figueroa, Tom Gorzelanny, Matt Harrison, and David Hernandez.

Shockingly, Carlos Zambrano wasn’t among the pitchers listed, even though he spent some time in the bullpen for the Cubs and some time as a starter. (Big Z was briefly the highest-paid setup man in the league.)

My guess for the 2011 season? Neftali Feliz of the Rangers was among the best closers this year but has the ability to start games as well. Most likely, though, it’ll be someone like Pelfrey, who was pressed into service in relief for an extra-inning game.

## Pinch Hitters from the BullpenJuly 6, 2010

Posted by tomflesher in Baseball, Economics.
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Occasionally, a solid two-way player shows up in the majors. Carlos Zambrano is known as a solid hitter with a great arm (despite the occasional meltdown), and Micah Owings is the rare pitcher used as a pinch hitter. Even Livan Hernandez has 15 pinch-hit plate appearances (with 2 sacrifice bunts, 6 strikeouts, and a .077 average and .077 OBP, compared with a lifetime .227 average and .237 OBP).

Like Hernandez, Zambrano has a very different batting line as a pinch hitter than as a pitcher. In 24 plate appearances as a pinch hitter, Big Z is hitting only .087 with a .087 OBP, compared to his .243/.249 line when hitting as a pitcher. Since we see the same effect for both of these pitchers, it seems like there’s some sort of difference in hitting as a pinch hitter that causes the pitchers to be less mentally prepared. Of course, these numbers come from a very small sample.

On the other hand, Micah Owings hits .307/.331 as a pitcher, and a quite similar .250/.298 as a pinch hitter. What’s the difference? Owings has almost double Zambrano’s plate appearances as a pinch hitter with 47. That seems to show that maybe Owings’ larger sample size is what causes the similarity. How can this be tested rigorously?

As we did with Kevin Youkilis and his title of Greek God of Take Your Base, we can use the binomial distribution to see if it’s reasonable for Owings, Hernandez and Zambrano to hit so differently as pinch hitters. To figure out whether it’s reasonable or not, let’s limit our inquiry to OBP just because it’s a more inclusive measure and then assume that the batting average as a pitcher (i.e. the one with a larger sample size) is the pitcher’s “true” batting average and use that to represent the probability of getting on base. Each plate appearance is a Bernoulli trial with a binary outcome – we’ll call it a success if the player gets on base and a failure otherwise.

Under the binomial distribution, the probability of a player with OBP p getting on base k times in n plate appearances is:

$\Pr(K = k) = {n\choose k}p^k(1-p)^{n-k}$

with

${n\choose k}=\frac{n!}{k!(n-k)!}$

We’ll also need the margin of error for proportions. If p = OBP as pitcher, and we assume a t-distribution with over 100 plate appearances (i.e. degrees of freedom), then the margin of error is:

$\sqrt{\frac{p(1-p)}{n-1}}$

so that 95% of the time we’d expect the pinch hitting OBP to lie within

$OBP \pm 2\times\sqrt{\frac{p(1-p)}{n-1}}$

$\Pr(K = k) = {n\choose k}p^k(1-p)^{n-k}$

with

${n\choose k}=\frac{n!}{k!(n-k)!}$

We’ll also need the margin of error for proportions. If p = OBP as pitcher, and we assume a t-distribution with over 100 plate appearances (i.e. degrees of freedom), then the margin of error is:

$\sqrt{\frac{p(1-p)}{n-1}}$

so that 95% of the time we’d expect the pinch hitting OBP to lie within

$OBP \pm 2\times\sqrt{\frac{p(1-p)}{n-1}}$

Let’s start with Owings. He has an OBP of .331 as a pitcher in 151 plate appearances, so the probability of having at most 14 times on base in 47 plate appearances is .3778. In other words, about 38% of the time, we’d expect a random string of 47 plate appearances to have 14 or fewer times on base. His 95% confidence interval is .254 to .408, so his .298 OBP as a pinch hitter is certainly statistically credible.

Owings is special, though. Hernandez, for example, has 994 plate appearances as a pitcher and a .237 OBP, with only one time on base in 15 plate appearances. It’s a very small sample, but the binomial distribution predicts he would have at most one time on base only about 9.8% of the time. His confidence interval is .210 to .264, which means that it’s very unlikely that he’d end up with an OBP of .077 unless there is some relevant difference between hitting as a pitcher and hitting as a pinch hitter.

Zambrano’s interval breaks down, too. He has 601 plate appearances as a pitcher with a .249 OBP, but an anemic .087 OBP (two hits) in 24 plate appearances as a pinch hitter. We’d expect 2 or fewer hits only 4% of the time, and 95% of the time we’d expect Big Z to hit between .214 and .284.

As a result, we can make two determinations.

1. Zambrano and Hernandez are hitting considerably below expectations as pinch hitters. It’s likely, though not proven, that this is a pattern among most pitchers.
2. Micah Owings is a statistical outlier from the pattern. It’s not clear why.

## Carlos Zambrano, Ace Pinch Hitter?June 21, 2010

Posted by tomflesher in Baseball.
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Earlier this year, Chicago Cubs manager Lou Piniella experimented with moving starting pitcher and relatively big hitter Carlos Zambrano to the bullpen, briefly making him the Major Leagues’ best-paid setup man. Zambrano is back in the rotation as of the beginning of June. I’m curious what the effect of moving him to the bullpen was.

The thing is that not only is Zambrano an excellent pitcher (though he was slumping at the time), he’s also a regarded as a very good hitter for a pitcher. He’s a career .237 hitter, with a slump last year at “only” .217 in 72 plate appearances (17th most in the National League), which was 6th in the National League among pitchers with at least 50 plate appearances. He didn’t walk enough (his OBP was 13th on the same list), but he was 9th of the 51 pitchers on the list in terms of Base-Out Runs Added (RE24) with about 5.117 runs below a replacement-level batter. Ubaldo Jimenez was also up there with a respectable .220 BA, .292 OBP, but -8.950 RE24.

It should be pointed out that pitcher RE24 is almost always negative for starters – the best RE24 on that list is Micah Owings with -2.069. Zambrano’s run contribution was negative, sure, but it was a lot less negative than most starters. Zambrano also lost a bit of flexibility as an emergency pinch hitter (something that Owings is going through right now due to his recent move to the bullpen) – he’s more valuable as a reliever, so they won’t use him to pinch hit. As a result, he loses at-bats, and that not only keeps him from amassing hits. It also allows him to get rusty.

It’s hard to precisely value the loss of Zambrano’s contribution, although he’s already on pace for -6.1 batting RE24. It’s likely, in my opinion, that his RE24 will rise as he continues hitting over the course of the year. His pitching value is also negative, however, which is unusual. He’s always been very respectable among Cubs starters. It’s possible that although he was pitching very well in relief, the fact that he has the ability to go long means that it’s inefficient to use him as a reliever. This is the opposite of, say, Joba Chamberlain, who is overpowering in relief but struggles as a starter.

As a starter, Zambrano has never been a net loss of runs. He needs to stay out of the bullpen, and Joba needs to stay there.