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Exactly how big an impact have those trades had?
*August 26, 2015*

*Posted by tomflesher in Baseball.*

Tags: bullpen, Pythagorean luck, trades, wins above expectation

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Tags: bullpen, Pythagorean luck, trades, wins above expectation

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The Mets made some huge deals near the trade deadline to pick up **Juan Uribe** and **Kelly Johnson** on July 25, **Tyler Clippard** on July 28, and **Yoenis Cespedes** on August 1. (Those are the dates of the first games the players appeared in for the Mets.) Let’s take a look at the effects of those trades. If there was no effect from the trades, then the Mets’ improvement would have to be basically indistinguishable from chance.

**April:**The Mets scored 97 runs and and allowed 81 for a 16-run differential and a .581 Pythagorean expectation. They went 15-8 for a win percentage of .652, giving them a Pythagorean differential of .071 and 1.63 Wins Above Expectation.^{1}**May:**95 runs scored, 105 allowed, 11-14, for an expected .455 winning percentage, .440 actual winning percentage, -.015 differential and -.36 WAE.**June:**84 runs scored, 105 allowed, 9-15, for an expected .413, actual .375, -.038 differential and -.90 WAE.**July:**89 runs scored, 83 allowed, 11-12, for an expected .532, realized .478, -.053 differential and -1.23 WAE.**August:**137 runs scored, 84 allowed, 16-5, for an expected .709, actual .762, .053 differential and 1.11 WAE.

Clearly, the jump in August has been enormous, especially since they only played 21 games in August; in fact, the Mets averaged 3.76 runs per game through July, but 8.2 in August. In fact, if we start on July 25, the Mets have averaged 9.26 runs per game. Between Uribe, Johnson, and Cespedes, that’s a huge improvement – five and a half runs per game!

What about Clippard? Well, for one, the Mets averaged 3.9 runs allowed through July; since August 1, we’re at 4.0. However, Clippy’s ERA with the Mets is 1.93, and the bullpen ERA overall is 3.08. The August ERA for the bullpen has been an alarming 3.59, but that includes the hilarious trip to Colorado, too. That makes Tyler’s low ERA even more impressive. (For the record, future Mets closer **Hansel Robles** has a 3.27 August ERA – that’s 4 ER in 11.0 IP – and current closer **Jeurys Familia** hasn’t allowed a run in 11 1/3 innings pitched in August.) Clippy’s definitely value-added in the bullpen, especially considering that the alternative might be **Dario Alvarez** or **Dillon Gee** unhappy in his role.

Most notably, though, since the Mets picked up Uribe and Johnson, their wins above expectation have been statistically zero. They’ve been playing to their potential, not above it, since July 25.

We’re in for an interesting end to the year.

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^{1} Pythagorean differential is computed as (Winning percentage – Pythagorean Expectation). Wins Above Expectation is computed as Pythagorean differential times games played. They measure the same concept but are scaled differently.

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Cueto sits on bench, sobs
*April 6, 2014*

*Posted by tomflesher in Baseball.*

Tags: Baseball, bullpen, game score, Ike Davis, Johnny Cueto, Juan Lagares, Mets, Tough Losses

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Tags: Baseball, bullpen, game score, Ike Davis, Johnny Cueto, Juan Lagares, Mets, Tough Losses

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**Johnny Cueto** is having a tough year so far. In yesterday’s game against the Mets, he pitched to a game score of 65, allowing two earned runs in seven innings; he left with a lead, followed quickly with a hold by **Sam LeCure** and a blown save by **J.J. Hoover**, who surrendered a pinch-hit grand slam to professional pinch hitter **Ike Davis**^{1}. 65 is a solid game score; the sabermetric definition of a quality start is a pitcher who adds value to his team by pitching to a game score above 50. In his first start of the year, Cueto threw seven innings of three-hit ball and struck out eight, pitching to a 74 game score and surrendering only one run. Unfortunately, that day, **Adam Wainwright** threw seven innings of three-hit ball and struck out nine, pitching to a 76 game score and surrendering no runs. Neither bullpen surrendered much, and so Wainwright took the win and dealt Cueto one of the toughest losses we’re likely to see this year.

Let’s give the devil their due – although it’s been easy to criticize the Mets’ bullpen, **Scott Rice** and **Carlos Torres** combined for a perfect inning and two thirds yesterday, keeping the score close enough that Ike was able to knock in the winning home run.

Meanwhile, **Juan Lagares**‘ slugging percentage is still up at .765, and with 13 total bases on 21 plate appearances he’s averaging about .62 bases every time he steps to the plate. Lagares’ slide into second yesterday was important for Ike’s hit to be a grand slam; if he’d been out, **Ruben Tejada** could easily have grounded into a double play and kept Ike out of the batter’s box. Still, Tejada’s OBP is at .389, and if he can keep that up, a shortstop who gets on base almost eight out of every 20 plate appearances is a valuable person to have on your roster.

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^{1}Davis’s first pinch-hit home run, and, according to Greg Prince via Twitter, the first come-from-behind walk-off grand slam in the history of the Mets.

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Good news, everyone!
*April 5, 2014*

*Posted by tomflesher in Baseball.*

Tags: "Good news everyone!", BABIP, bullpen, Kyle Farnsworth, setup man

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Tags: "Good news everyone!", BABIP, bullpen, Kyle Farnsworth, setup man

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Perhaps I’m just giddy with the excitement of the Mets notching their first win of the season last night. Everything seemed to fit together – **Jenrry Mejia** was solid early on, and despite two brushes with injury, he pitched six excellent innings (6 IP, 4 H, 1 R (earned), 4 BB, 8 K) before turning it over to the bullpen. **John Lannan** is struggling as a reliever, credited with a hold despite allowing two runs on as many hits (one home run) and striking out one in his 2/3 of an inning; **Kyle Farnsworth** pitched a baffling perfect inning and a third before **Jose Valverde** came in and struck out one, walking one, to get his first save of the inning.

Professor Farnsworth was similarly perfect in nineteen games last year. Those include three appearances with one batter faced, four with two batters faced, thirteen complete innings, and one five-out situation. Three of the complete innings were finished games for Pittsburgh, where he finished seven games, most of them losses. Shockingly, Farnsworth blew only one save, earning two saves in Pittsburgh and two one-out holds in Tampa Bay. That means with last night’s hold, Farnsworth is halfway to last year’s mark. Hopefully, Farnsworth won’t be pressed into service as an emergency closer this year: His time in Tampa Bay had a 5.70 ERA and a .337 batting average on balls in play against a .298 league average BAbip. Since Tampa Bay’s team BAbip was .286, that means they got *a little* lucky, and Farnsworth got unlucky sometimes. When he headed to Pittsburgh, though, it was like Farns was a totally different player – and he was. Against an NL with a league average .296 BAbip, and playing for Pittsburgh with a team .289 BAbip against, Farnsworth’s BAbip was a surprisingly low .250. That’s a .087 drop from his Tampa Bay average, or about 2 hits every 23 balls in play. Hopefully, Farnsworth can keep up the luck in 2014, but frankly the better news would be if we had a more reliable setup man.

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Pinch Hitters from the Bullpen
*July 6, 2010*

*Posted by tomflesher in Baseball, Economics.*

Tags: binomial distribution, bullpen, Carlos Zambrano, Livan Hernandez, margin of error, Micah Owings, pinch hitter, sabermetrics

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Tags: binomial distribution, bullpen, Carlos Zambrano, Livan Hernandez, margin of error, Micah Owings, pinch hitter, sabermetrics

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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:

with

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:

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

with

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:

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

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.

- 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.
**Micah Owings**is a statistical outlier from the pattern. It’s not clear why.

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

*Posted by tomflesher in Baseball.*

Tags: Baseball, baseball-reference.com, bullpen, Carlos Zambrano, Cubs, Joba Chamberlain, Lou Piniella, Micah Owings, RE24, relief, setup man, starter, Ubaldo Jimenez

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Tags: Baseball, baseball-reference.com, bullpen, Carlos Zambrano, Cubs, Joba Chamberlain, Lou Piniella, Micah Owings, RE24, relief, setup man, starter, Ubaldo Jimenez

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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.