## Utility Pitchers II: Alternate DefinitionJanuary 3, 2011

Posted by tomflesher in Baseball.
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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.

## Matt Garza, Fifth No-Hitter of 2010July 26, 2010

Posted by tomflesher in Baseball.
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Tonight, Matt Garza pitched the fifth no-hitter of 2010. He joins Edwin Jackson, Roy Halladay, Dallas Braden, and Ubaldo Jimenez in the Year of the Pitcher club.

As I pointed out when Jackson hit his no-hitter, no-hit games are probably Poisson distributed. Let’s update the chart.

The Poisson distribution has probability density function

$f(n; \lambda)=\frac{\lambda^n e^{-\lambda}}{n!}$

Maintaining our prior rate of 2.45 no-hitters per season, that means $\lambda = 2.45$. Our function is then

$f(n; \lambda = 2.5)=\frac{2.45^n (.0864)}{n!}$

The probabilities remain the same:

 n p cumulative 0 0.0863 0.0863 1 0.2114 0.2977 2 0.2590 0.5567 3 0.2115 0.7683 4 0.1296 0.8978 5 0.0635 0.9613 6 0.0259 0.9872 7 0.0091 0.9963 8 0.0028 0.9991 9 0.0008 0.9998 10 0.0002 1.0000

And though the expectation (E(49)) and cumulative expectation (C(49)) remain the same, the observed values shift slightly:

 E(49) Observed C(49) Total 4.23 5 4.23 5 10.36 11 14.59 16 12.69 8 27.28 24 10.36 17 37.65 41 6.35 1 43.99 42 3.11 5 47.10 47 1.27 1 48.37 48 0.44 0 48.82 48 0.14 1 48.95 49 0.04 0 48.99 49 0.01 0 49.00 49

The tailing observations (say, for 4+ no-hitters) don’t quite match the expected frequencies, but the cumulative values match quite nicely. There might be some unobserved variables that explain the weirdness in the upper tail. Still, cumulatively, we have 47 seasons with 5 or fewer no-hitters, which is almost exactly what’s expected. This is unusual, but not outside the realm of statistical expectation.