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.

Tough LossesJuly 8, 2010

Posted by tomflesher in Baseball.
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Last night, Jonathon Niese pitched 7.2 innings of respectable work (6 hits, 3 runs, all earned, 1 walk, 8 strikeouts, 2 home runs, for a game score of 62) but still took the loss due to his unfortunate lack of run support – the Mets’ only run came in from an Angel Pagan solo homer. This is a prime example of what Bill James called a “Tough Loss”: a game in which the starting pitcher made a quality start but took a loss anyway.

There are two accepted measures of what a quality start is. Officially, a quality start is one with 6 or more innings pitched and 3 or fewer runs. Bill James’ definition used his game score statistic and used 50 as the cutoff point for a quality start. Since a pitcher gets 50 points for walking out on the mound and then adds to or subtracts from that value based on his performance, game score has the nice property of showing whether a pitcher added value to the team or not.

Using the game score definition, there were 393 losses in quality starts last year, including 109 by July 7th. Ubaldo Jimenez and Dan Haren led the league with 7, Roy Halladay had 6, and Yovani Gallardo (who’s quickly becoming my favorite player because he seems to show up in every category) was also up there with 6.

So far this year, though, it seems to be the Year of the Tough Loss. There have already been 230, and Roy Oswalt is already at the 6-tough-loss mark. Halladay is already up at 4. This is consistent with the talk of the Year of the Pitcher, with better pitching (and potentially less use of performance-enhancing drugs) leading to lower run support. That will require a bit more work to confirm, though.

Edwin Jackson, Fourth No-Hitter of 2010June 25, 2010

Posted by tomflesher in Baseball, Economics.
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Tonight, Edwin Jackson of the Arizona Diamondbacks pitched a no-hitter against the Tampa Bay Rays. That’s the fourth no-hitter of this year, following Ubaldo Jimenez and the perfect games by Dallas Braden and Roy Halladay.

Two questions come to mind immediately:

1. How likely is a season with 4 no-hitters?
2. Does this mean we’re on pace for a lot more?

The second question is pretty easy to dispense with. Taking a look at the list of all no-hitters (which interestingly enough includes several losses), it’s hard to predict a pattern. No-hitters aren’t uniformly distributed over time, so saying that we’ve had 4 no-hitters in x games doesn’t tell us anything meaningful about a pace.

The first is a bit more interesting. I’m interested in the frequency of no-hitters, so I’m going to take a look at the list of frequencies here and take a page from Martin over at BayesBall in using the Poisson distribution to figure out whether this is something we can expect.

The Poisson distribution takes the form

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

where $\lambda$ is the expected number of occurrences and we want to know how likely it would be to have $n$ occurrences based on that.

Using Martin’s numbers – 201506 opportunities for no-hitters and an average of 4112 games per season from 1961 to 2009 – I looked at the number of no-hitters since 1961 (120) and determined that an average season should return about 2.44876 no-hitters. That means

$\lambda = 2.44876$

and

$f(n; \lambda = 2.44876)=\frac{2.44876^n (.0864)}{n!}$

Above is the distribution. p is the probability of exactly n no-hitters being thrown in a single season of 4112 games; cdf is the cumulative probability, or the probability of n or fewer no-hitters; p49 is the predicted number of seasons out of 49 (1961-2009) that we would expect to have n no-hitters; obs is the observed number of seasons with n no-hitters; cp49 is the predicted number of seasons with n or fewer no-hitters; and cobs is the observed number of seasons with n or fewer no-hitters.

It’s clear that 4 or even 5 no-hitters is a perfectly reasonable number to expect.

 2.44876

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.

NL Cy Young: Heating up earlyMay 31, 2010

Posted by tomflesher in Baseball.
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There’s considerable debate, following Roy Halladay‘s perfect game, as to whether he or Ubaldo Jimenez should be considered the top contender for the National League’s Cy Young Award. Of course, it’s way too early to make those sorts of decisions, but let’s take a look at some of the data quickly.

Jimenez is sitting at 3.7 Wins Above Replacement and 38 Runs Above Replacement in 10 starts:

Year Age Tm Lg IP GS R Rrep Rdef aLI RAR WAR Salary
2010 26 COL NL 71.1 10 7 45 0 1.0 38 3.7 $1,250,000 5 Seasons 577.2 93 241 362 0 1.0 121 12.2$2,392,000
Provided by Baseball-Reference.com: View Original Table
Generated 5/31/2010.

Halladay has considerably less, with 22 RAR and 2.4 WAR:

Year Age Tm Lg IP GS R Rrep Rdef aLI RAR WAR Salary
2010 33 PHI NL 86.0 11 23 45 3 1.0 22 2.4 $15,750,000 13 Seasons 2132.2 298 893 1407 19 1.0 514 49.8$88,991,666
Provided by Baseball-Reference.com: View Original Table
Generated 5/31/2010.

Of course, 10 or 11 starts is far too small a sample to draw conclusions from this early in the season. Halladay has a perfect game; Jimenez has a no-hitter. Still, there’s no reason to believe that a perfect game, in and of itself, is enough to get Doc a Cy Young Award. After all, Mark Buehrle didn’t win the Cy last year, and Dallas Braden isn’t even in contention.

If both players keep pitching at or near this level, Halladay becomes a realistic contender, because at that point his marginal contribution may make the difference between whether the Phillies make the playoffs or not. As it stands right now, the NL East is entirely too volatile to make that decision.

(Incidentally, I love Baseball-Reference.com’s new stat sharing and player link tools!)