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Matt Garza, Fifth No-Hitter of 2010 July 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.

Adventures in the Mets Bullpen: One-Run No-Decisions and Vulture Wins July 19, 2010

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A close cousin of the Tough Loss discussed earlier is what Jayson Stark of ESPN calls the Criminally Unsupported Start. Stark defines a CUS as a start in which the pitcher pitches 6 or more innings but the offense scores one run or less in support. Johan Santana didn’t fit that definition last night, but he was close: he left the game with a 2-1 lead after 8 innings pitched and ended up with a no-decision. (A friend of mine liked to call that “the ol’ Roy Halladay” back when Doc was pitching in Toronto.) Just as he was the centerpiece of Jayson Stark’s CUS standings back in 2007, Santana currently leads the league in starts with 6.0 or more innings pitched, at most one run allowed, and no decision. He has six such games, and no other pitcher has more than four. (Yovani Gallardo, however, has a respectable 3.)

In all of 2009, no one hit the six-game mark in one-run no-decisions. Surprisingly, this year the Mets aren’t leading the league in these one-run no-decisions – the Cubs are, led by Randy Wells and his impressive 4, along with Ted Lilly with 3.

Francisco Rodriguez also picked up his third Vulture Win of the year last night. A vulture win is the combination of a blown save and a win in the same game. Usually, that happens when a hometown closer blows the save in the top of the 9th and his teammates score in the bottom for the win. Frankie blew the save in the bottom of the 9th last night, but they left him in to pitch the bottom of the 10th and he held on (despite Phil Cuzzi’s hissyfit and some questionable umpiring going in both directions). Tyler Clippard leads the league in vulture wins this year with four.

Cheap Wins July 16, 2010

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The opposite of the Tough Loss discussed below (which R.A. Dickey unfortunately experienced tonight in a duel with Tim Lincecum) is a Cheap Win. Logically, since a Tough Loss is a loss in a quality start, a Cheap Win (invented by Bill James) is a win in a non-quality start – that is, a start with a game score of below 50 (or, officially, a start with fewer than 6.0 innings pitched or more than 3 runs allowed).

The Chicago White Sox’ starter, John Danks, picked up a Cheap Win in Thursday’s game against the Twins. Although he pitched six innings, he gave up six runs (all earned) in the second inning, leading to an abysmal game score of 33. Danks had two of last year’s 304 Cheap Wins. Ricky Romero led the pack with six, and Joe Saunders and Tim Wakefield were both among the six pitchers with five Cheap Wins. Even Roy Halladay had two.

Through the beginning of the All-Star Break, there have been 136 Cheap Wins in 2010. That includes one by my current favorite player, Yovani Gallardo. John Lackey is already up to 5, and Brian Bannister is knocking on the door with 4.

It’s hard to read too much into the tea leaves of Cheap Wins, since they’re not all created equal. In general, they represent a pitcher sliding a little bit off his game, but his team upping their run production to rescue him. To that end, Cheap Wins might be a better measure of a team’s ability than Tough Losses, since, while Tough Losses show a pitcher maintaining himself under fire, Cheap Wins represent an ability to hit in the clutch (assuming that run production in Cheap Wins is significantly different from run production in other games). That’s hard to validate without doing a bit more work, but it’s a project to consider.

Tough Losses July 8, 2010

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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 2010 June 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.

2.448760831

NL Cy Young: Heating up early May 31, 2010

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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!)

Roy Halladay's Perfect Game May 30, 2010

Posted by tomflesher in Baseball.
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Just what the Doctor ordered.

Andy at Baseball-Reference.com has an interesting blog entry about Doc’s perfect game. Roy Halladay was 0-3 in the game with two strikeouts, threw 115 pitches to 27 batters, and had a 98 Game Score.

Compared to Dallas Braden, Doc was much, much more likely to achieve this. Halladay’s opposing OBP is a miniscule .297 career, .258 this year, with his complementary probabilities of getting a batter out at .703 and .742. Using his career numbers, his probability of getting 27 consecutive batters out would be .703^{27}, or .0000738, which is approximately 7/100000.

Interestingly, the last 3 perfect games have all had Florida teams as the victim.

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