Matt Garza, Fifth No-Hitter of 2010

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

Posted by tomflesher in Baseball.
Tags: Dallas Braden, Edwin Jackson, Matt Garza, no-hitters, Roy Halladay, Ubaldo Jimenez, Year of the Pitcher
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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.

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1. Justin Verlander, Second No-Hitter of 2011 « The World's Worst Sports Blog - May 8, 2011: […] “Year of the Pitcher,” I would be careful about making that conclusion. Remember that no-hitters are probably poisson distributed, so we should expect clumps of them. If pitchers keep it up, I’ll start crunching more […]

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