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

*Posted by tomflesher in Baseball, Economics.*

Tags: baseball-reference.com, BayesBall, Dallas Braden, Diamondbacks, Edwin Jackson, no-hitters, poisson distribution, Rays, Roy Halladay, Ubaldo Jimenez

2 comments

Tags: baseball-reference.com, BayesBall, Dallas Braden, Diamondbacks, Edwin Jackson, no-hitters, poisson distribution, Rays, Roy Halladay, Ubaldo Jimenez

2 comments

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:

- How likely is a season with 4 no-hitters?
- 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

where is the expected number of occurrences and we want to know how likely it would be to have 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

and

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.

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