A pitcher’s Earned Run Average for a given game is defined as runs earned against him divided by the fraction of a game that he pitched.

To calculate a season ERA, sabrmatricians take the mean of this stat over all games played.

Phillies pitcher J.D. Durbin has a high ERA.

Over the course of the 2007 season, Phillies pitcher J.D. Durbin has accumluated an ERA of 6.27. But yesterday, Durbin accomplished something truly extraordinary. He gave up seven runs in the first inning without recording an out. In other words, he gave up seven runs without pitching one inning — or even a fraction of an inning.

Take another look at the formula above. Plug in seven runs, and zero innings. But wait: remember anything spooky from high school about dividing by zero?

You’ll never hear a mathematician say that Durbin’s ERA equals infinity; infinity is not even a real number. Instead, they’d say that for any integer N you care to choose, Durbin’s ERA for that game is larger than N.

So Durbin’s ERA is larger than N = 100,000,000.

It is larger than N = 999,999,999,999,999,999,999,999,999.

It is even larger than O’s revliever Paul Shuey’s ERA from last week’s record setting 30-3 loss to the Rangers (40.5).

If we plotted Durbin’s ERA as a function of time, there would be a point way up at infinity at t = yesterday’s game. Mathematicians would say that at t = yesterday’s game, his ERA “blows up”.

Luckily for Durbin, the Lebesgue theory of integration says that an integral can still have finite value even if it blows up at certain times, as long as those times occur on “sets of measure zero.” Since it appears that we count innings as discrete units, Durbin’s recent pitching debacle indeed occurred on such a set. Thus he owes a few beers to turn-of-the-century french mathematicians for his bloated yet finite 6.27.

Suz Tolwinski, who is getting her PhD in applied mathematics at the University of Arizona and is also my girlfriend, did most of the heavy lifting for this post.

Righthander J.D. Durbin, who will start for the Phillies in Game 1 of tomorrow’s doubleheader against the New York Mets at Citizens Bank Park, gets around. And when I say he gets around, I mean the man gets around.

Durbin has been with four organizations this season. Take a look at his travel schedule, as reported by the Philadelphia Inquirer:

Late March - The Twins, who drafted him in the second round in 2000, designated him for assignment.

March 29 - The Diamondbacks claimed him off waivers.

April 4 - He allowed seven hits and seven runs in two-thirds of an inning against Colorado.

April 5 - Arizona designated him for assignment.

April 9 - The Red Sox claimed him off waivers.

April 10 - Durbin arrived at his Boston hotel at 1 a.m. only to learn he had no reservation. He checked into another hotel and fell asleep about 2 a.m. Durbin took a call at 9:30 a.m. to learn the Red Sox no longer needed him and he had been designated for assignment. “I never dressed [with the Sox],” Durbin said. “I went to the stadium, picked up my meal money, said hi to the guys and took off. It was a quick turnaround.”

April 13 - The Phillies claimed him off waivers.

April 16 - Durbin learned just hours after he took a physical in Clearwater, Fla., that he had been designated for assignment. He cleared waivers and the Phillies sent him to triple-A Ottawa, where he went 2-4 with a 4.55 ERA in 10 starts.

Now, Durbin will be starting against the Mets in what has become a crucial series for the Phils, who trail New York by 3.5 games. He says he’s too tired to worry:

“No pressure,” he said. “I’ve been through enough right now that there really isn’t any pressure on me. And I think that might help me out a little bit. It is what it is. I’ve been through it all, so I’m just going to go out there and throw the baseball.”

I’m sorry to break it to you, J.D. But if constant rejection and mediocre past performance were a recipe for success, Jose Mesa would be tinkering with his Cooperstown induction speech between innings.