## Baseball Probability

I happen to love sports. I’m a die-hard Pittsburgh Steelers fan, I’ll attend any baseball game I can get tickets to, and don’t even think about calling my house during March Madness or the NBA Finals — I won’t answer the phone.

But if you’re one of those math folks who prefers numbers to games, here’s a primer on recent events, as well as a joke you can tell at the next math department happy hour if the conversation turns to sports.

A perfect game in baseball is one in which a pitcher retires every batter he faces. No players get on base during the entire game — no hits, and no walks. Twenty-seven players come to bat, and all 27 of them make an out.

As you might expect, perfect games are extremely rare. There have been only 20 in major league history.

But recently, they seem to be a little less rare. On Sunday, May 9, pitcher Dallas Braden of the Oakland A’s threw a perfect game against the Tampa Bay Rays. Just 22 days later, Roy Halladay of the Philadelphia Phillies was perfect against the Florida Marlins. And 4 days after that, Armando Galarraga of the Chicago White Sox threw what has been officially ruled a one-hit shut-out… but because of an incorrect call by one of the umpires, most folks think it should count as a perfect game.

Two perfect games in a month is astonishing. Three perfect games in a month is nearly impossible. Don Leypoldt of Hardball Times claims that the odds of throwing three perfect games in a month are approximately 2,000,000 to 1.

But perfect games are not the most rare events in baseball. Can you name at least two single-game events that are less likely? (Of course, some events are completely impossible — such as a cow hitting a home run off a curveball thrown by a left-handed pig because, as we all know, every pig is right-handed. But by “events that are less likely,” I’m referring to events that have happened more than once, are considered extraordinary, and just aren’t commonplace.) Answers follow the joke below… and I should probably mention that there are way more than two.

The best pitcher on the baseball team failed his math mid-term. His coach, distraught at the possibility of losing his star player, cut a deal with the professor. In the locker room, the coach explained the situation to the pitcher.

“I was able to convince your math professor,” the coach began, “that if you could answer one math question correctly, you wouldn’t have to miss any games. So I’m going to ask you one question, and I need you to focus. If you answer it correctly, you can play in tomorrow’s big game. But if you miss it, you’re academically ineligible until your grades improve.”

“Okay, coach,” the player said. “I’ll do my best.”

“Great,” the coach said. “Here’s your question: What is 2 + 2?”

The player thought for quite some time. Finally, he said hesitantly, “Um, 4?”

“Really?” the coach asked excitedly. “Really? Did you really just say that 2 + 2 is 4?”

Upon hearing this, the other players in the locker room screamed out, “Aw, c’mon, coach… give him another chance!”

A lot of events in baseball are more rare than perfect games:

• Losing a perfect game on the 27th batter. Armando Galarraga can apparently take solace — he’s the tenth player in MLB history to whom this has happened. But with only 10 occurrences, losing a perfect game on the last batter is more rare than pitching a perfect game.
• The unassisted triple play. There have only been 15 in Major League history. But like perfect games, they’ve been less rare recently — Troy Tulowitzki completed one in 2007, Asdrubal Cabrera had another in 2008, and Eric Brunlett recorded a game-ending unassisted triple play in 2009.
• Four or more home runs by the same player in a single game. Only 15 of these, too, just like unassisted triple plays. No player has ever hit five or more home runs in a game.
• Grounding into four double-plays in a single game. Joe Torre is the only one to hold this distinction.
• Stealing six or more bases in a game. Two players stole 7 bases in a game: George Gore (1881) and Billy Hamilton (1894). Five other players have stolen six, a feat that Eddie Collins of the Philadelphia Athletics accomplished twice (on September 11, 1912, and then again 11 days later on September 22, 1912).
• Three or more triples in a game. George Streif (1885) and Bill Joyce (1897) both had 4 triples in a game, and 12 players have had 3 triples in a game.
• Twenty strike-outs in a nine-inning game. Only three have done this, the most recent Kerry Wood in 1998.

There are a lot of single-game records that are more rare than perfect games. If you’re interested in other crazy baseball statistics and records, check out the Play Index at Baseball-Reference.com.

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• 1. Mr. Pi  |  June 8, 2010 at 6:50 pm

Great post. I found your blog while searching tags that I use on my blog!

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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