## Posts tagged ‘baseball’

### Math for Figger Filbert*

A well-known problem:

A man walks 1 mile south, 1 mile east, and 1 mile north. He arrives at the same place where he started, and then he sees a bear. What color is the bear?

The answer, of course, is white. It’s a polar bear. These three moves will let a person return to the same place if he starts at the North Pole. (The person could also return to the same place if he starts at an infinite number of points near the South Pole, too. He could start at a point so that when he walks 1 mile south, he is at a point such that the east-west circle on which he is standing has a circumference of 1 mile. Then, he can walk 1 mile east to return to the same spot. Finally, he can walk 1 mile north, and he’s back where he started. Then again, he could also start at a point so that he can walk 1 mile south to a point where the circumference of the east-west circle is 1/2 mile, do that loop twice, then walk 1 mile north. Or find points where the circumference is 1/3 mile, 1/4 mile, 1/5 mile, etc. You get the idea. However, since there are no bears in Antarctica, the answer to my original question is still correct.)

Two points about this:

- In answer to the question, “Are there polar bears in Antarctica?” there is only one correct answer:
*Only if they are bipolar.* - I really don’t care to receive silly comments about how a bear trapper could capture a grizzly and take him to Antarctica, or how a brown bear might mistakenly meander north to the Arctic Circle.

Here is a similar question:

A man runs 90 feet, turns left, runs another 90 feet, turns left, runs another 90 feet, and turns left. He is now headed home, and two men with masks are waiting for him. Who are they?

If you don’t know the answer to this riddle, remember that today is the first day of the World Series. My prediction? The Rangers will win easily. It’s not really a fair fight. I mean, members of the Lone Star State’s law enforcement agency with opposable thumbs and automatic weaponry versus defenseless birds? Seriously, if the Rangers don’t win, then we need to seriously reconsider the theory of natural selection.

If you watch the first game of the World Series tonight, remember to enjoy the game. Please don’t get caught up trying to figure out if it converges or diverges.

Here are a few baseball-related math puzzles:

- A baseball player has four at-bats in a game. At three different times during the game, his batting averages for the entire season (rounded to three decimal places) have no digits in common. What was his average at the end of the game?
- During a little league game, the visiting team scored 1 run per inning, and the home team scored 2 runs per inning. What is the final score of this seven-inning game?
- During the first half of the season, Derek batted .100, but his average was .300 during the second half of the season. Similarly, Alex batted .200 the first half of the season and .400 the second half of the season. Both players ended up with the same number of total at-bats, yet Derek had a higher batting average for the entire season. How is this possible?

* *Figger Filbert* is a term for baseball fans who are obsessed with statistics. Such fans are easily identified; they will make statements like, “Did you know that Albert Pujols is batting .275 when facing married pitchers in suburban ballparks that only sell popcorn on the mezzanine level?” It’s a synonym for *number nut*.

### Eddie Gaedel, a Man of Stature

Sixty years ago today, baseball player Eddie Gaedel stepped to the plate for the only at-bat of his major league career. Standing just 3’7″ tall, he drew a walk on four straight pitches.

Why mention this on a math jokes blog? Gaedel’s uniform number was 1/8.

This reminds me of a math question that my friend Harold Reiter likes to use to start a class discussion about size of numbers.

Which of the following is the largest fraction?

1/2

1/4

1/6

1/8

It also reminds me of the priest who tells his congregation that he understands how difficult it is to tithe. “If you can’t afford to give 1/10 of your salary to the church,” he tells them, “then just give 1/9 or 1/8.”

Officially, Gaedel had 1 base‑on‑balls (BB) and 0 at-bats (AB). In baseball, a plate appearance does not offically count as an at-bat if the player is walked. This gave Gaedel an on-base percentage (OBP) of 1.000, the highest possible. As it turns out, he’s not the only player with an OBP of 1.000; nearly 30 others have accomplished the same feat.

The official formula for on-base percentage is

OBP = (H + BB + HBP) ÷ (AB + BB + HBP + SF)

where

- H = hits
- HBP = hits-by-pitch
- SF = sacrifice flies

An interesting question is:

How can a player have a higher batting average than on-base percentage?

Though rare, it occasionally happens when a player has a relatively low number of at‑bats with few walks and several sacrifice flies. For instance, a player with 1 hit in 2 at-bats with a sacrifice fly would have a batting average of 0.500 and an on-base percentage of 0.333.

### 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.