Guess the Graph on Square Root Day

Today is Opening Day in Major League Baseball, and 13 games will be played today.

It’s also Square Root Day, because the date 4/4/16 transforms to 4 × 4 = 16.

With those two things in mind, here’s a trivia question that seems appropriate. Identify the data set used to create the graph below. I’ll give you some hints:

• The data set contains 4,906 elements.
• It’s based on a real-world phenomenon from 2015.
• The special points marked by A, B, and C won’t help you identify the data set, but they will be discussed below.

Got a guess?

No clue? Okay, one more hint:

• The horizontal axis represents “Distance (Feet)” and the vertical axis represents “Frequency.”

Still not sure? Final hints:

• Point A on the graph represents Ruben Tejada’s 231-foot inside-the-park home run on September 2, 2015.
• Point B on the graph represents the shortest distance to the wall in any Major League Baseball park — a mere 302 feet to the right field fence at Boston’s Fenway Park.
• Point C represents the longest distance to a Major League wall — a preposterous 436 feet to the deepest part of center field at Minute Maid Park in Houston.

Okay, you’ve probably guessed by now that the data underlying the graph is the distance of all home runs hit in Major League Baseball during the 2015 season. That’s right, there were 4,906 home runs last year, of which 11 were the inside-the-park variety. The distances ranged from 231 to 484 feet, with the average stretching the tape to 398 feet, and the most common distance being 412 feet (86 HRs traveled that far). The data set includes 105 outliers (based on the 1.5 × IQR convention), which explains why a box plot of the data looks so freaky:

The variety of shapes and sizes of MLB parks helps to explain the data. Like all math folks, I love a good graphic, and this one from Louis J. Spirito at the Thirty81Project.com is both awesome and enlightening:

click the image to see the full infographic

Here are some more baseball-related trivia you can use to impress your friends at a cocktail party or math department mixer.

1. Who holds the record for most inside-the-park home runs in MLB history?
   Jesse Burkett, 55 (which is 20 more than he hit outside-the-park)
   
2. Which stadium has the tallest wall?
   The left field fence at Fenway Park (a.k.a., the “Green Monster”) is 37 feet tall.
3. Which stadium has the shortest wall?
   This honor also belongs to Fenway Park, whose right field wall is only 3 feet tall.
4. Although only 1 in 446 home runs was an inside-the-park home run in 2015, throughout all of MLB history, inside-the-park home runs have represented 1 in ____ home runs.
   158
5. Name all the ways to get on first base without getting a hit.
   This is a topic of much debate, and conversations about it have taken me and my friends at the local pub well into the wee hours of the morning. I have variously heard that there are 8, 9, 11, and 23 different ways to get on base without getting a hit. I think there are 8; below is my list.
   (1) Walk
   (2) Hit by Pitch
   (3) Error
   (4) Fielder’s Choice
   (5) Interference
   (6) Obstruction
   (7) Uncaught Third Strike
   (8) Pinch Runner
   
6. What is the fewest games a team can win and still make the playoffs?
   39. The five teams in a division play 19 games against each of the other four teams in their division. Assume that each of those teams lose all of the 86 games against teams not in their division. Then they could finish with 39, 38, 38, 38, and 37 wins, respectively, and the team with 39 wins would make the playoffs by winning the division.
7. Bases loaded in the bottom of the ninth of a scoreless game, and the batter hits a triple. What’s the final score of the game?
   1-0. By rule, the game ends when the first player touches home plate.
8. In a 9-inning game, the visiting team scores 1 run per inning, and the home team scores 2 runs per inning. What is the final score?
   16-9. The home team would not bat in the bottom of the ninth, since they were leading.