## Math Jokes for Pitchers and Catchers

*February 9, 2013 at 2:10 pm* *
4 comments *

Pitchers and catchers in Major League Baseball report to spring training this week. Here’s a math joke for baseball players. (And while I’m not certain who said this originally, it’s a solid bet that this quote comes from Dave Barry, though I haven’t been able to confirm that.)

Everyone knows that if a mathematician had to choose between solving a difficult story problem and catching a fly ball, he would surely solve the problem without thinking twice about whether the Infield Fly Rule was in effect.

And since we’re talking baseball…

What do you do with an elephant with three balls?

Walk him, and pitch to the rhino.

Here are some baseball and math trivia questions for you **[updated 2/10/2013]**, some based on problems from Erich Friedman’s Baseball Puzzles page:

- In the bottom of the ninth inning in a game with no score, the bases are loaded. The batter hits a ball that rolls into the right field corner. Before the ball is thrown home, all four base runners cross the plate. What is the final score of the game?
- If the visiting team scores 2 runs per inning, and the home team scores 3 runs per inning, what is the final score of a nine-inning game?
- A player has four at-bats in a game, and he got a hit in his last of these at-bats. His batting averages for the season (rounded to three decimal places, as usual) at three different times during the game do not have any digits in common. What was his batting average at the end of the game?
- What is the minimum number of games a Major League Baseball team must win to make the playoffs?

Answers

- The final score is
**1-0**. Once the first player touches the plate, the home team wins, and the game is officially over. - The final score is
**24-18**. With a lead in the middle of the ninth inning, the home team does not bat in the bottom of the ninth. - At the end of the game, his average was
**.409**. He was 5 for 18 (.278) at the beginning of the game, 6 for 19 (.316) after one at-bat, and 9 for 22 (.409) after three more at-bats. - A team only has to win
**28 games**. There are four teams in the American League West division, and the requirement in Major League Baseball is that every team must play either 18 or 19 games against the other teams in their division. That means that each of these four teams could play as few as 54 divisional games. If each of them loses the 108 non-divisional games that they play, then the four teams could conceivably finish with 28, 27, 27, and 26 wins, respectively. Under this scenario, the division winner is the team with just 28 victories.

There are many who complain that, because of the Electoral College, it’s possible for a candidate to be elected President with less than 30% of the popular vote. Yet this situation is worse — a team could make the playoffs by winning just 17% of its games. (Of course, the Presidential election has slightly more consequence. Maybe.)

Entry filed under: Uncategorized. Tags: baseball, catchers, Infield Fly Rule, MLB, pitchers.

1.Joshua Zucker | February 9, 2013 at 3:46 pmMy friend Jeff points out that #1 is not possible (it’s a single, not a home run). He also suggests that you rephrase #3 as having 9 distinct digits to rule out things like 1 for 3 as the starting average.

We both would like to know whether the solution to #3 is unique but neither of us has spent the time to check that yet.

2.Jeff Sonas | February 9, 2013 at 4:09 pmI wrote a spreadsheet in Excel to check this, and found another solution for #3:

You start 1 for 12 (.083), then get a hit and you are 2 for 13 (.154), then get two straight hits and you are 4 for 15 (.267)

That is the only other one that works!

3.Joshua Zucker | February 9, 2013 at 4:26 pmJeff found one using Excel to figure it out exhaustively – you start 1 for 12 (.083), then get a hit and you are 2 for 13 (.154), then get two straight hits and you are 4 for 15 (.267)

4.venneblock | February 9, 2013 at 11:51 pmYeah, Jeff’s right on both counts. I updated the wording on #1 and #3 to reflect this. How’d I do?

I still didn’t prove uniqueness, but I did confirm that there are no answers with fewer total at-bats for the season.