Baseball is a game that lends itself to mathematics. From 3 strikes and 3 outs to the geometry of the infield diamond...From hitting .300 or .406, to throwing a curveball on 3-2 count in the bottom of the 9th inning, math is everywhere in baseball.

Fenway Park

Boston, Massachusetts

In the majors, most organizations rely heavily on baseball-oriented statistics to evaluate talent. Coaches at all levels use mathematics to help determine in-game strategy. So, whether you love baseball or mathematics or both, I hope this sheds a little light on the connections between mathematics and America's National Pastime.

[Probability and Statistics, Numbers and Operations]

The Diamond?

Baseball, as we now know it, has been played in America since the 1800s. While the inventor of the sport is up for debate, Alexander Cartwright is said to have invented the baseball field, as we know it today, in 1845.

Cartwright's New York Knickerbocker club trotted 9 defensive fielders out on to the field, with the infielders settling on a wide swath of dirt connecting first base to second base and second to third.

Two narrow strips of dirt connect home plate with first base and third base. The four bases became known as "the diamond." There is a problem with this description, however. When most people envision a diamond, they think of a type of rhombus with four sides of the same length and opposite angles of the same measure.

A baseball "diamond" is in fact a square. It is a rhombus, but with four sides of the same length and all four angles equal to 90 degrees. Ninety is a popular number on the diamond. The distance between the bases in 90 feet.



http://www.baseballfielddesign.com/index_files/500px-Baseball_diamond.png

More than 150 years later, kids and adults alike still refer to baseball fields as baseball diamonds.

[Measurement, Geometry]

Field Dimensions

Besides 90 feet between bases, what other dimensions make up a baseball field?

The other required dimensions in the infield include the distance between the pitching rubber and home plate is 60 feet, 6 inches. The pitching rubber sits on top of a dirt mound 10 and 1/2 inches above the ground.

http://www.pitchingmounds.com/images/121907/mound.jpg

Baseball is unique, at least among the four major American professional sports, in that beyond the infield diamond, it does not have set dimensions for its playing surface. In fact, none of the 30 Major League Baseball parks have the same outfield and foul territory dimensions.

[Geometry, Measurement]

Innings, Outs, and Strkeouts

Americans use the base-10 system of numbering and America's Pastime does as well. However, the multiples of 10 are not prevalent in the set-up of the game.

You be the judge. Here is the format of a Major League Baseball game:

A complete game: 9 innings
A complete inning: 6 outs
A half-inning: 3 outs
A strikeout: 3 strikes
A walk: 4 balls

Statistics

After a goal is scored in soccer or hockey, the goal scorer and players with an assist are recorded. In basketball, statistics such as points, rebounds, assists, steals, and free-throw shooting percentage are recorded. Football uses such categories as tackles, touchdowns, sacks and rushing yards.

In baseball, statistics are broken down by hitting, pitching and fielding.

Hitting

Offensively, statistics such as batting average, home runs and RBI (runs batted in) are common. Home runs and RBIs are totals - as in 44 home runs in a season. Batting average is determined
by a players' total number of at bats divided by his total number of hits.

A starter will typically get 550 at bats in a season. If he gets 175 hits, his batting average will be .314.

Fielding

A player is judged the number of errors he commits and by the number of errors he commits versus the number of fielding chances he had. A second baseman may make 13 errors during a season. If he had 300 chances, his fielding percentage would be .956.

Pitching

Typical categories are wins, losses, and ERA or earned run average. ERA is a statistic that often reflects a more accurate depiction of the pitcher. Earned run average is determined by taking the number of innings and dividing by the number of earned runs a pitcher gives up. ERA is all based around 9 innings (a complete game).

Pitch Count

Coaches or managers have a difficult decision to make in every game: when to pull the starting pitcher and replace him with a reliever. Oftentimes, for this decision, the manager is skewered by the press and the public. To this day, Red Sox fans still debate Grady Little's decision to leave Pedro Martinez in the game late in Game 7 of the 2003 American League Championship Series.



http://images.dailyradar.com/media/uploads/ballhype/story_large/2009/03/09/pedro_martinez.jpg

So the question remains. At what point should a manager pull his starting pitcher? The school of thought today is between 100-110 pitches. Coaching youth baseball, I usually look at pulling the starter at somewhere betweeen 55-65 pitches.

[Number and Operations]

Regular Season and Playoffs

The regular season in the majors league is 162 games. At the end of the regular season, 4 teams from each league, the American League and the National League, qualify for the playoffs.

In what is called the division series, or the opening round,the series are best of 5. The first team to win 3 games wins the series. The winners of the 2009 American League Division Series were the New York Yankees and the Los Angeles Angels of Anaheim. The winners of the 2009 National League Division Series were the Philadelphia Phillies and the Los Angeles Dodgers.

In the league championships that follow, and World Series, the series are the best of 7. The Yankees and the Phillies advanced to the 2009 World Series, with the Yankees winning 4 games to 2.

Teaching Base Running

Base running is one of the most overlooked aspects of the game of baseball, in my opinion. As a coach, I teach all aspects of base running: taking leads, stealing bases, rounding the bag, tagging up, picking up the third base coach, and reading the ball off the bat.

Here is Florida Marlins outfielder Cameron Maybin, a prolific base runner.

http://www.cameronmaybin.tv/images/futures_2006_baserunning.JPG

One of the first things we address as a team each spring is how to take a proper lead from first base. It is simple and becomes automatic with practice. Starting with your left foot on the edge of the bag, lead with your right foot 3 and 1/2 steps. Be sure to bend your knees to about a 110-120 degree angle. Place the majority of weight on the balls of your feet.

Now you are in good starting position to steal second base or run when the ball is hit.

[Numbers and Operations]

Sacred Numbers

Ask any baseball fan worth his or her slat and they'll be able to tell you the significance of the following special baseball numbers:

.406


https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO27MvMblj-d1WzNb_1oDrkNz-Jyu8UE3KHm8HfQlgsgjWtGxmHxf3WdLM-8MUjZFIg8Hc4WuhtEPcHdMnQDF6UxCnzclfs6wydQ0nKEP884gnGiWEWXwNQwTWlGnhVmddvTPOKflT0nU/s320/williams.jpg

Ted Williams hit .406 for the Boston Red Sox in 1941. No player has hit .400 since.


56

http://www.gallerym.com/pixs/photogs/ea/selections/images/Joe%20Dimaggio%20by%20Alfred%20Eisensteadt.jpg

Joe Dimaggio hit in a record 56 consecutive games - a record that still stands today.

The Scorebook and the Fielding Positions

Have you ever been listen to a baseball game on the radio or to the broadcasters on television and heard the phrase "6 - 4 - 3?" What does that mean?



Simply put, that's baseball lingo for a double-play started by the third baseman, who threw to the second baseman, who tagged second base and threw on to first base to complete the double play. Simple right?

In order to keep the most detailed, accurate accounting of a game, each position is given a number 1 through 9 shown below.

Perfection

One of the loudest arguments about the extraordinary nature of the game of baseball is that anything can happen on any given day at the ballpark.

There are three accomplishments I think stand out among all others:

- pitching a no-hitter
- hitting for the cycle
- pitching a perfect game

Since what is now known as the Major Leagues began in 1871, more than 390,00o games have been played. Batters have slugged more than 3.5 million hits.

As of April 25, 2010 here are the astonishing statistics:

- Only 264 no-hitters have been thrown. That is one in approximately every 1477 games.

- Only 288 times has a player hit for the cycle in a game.

- Only 18 players in Major League Baseball history have pitched a perfect game. A perfect game is defined as a complete 9-inning game in which no runs reach base safely. No hits. No walks. No hit batsman. No runs. In short..."27 up. 27 down."

[Numbers and Operations]

Milestone Numbers

Baseball, probably due mostly to its long history, is a sport with "milestone numbers."

Pitchers
300 wins
The magical number. Only 24 players in history have reached that number, most recently Randy Johnson, pitching for the San Francisco Giants in 2009. Changes in the game make this a nearly impossible task for pitchers in the future. Teams rely heavily now on the bullpen giving starters less of a chance of picking up wins.


Hitters
3000 hits
A guaranteed ticket to the Baseball Hall of Fame in Cooperstown, NY. Only 27 players in history have reached that number, most recently Craig Biggio of the Houston Astros in 2007.


http://2outsbasesloaded.com/blog/wp-content/uploads/2010/01/baseball-hall-of-fame.gif

[Numbers and Operations]