Math involved in Major League Baseball - By: Alexa Long

Math involved in
Major League Baseball
By: Alexa Long

Batting Averages
(Data Analysis as well as Operations)

 The batting average measures the performance of baseball players at
  the plate

 The batting average is calculated by dividing the amount of hits that
  season by the amount of ‘at-bats’ the player has received.

 A batting average can be calculated for a season, a career, a
  months span, or to see how a batter has done against a particular
  team or pitcher.

 A batting average can be a team or an individual statistic and is
  shown and read as a decimal

 Example:
      Derek Jeter’s 2012 Batting Average: .396 (36 hits / 91 at bats)
      Derek Jeter’s Career Batting Average: .314 (3122 hits / 9956 at bats)

Field Measurements (Measurement)
 The dimensions of a baseball field are very important to the game.

 The distance from the pitchers mound to home plate is exactly 60ft 6
  inches, and the distance between each base is exactly 90ft

 The dimensions of a field determine factors such as how quickly one
  can run from base to base, or what is considered a fair or foul ball

Pitch Count
(Number and Operations)
 A pitch count is a statistic used to determine the
  number of pitches thrown by a pitcher in a
  game.

 Coaches of teams rely on a pitch count to show
  them when a pitcher needs to be taken out of a
  game, or how much longer they can last in a
  game. If a pitcher throws too many pitches, he
  will inevitably get tired and could possibly injure
  his arm.

 The less pitches a pitcher throws while getting
  batters out, the better.

Earned Run Average (ERA)
(Data Analysis as well as Operations)

 A pitchers ERA is the mean of earned runs given
  up by a pitcher per 9 innings pitched
   An earned run is defined as a run that is not
    affected by defensive errors, and scored solely
    by hits/runners on base from the offensive team

  An ERA is presented as a decimal

  Example: Tim Lincecum 2012 ERA: 5.74 (17
    earned runs, 26.2 total innings pitched)

Number of Games
(numbers)

 There are 162 total games played in a Major
  League Baseball regular season
 The season begins on Opening Day and runs
  for 26 total weeks
 Teams that advance to the playoffs
  because of a certain amount of wins, will
  play more games than shown in the regular
  season schedule
 The amount of games played in the playoffs
  is also a result of wins and losses

Regulation Rules
(Numbers)

 Regulation rules are what make the game of
  baseball

 There are 9 innings in a Major League Game

 3 outs are needed in order to switch the teams
  from offense to defense

 There are 9 defensive positions on the field, and 9
  batters allowed in the lineup

Individual Player Statistics
(Data Analysis)

 Individual player statistics allow players and fans to
  determine how well or poorly they are producing
  during a season or for the entirety of their career.
 Individual player statistics can be batting average,
  ERA, total number of career hits, On-Base
  percentage, amount of Runs Batted In (RBI).. Etc

 Example: Josh Hamilton Individual Statistics:
     Career Batting Average: .311
     2012 Batting Average: .388
     Career Amount of Hits: 731
     Career Amount of RBI’s: 449

Position Numbering
(numbers)
 In baseball, the defensive positions are given a number 1-9. These numbers are
  used by coaches, fans and statisticians alike to keep track of plays made in the
  field.

 For example: a double play made by the shortstop throwing to the second
  baseman who then throws to first base is a common play entitled the “6-4-3
  double play”

 The numberings are as follows
   1- pitcher
   2- catcher
   3- first base
   4- second base
   5- third base
   6-short stop
   7- left field
   8- center field
   9- right field

Position Numbering Guide

Reaction Time
(numbers and operations)

 A batter’s reaction time is very important to the
  game of baseball because it determines how fast
  they need to react in order to hit the ball the
  pitcher is throwing
 A batter’s reaction time is based off of distance,
  velocity, and timing
 A major league pitcher is 60ft and 6inches away
  from home plate, and if he is throwing a ball 95
  mph, that calculates into 139.33 ft per second.
 This means the batter has .434 of a second to
  decide whether he wants to swing the bat or not,
  as well as whether the pitch is appropriate to swing
  at

Win to Loss Ratio
(Probability)
   Standings in Major League Baseball are important to the teams playing as well as the fans

   The number of wins a team acquires is compared to the losses they will inevitably acquire
    as well during the 162 game regular season

   This is then translated into a ‘win percentage’ which is presented as a decimal but can be
    looked at as a percentage as well.

   This Win to Loss Ratio plays a significant part in the decision of which teams will advance
    to the playoffs

   Whether or not a team makes the playoffs based on their win to loss ratio, is a probability
    problem

   Example:
       2012 Baltimore Orioles:
           Wins: 14
           Losses: 8
           Win %: .636 (aka they have won approximately 64% of their games this year)
           W/L Ratio: 14:8

Fan Attendance
(numbers and operations)

 The size of a stadium and seating determines the
  maximum amount of fans that can be present at a game

 There are thousands of people in stadiums at one time,
  whether they are fans, employees or players

 The amount of tickets sold shows how many fans will be in
  attendance at the games.

 The number of fans/tickets sold is usually based upon the
  success of the team and the organization as a whole

 Example: New York Yankees, Yankee Stadium Seating
   Capacity- 50,291
   Seat width- 18 inches
   Seat length- 29.5 inches

Records
(Data Analysis)

 Teams, as well as individuals, can hold statistical records in the game of
  baseball

 Statistical records show the success of the team or the individual, and where
  they stand compared to other teams and individuals

 When an individual player, or a a team, has a prominent statistic, they are
  numbered and ranked among others who have excelled in that field.

 Example:
     The New York Yankees have won 27 World Championships.
     They are ranked #1 in the amount of World Championships won, the #2 team is the St Louis
      Cardinals with 11.

  Example:
      Derek Jeter has 3,122 career hits
      He is ranked #19 in the all-time career hits record. The #1 amount of career hits is Pete Rose
      with 4,256