Play Ball - Equally: Math Programming Lends a Hand to Little League Baseball
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I.
/ 6 ¡sue 2 June - ep1enther 2003
Play Ball - Equally: Math Programming
Lends a Hand to Little League Baseball Francis J. Vasko Mathcinatics & CIS Department, Kutztown I.JnivcrsityKutziown, PA 19530
He explained to mc that each of twelve
Recently a friend asked me if mathematics could be used to solve a problem that happens all too
members on the team had several positions he or
she wanted to or could play.
The specific positions for each player are given in Table 1. The number after each position is a measure of how desirable it is to have that team member play that particular position. The higher the
often with Little League baseball teams. With the current Little League season ending, he was frustrated with the problem of trying to get each team member to play about the same amount of time. He felt strongly that Little Lcague baseball should be about developing the skills of all the team members, and that not just the best players should be on the field most of the time with the
number the more desirable it is to have that team member play that particular position.
players who really need the practice and experience sitting on the bench.
TABLE I TEAM MEMBER
PLAYABLE POSITIONS
#1
PITCHER (8), SECOND BASE (4), EXTRA HITTER PITCHER (5), SHORT STOP (2), THIRD BASE (8), EXTRA HITTER PITCHER (2), RIGHT FIELD (3), CENTER FIELD (8), LEFT FIELD (4), EXTRA HITTER FIRST BASE (9), RIGHT FIELD (2), CENTER FIELD (3). LEFT FIELD (4), EXTRA HITTER SECOND BASE (7), RIGHT FIELD (2), CENTER FIELD (2), LEFT FIELD (2), EXTRA HITTER FIRST BASE (4), SHORT STOP (7), THIRD BASE (3), EXTRA HITTER PITCHER (4), FIRST BASE (7). EXTRA HITTER CATCHER (8), SHORT STOP (5), THIRD BASE (2), EXTRA HITTER CATCHER (6), RIGHT FIELD (3), CENTER FIELD (3), LEFT FIELD (3), EXTRA HITTER PITCHER (9), THIRD BASE (2), EXTRA HITTER PITCHER (3), SHORT STOP (7), THIRD BASE (3), EXTRA HITTER CATCHER (4), SECOND BASE (4), RIGHT FIELD (4), CENTER FIELD (3), LEFT FIELD (2), EXTRA HITTER
#2 #3
#4 #5
#6 #7 #8
#9
#10 #11
#12
16
F-Te fùrther explained that the season consisted of
17 games with each game split into two half games. Players typically played for a complete
half game. Even if, for example, a pitcher was having difficulty he would be switched with another player on the field as opposed to being taken out of the game. If necessary, players could be replaced half way through the game.
Also, in addition to the traditional nine field
positions there was a tenth non-fielding position referred to as the extra hitter (EH) position. The EH got to bat but did not play the field. With 1 7 games per season (34 half-games), and
since there are 10 positions and 12 team
members, each team member should ideally play (10/12)34 = 28 1/3 half-games. Since ball players typically play complete half-games, the best that could be achieved is to make sure that
on the above discussion is now given.
LL BASEBALL FORMULF1ON 1:
Maximize ij pijxij Subject to: MAXGAMES aijxij
jaijxijMINGAMES aixij = NUMGAIVIES
Xij nonnegative integer
= 1,.
i
i
j=
Data Loading...
