Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 2 (September 9, 1998)
Topic: More on Percentages : Baseball Standings

On Thursday August 6, 1998, the standings in the Central Division of the
National League were presented in the newspaper as follows:

TEAM          W     L     Pct.  GB 
_____________________________________

Houston      68    46    .658    --
Chicago      64    51    .557    4 1/2
Milwaukee    57    57    .500    11
St. Louis    53    60    .469    14 1/2
Cincinnati   51    63    .447    17
Pittsburgh   51    63    .447    17
 
The column W lists the number of games won, the column L lists the games lost.
The total number of games played is W+L. The fraction of games won is

                       W
                     ----- .
                      W+L

For Chicago, W=64, L=51, W+L=115, and

                       W      64
                     ----- = ---- = 0.556521...,
                      W+L    115

which is rounded off to three decimal places to 0.557. To find the
*percentage* of games won from the *fraction* of games won, we should multiply
by 100 to get 55.7%. To write .557 in the column labeled Pct., as newspapers
do, is a misuse of the word percent. 

                   PROBLEMS

1. Suppose that Chicago wins its next game. Find the number that will appear
in the Pct. column for Chicago and the percentage of games won. 

2. Suppose that Chicago loses its next game. Find the number that will appear
in the Pct. column for Chicago and the percentage of games won. 

3. Of the next seven games it plays, suppose Milwaukee wins 5 games and loses
2. Find the number that will appear in the Pct. column for Milwaukee and the
percentage of games won. 

4. How many games must Cincinnati win in a row in order to bring its
percentage of games won to 50%? 

5. How many games must Cincinnati win in a row in order to bring its
percentage of games won to 60% or more? 

6. How many games must St. Louis lose in a row in order to bring its
percentage of games won down to 40% or less? 

7. Now consider the column labeled GB (stands for 'Games Behind').  Looking at
the numbers in this column, determine the method used for computing these
numbers.

8. Suppose of the next 10 games played, Houston wins 6 and loses 4, Chicago
wins 5 and loses 5, Milwaukee wins 6 and loses 4, St. Louis wins 8 and loses
2, Cincinnati wins 2 and loses 8, and Pittsburgh wins 3 and loses 7. Find the
numbers in the GB column. 

9. Suppose in the East Division of the National League, Atlanta is in first
place, and New York is 14 1/2 games behind Atlanta. If of the next 20 games
played, Atlanta wins 8 and loses 12, and New York wins 13 and loses 7.  How
many Games Behind Atlanta is New York?