Chapter 4: Decimals Numbers in the Real World

Slugging It Out

If you follow baseball, then you know about baseball statistics.  There are statistics for virtually every facet of the game.  Many newspapers, magazines, and Web pages provide these statistics to fans of professional baseball.  The Sporting News, for example, is a weekly magazine with great statistics that also hosts a home page.  Check out their statistics page.

Below is a sample page of baseball statistics.
 

1997 AMERICAN LEAGUE Home Run Leaders (as of 8/24/97)

Rank	Name	Team	Games	At Bats	Hits	Runs	Batting  Average	Home Runs	Runs Batted In	Doubles	Triples	Total Bases	Slugging  Percentage
1	Ken Griffey Jr.	SEA	125	487	148	95	.303	41	116	31	2	306	.628
2	Tino Martinez	NYY	128	492	148	85	.300	40	121	26	2	298	.605
3	Jim Thorne	CLE	117	397	115	85	.289	36	91	20	0	243	.612
4	Jay Buhner	SEA	128	446	106	84	.237	30	101	18	2	227	.563
5	Juan Gonzalez	TEX	100	403	115	61	.285	30	101	18	2	227	.563

 
The batting average is computed by dividing the number of hits by the number of at bats.  Compute each batting average to five decimal places and compare that answer to the statistics provided.
 

Are the batting averages rounded off as we normally do in math (raise the third digit by 1 if the fourth digit is 5 or larger, keep the third digit if the fourth digit is smaller than 5)?    If not, how are the averages rounded?

What result do you get if you multiply the number of at bats by the batting average?

If you knew someone had 422 at bats and had a batting average of .267, compute how many hits the batter would have to the nearest tenth? 
Would you round this value off with respect to 5, round it down, or round it up?  Explain your answer in relation to the way the batting averages were rounded.
 

Total bases is the sum of all the bases that the batter steps on as a result of his hit.  Therefore, a single hit results in 1 base, a double results in 2 bases, a triple results in 3 bases, and a home run counts as 4 bases.  Verify the total bases figure for Tino Martinez and Juan Gonzalez.

The slugging percentage is computed by dividing the total number of bases by the number of at bats.  Verify the percentage for each player by computing its value to five decimal places and comparing that answer to the actual figure.
 

If Jim Thorne could have stretched three doubles into triples, how much would that increase his total bases? 
How much would that increase his slugging percentage? 

How many additional bases would Jay Buhner have had to get in order to reach the slugging percentage of Tino? 

Which of these players had the greatest number of at bats per game? 

At their next game, which player has the greatest chance of hitting a home run?    Explain your reasoning.