Record Breaking News |
Sportscasting
Applications of Mathematics 9 |
Lesson Idea by: Cindy Botnen
School District #23 (Central Okanagan)
The next time you watch a sportscast on television, listen carefully. You will hear the sportscaster using lots of numbers to report the top sports news of the day. Some of those numbers are scores, and some are statistics.
Sportscasters don't use just any old statistics in their reports. They have to be able to interpret these statistics in a way that will make sense and support their sports commentary. If sportscasters use numbers indiscriminately, they run the risk of confusing or boring their audience.
"You can have statistics overload -- where you give out too much information," says Scott Morrice, a sportscaster for CJDC Television in Dawson Creek, B.C. "You have to maintain a balance."
The sportscaster gets his statistics from two main sources: news services, or "newswires" as they're sometimes called, and the statisticians employed by the various sports leagues.
Morrice recently worked on an interesting story about the prospect of a long-standing baseball record being broken. All season long, the St. Louis Cardinal player, Mark McGwire, hit homer after homer. With four games remaining, McGwire had 56 home runs. One of the greatest records in baseball is the one Roger Maris set when he hit 61 home runs in one season.
It's big news whenever a record looks like it might be shattered. Yet, Morrice couldn't tell whether the record was likely to be shattered just by looking at the number of home runs alone. In cases like this, a sportscaster has to use statistics in order to determine the "probability" of the record being broken. The only way to find out the probability is to do some mathematical calculations first. Without using statistics, the sportscaster will miss out on the biggest sports story of the season.
Some other factors are also worth noting. The average sports report is less than a minute long - the sportscaster doesn't have the time to recite an endless string of numbers. Plus, it doesn't do the viewers any good to be told, "According to the newswire, McGwire averages one home run for every 9.31 times at bat. A player averages 3.46 times at bat during a game." They want to hear the sportscaster's interpretation of those numbers, and they want it fast, exciting and accurate.
Create your own sports statistics. Set up a makeshift baseball diamond inside your classroom or school using a soft foam ball, a small stick (try a ruler) and a target. Form teams of four or five people. Following formal batting rotation, take turns hitting the ball at the target. Place the target far enough away to make hitting it a little bit of a challenge. In your notebook, record the number of times you are at bat and the number of times you hit the target. Record target hits as home runs. Continue batting until everyone has 61 "home runs". You have now replicated Maris's record.
As a group, answer the following questions:
- How many times at bat did it take you to hit 61 home runs?
- If you had the same number of at bats per game as McGwire, how many games would you have played? A player averages 3.46 times at bat during a game.
(Hint: divide the number of times you were at bat by the average)
- What was your average number of home runs per times at bat?
(Hint: divide the number of at bats by 61)
- How many more times at bat would it take you to get 100 home runs, if you maintain the same average?
(Hint: Calculate the difference between your total home runs and 100. Then multiply that number by your average number of home runs per times at bat).)
- With your team members, discuss why statistics are kept in sports. How do coaches use the statistics to help individual players and the team as a whole? What kinds of statistics are kept in baseball? What connection do statistics have with money? How can you use statistics to make predictions?
Now you're the sportscaster. Prepare a brief report for tonight's sportscast on McGwire and his chances of beating Maris's record. If he is going to break the record he'll need to get to bat. What is the likelihood he will get to bat enough times to break the record?
Use your knowledge of mathematics to estimate McGwire's chances. Make a guess before you do your calculation. Working with a partner, discuss the likelihood that McGwire will break the record. Record your prediction in your mathematics notebook.
Next, work with your partner (use your calculator) to calculate the number times McGwire is likely to get "up-to-bat" during the remainder of the season. Also calculate the number of home runs he is likely to get.
Is it enough to break the record? Remember, there are only four games left in the season and statistics show that McGwire hits a home run every 9.31 times at bat.
Check your problem solving strategy against the following:
Using an average of 3.46 "at bats" per game, you must multiply the average by the number of remaining games (3.46 x 4=13.84). Then for every 9.31 times at bat, he averages one home run. So, you must divide the number of times "at bat" by the home run average to arrive at the estimated number of home runs. (13.84 / 9.31 = 1.50 home runs)
Therefore, it is unlikely that McGwire will break the record. McGwire will likely hit one or two home runs before the end of the season, which means he'll finish the season with 57 or 58 home runs -- which isn't enough to tie or break the record of 61 home runs.
Challenge yourself by answering the following questions:
1. How many times at bat would McGuire need to get the six home runs he needs to break the record?
2. How many more games is that?
Professional hockey teams also record statistics for all their games. Using the NHL statistics below, and assuming there are 80 games in a regular hockey season, make the following predictions:
1. How many games is each team likely to win?
2. How many games is each team likely to win at home and on the road?
3. How many goals will each team score (GF)?
4. Try making up other predictions using these statistics.
(The acronyms below stand for: games played, wins, losses, ties, points, goals for, goals against, games won-lost-tied at home and games won-lost-tied on the road.
PACIFIC DIVISION |
GP |
W |
L |
T |
PTS |
GF |
GA |
HOME |
ROAD |
COLORADO |
20 |
10 |
4 |
6 |
26 |
60 |
48 |
5-1-4 |
5-3-2 |
LOS ANGELES |
20 |
9 |
7 |
4 |
22 |
71 |
55 |
6-4-0 |
3-3-4 |
ANAHEIM |
20 |
8 |
7 |
5 |
21 |
54 |
55 |
3-5-3 |
5-2-2 |
EDMONTON |
19 |
5 |
10 |
4 |
14 |
44 |
65 |
3-5-1 |
2-5-3 |
SAN JOSE |
20 |
6 |
13 |
1 |
13 |
51 |
66 |
3-7-1 |
3-6-0 |
VANCOUVER |
20 |
4 |
13 |
3 |
11 |
49 |
73 |
2-5-2 |
2-8-1 |
CALGARY |
20 |
3 |
13 |
4 |
10 |
51 |
69 |
3-7-1 |
0-6-3 |
(Note to Teachers: This activity can be extended to create other sports statistics-based projects that may satisfy the outcomes in other Applied Academics curricula, e.g., Technical and Professional Communications and Information Technology. For example, have your students create additional problems that require using sports statistics to make predictions and answer interesting sport-related questions. To find more statistics, visit The Sports Network (TSN) Web page at: www.tsn.ca/. Your local or provincial newspaper is another easily accessible and economical source of sports statistics.
| Course/Grade: Applications of Mathematics 9 |
Curriculum Organizer(s):
Statistics and Probability
|
Curriculum Sub-organizer(s):
Demonstrate an understanding of the role of
probability and statistics in society. |
Prerequisites:
Basic math skills
|
Resources:
· Calculator
· Nerf or foam ball
· Ruler, bats
· targets |
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