The Winning Edge: Predicting Results 2

SCORE Mathematics

Standards Connections

The Winning Edge: Probability in Basketball

Lesson 3: On The Line: Predicting Results; Extending the Probability

Introduction: Only 2 seconds remain in the big basketball game, and the Up-state College Tigers are behind by one point. However, your opponent has been "whistled" for a technical foul and Up-state will receive two free throws. You're the coach. Which player should you send to the line to give you the best chance of winning? What is the probability that that player will win the game, tie the game or lose the game? This is one is a series of on-line interactive pages exploring probability and statistics in real life.

Prior Knowledge: Calculating percentages from given ratios; concept of conditional probability and how to use it to solve for rules of basketball, Basketball rules.

Grade Levels: 10th - 12th (This Lesson); 6th through 12th grades for the entire series.

Objective: Students will calculate the probability of outcomes based upon a large number of discrete events (i.e. endgame free-throw attempts).

Resources: Student worksheet 4 (html) or Student worksheet 4 (pdf), javascript-enabled browser, pencil, calculator, if desired.

Process: Start Here: Click Starting Page
    First -- Students will use an on-line simulation to generate endgame free-throw results for 5 selected players on a fictional basketball team.
    Second -- They will then compile the results and calculate the probability of tying, of winning, or of either winning or tying for each of the five players.
    Lastly -- Students will use their findings to decide which "player" was most effective at winning the game.

Learning Advice:
Due to the random function of the computer simulation, results for any given set of trials for any given player will vary -- just like in real life. Checking the accuracy of the results thus requires matching the data from the simulation (games won versus games played) with the resulting winning percentage.
If only one "station" computer is available, it is suggested that students be grouped in teams of 5, each member would then choose a different player and would do the "shooting", recording and calculating of winning percentages for his/her selected player, the group would then combine results. The lesson can be completed (worksheet 4) either as a group or individually.

Evaluation: Completeness of the endgame data; accuracy of the derived probabilities; student conclusions based upon their data

Extensions: Other lessons in the series
Basketball-related sites

Conclusion: "Which of the 5 players whom you chose would you most want to have "On the Line" shooting free throws to decide the outcome of the game? Why?"

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California Academic Content Standards:

Grade 8-12:
Probability and Statistics
1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.