Expected Value on the Target: Pick the Zone That Pays Best

Each student estimates their probability of success by tossing beanbags into hoops at three distances with different point values and calculates the expected value of each zone. Then they play a team game where they must decide which zone to aim for based on their data and the score.

How to play

1. Explain relative frequency as an estimate of probability, and expected value as points times probability of success (4 min).
2. In each lane, chalk three hoop zones: at 4 m it's worth 1 point, at 7 m it's 3 and at 10 m it's 6 (2 min).
3. Data phase: in pairs, each student tosses 10 beanbags at each zone; the partner records hits on the worksheet (10 min).
4. Each student calculates their probability and expected value for each zone and decides which one is best for them; compare choices across the class (4 min).
5. Team game in groups of four: five rounds where each player picks a zone before tossing; in the last round the trailing team can call double points on the far zone (8 min).
6. Wrap-up: check whether teams that followed their data scored more, and when taking a risk pays off (2 min).

Rules

• Nobody enters the hoop area until the whole lane has thrown.
• Beanbags are tossed underhand.
• The toss is redone if the thrower steps on the line.
• Record data honestly: one fake entry ruins the whole team's strategy.

Variations

Adaptations

• Limited mobility: toss seated from the same line, with hoops moved closer to keep the same gap between distances.
• Visual impairment: the hoop has a sound source, or a partner claps from the center of the target.
• Math difficulties: use a two-way table that gives the expected value based on hits.

Learning goals

• Estimate probabilities from relative frequencies in a motor task.
• Make tactical decisions based on expected value and game score.
• Analyze the balance between risk and reward in sports.

Equipment for a class of 25

• beanbags: 30
• hoops: 18
• cones: 12
• worksheets: 28
• chalk: 4

Teacher tip

Connect it to the three-pointer versus the two-point shot in basketball: it's the same logic used in professional analytics. Prepare worksheets with the table already drawn.

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