As Bernardin (2010) points out, some irrational thinking is the result of trying to come up with logical explanations for something that is simply due to chance. For example, when people see a pattern of behavior, they want to generate a logical explanation for that pattern (Bernardin). People reason that the pattern could not be due to chance because chance is random and therefore does not follow patterns. However, people are wrong: Chance, especially in the short run, can create patterns. The following exercises, inspired by simulations performed by Bernardin, can help your students understand that chance can produce patterns that do not look random and that chance may be responsible for variations in human behavior.  The simulations overlap so you should not have the same students do both Simulation A and Simulation B.


 

 

 

Simulation A

 

Instructions: Pretend that you are playing a basketball game. In this game, flipping a coin represents taking a shot, getting a “heads” represents making that shot, and getting a “tails” represents missing that shot. In addition, assume that you will take 5 shots in every quarter of play and that you will take 2 shots in every overtime (OT) period. Thus, your first 5 flips will represent the 5 shots you would take in the first quarter.

To get started, get a coin and flip it 5 times. Record the number of heads in your first 5 flips in the table below. Specifically, put the number of heads in the “Heads (Makes)” row of the “1st quarter: 1st 5 attempts” column—the square with a blank in it. Flip the coin 5 more times and record the number of heads for those flips in the “Heads (Makes)” row of the “2nd quarter: 2nd 5 attempts” column.  Keep flipping and recording until you have results for the 3rd quarter, the 4th quarter, and the two overtime (OT) periods. Then, add up the total number of heads and put that result in the “Heads” row of the “Total” column. Finally, fill in the percentage of heads (the “shooting percentage”) by filling in all the cells in the shaded “Shooting percentage” row. For obtaining the shooting percentage, you may find the following information helpful: For each quarter, 0 heads = 0%, 1 head = 20%, 2 heads = 40%, 3 heads = 60%, 4 heads = 80%, and 5 heads = 100%. For the overtimes, 0 heads = 0%, 1 head = 50%, and 2 heads = 100%). For the “Total” column, 8 heads = 33%, 9 heads = 37%, 10 heads= 42%, 11 heads = 46%, 12 heads = 50%, 13 heads = 54%, 14 heads = 58%, 15 heads = 63%, 16 heads = 67%.

 

 

 

1st

 quarter

(1st 5 flips)

2nd quarter

(2nd 5 flips)

3rd quarter

(3rd 5 flips)

4th quarter

(4th 5 flips)

1st OT

(2 flips)

2nd OT

(2 flips)

Total

Heads (“Makes”)

 

 

 

 

 

 

 

 

 

 

Shooting percentage

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

1.      In what quarter or overtime period did you have the highest shooting percentage? In what quarter or overtime period did you have the lowest shooting percentage?

2.      Can you form a general rule about how likely your coin is to “make” a basket?

3.      Would it make sense to try to explain any particular “miss” or “make”?

4.      Imagine your data reflected the actual shooting percentages of LeBron James in a playoff game. How would the announcers explain the variations in LeBron’s performance?

5.      What have you learned from this exercise that you could use for

a.       Accepting the newspaper’s explanations for why the stock market dropped 100 points yesterday?

b.      Accepting explanations for why your roommate has been in a bad mood three days in a row?

c.       Accepting the statement that Duke was the best college basketball team in the country last year because they won the NCAA tournament, beating Butler 54-52 in the finals?

d.      Understanding that to be scientific rather than superstitious, one must understand how random events affect behavior?

 

 


Simulation B

 

 

Instructions: Form two teams: Team Jacob and Team Edward. Play a simulated basketball game by flipping coins. Team Jacob will go first. From then on, take turns. If the coin comes up heads, your team earns 2 points; if it comes up tails, you get no additional points. You will record your results on the score sheet at the bottom of the page by recording your cumulative score in the appropriate boxes. To see how you record your score, look at the following example.

 

 

If Team Jacob started with a “tails,” whereas team Edward started with  a “heads,” your  score sheet should look like this:

 

 

1st quarter

2nd quarter

3rd quarter

4th quarter

Total

J

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If, on the second possession, both team Jacob and Team Edward “scored” (both got a “heads” when they flipped a coin), the sheet would look like this:

 

 

 

1st quarter

2nd quarter

3rd quarter

4th quarter

Total

J

0

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E

2

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If, on the third possession, team Jacob scored but Team Edward did not, the sheet would look like this:

 

 

 

1st quarter

2nd quarter

3rd quarter

4th quarter

Total

J

0

2

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E

2

4

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If the other team makes a run, you may call a 30-second timeout to try to stop that run-but make a note of what the score was when you called the timeout.

Now, begin your game and record your scores in the box below. Start by letting Team Jacob flip first. Then, alternate flips until the end of the game.

 

 

Official Scoring Sheet

 

1st quarter

2nd quarter

3rd quarter

4th quarter

Total

J

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

1.      In what quarter did your team’s offense do best? If this had been a real game (e.g., between the Celtics and the Lakers) and a team had done well in that quarter, how would announcers or sportswriters have explained that outcome?

2.      In what quarter did your team’s defense do best?  If this had been a real game and a team had done well in that quarter, how would announcers or sportswriters have explained that outcome?

3.      Did you call a time out? Did the time out seem to help? If so, how can you explain the success of your time out?

4.      Explain any streaks that occurred in the game. How much of a role did momentum play in the game’s outcome?

5.      If you lost, how would you explain your loss? If you won, how would you explain your win?

6.      What have you learned from this exercise that you could use for

a.       Accepting the newspaper’s explanations for why the stock market dropped 100 points yesterday?

b.      Accepting explanations for why your roommate has been in a bad mood three days in a row?

c.       Accepting the statement that Duke was the best college basketball team in the country last year because they won the NCAA tournament, beating Butler 61-59 in the finals?

d.      Understanding that to be scientific rather than superstitious, one must understand how random events affect behavior?