Is a Basketball Free-Throw Sequence Nonrandom? A Group Exercise for Undergraduate Statistics Students

Figures & data

Figure 1. Sequence of 200 consecutive basketball free-throws by a single shooter. Black circle = success, open circle = failure. Sequence begins at upper left, and each row is read from left to right.

Figure 2. Frequency distribution of the number of runs, u, obtained by randomly rearranging the data shown in Fig. 1 (10,000 replicates).

Table 1. Observed transitions in the series of free-throws shown in Fig. 1.

		To
		Success	Failure
From	Success	97	42
	Failure	42	18

Table 2. Expected number of transitions under the null hypothesis that each free-throw is an independent event.

		To
		Success	Failure
From	Success	97.09	42.91
	Failure	41.91	18.09

Table 3. Outcome of free-throw trials broken into successive blocks of 20 (using data shown in Fig. 1).

Successes	Failures
9	11
15	5
16	4
14	6
14	6
13	7
17	3
18	2
9	11
15	5

Table 4. Transitions in the simulated series of free-throws shown above.

		To
		Success	Failure
From	Success	105	34
	Failure	34	26