Runs Test (Wald-Wolfowitz Test)
The runs test compares the number of consecutive groups of identical binary outcomes with the number expected under randomness. Too few or too many runs can indicate a departure from randomness.
THE IDEA
The runs test is used to determine if a sequence of dichotomous outcomes is random. A 'run' is a series of consecutive identical outcomes. The test computes the observed number of runs and compares it to the expected number under the null hypothesis of randomness. A significant deviation (too few or too many runs) suggests non-randomness. In a study of the Philadelphia 76ers, run tests were performed on individual player game records. For 727 player-game records with more than two runs, the observed and expected runs were compared. The test yielded a t-statistic with 726 degrees of freedom less than 1, providing no basis to reject the null hypothesis. This analysis detected no significant departure from randomness; it does not prove that the sequences were random.
When to use it
Evaluating randomness of shot outcomes in basketball to detect hot-hand phenomena
Analyzing streaks in stock market returns to assess market efficiency
Checking binary quality control data for patterns in manufacturing defects
Testing the randomness of coin flips or other simple random processes
FROM THEORY TO EVERYDAY LIFE
In practice
Philadelphia 76ers Player Performance Analysis
Researchers analyzed sequences of individual player successes and failures within games for both the 76ers and their opponents. With 727 records containing more than two runs, the observed number of runs did not significantly differ from the expected number, so this analysis did not detect a departure from randomness in the within-game sequences.
A MOMENT TO REFLECT
Put it to work.
Why is it important to test whether a player's performance streaks are random or systematic?
What would it imply if a player's sequence of successful and unsuccessful shots showed significantly fewer runs than expected?
How might the runs test be applied to detect cheating or bias in a sports competition?
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)