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(solution) On February 23, 1994, All-American basketball player Glenn Robinson of Purdue University scored...


On February 23, 1994, All-American basketball player Glenn Robinson of Purdue University scored 40 points in a game against Ohio State University. He shot the ball 45 times, scoring on 30 of them. The sequence of made and missed shots was as follows: μ, 1, 0, 0, 0, 0, 2, 1, 1, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 0, 1, 1, 1, M, 0, 1, 1 (a “2” corresponds to a score on a shot from the floor; a “1” corresponds to a score on a free throw; a “0” corresponds to a missed shot from the floor; and an “M” corresponds to a missed free throw). There is a long-standing debate in basketball about the existence of the so-called hot hand. Proponents of the “hot hand” claim that players experience periods of time when they “just can’t miss.” There is a similar theory of the “cold hand” which has the obvious meaning. Others argue that there is no “hot” or “cold hand,” just the natural runs of made and missed shots that would be expected in a random process. (a) Develop a model of Glenn Robinson’s shooting that could be used to predict his sequence of made and missed shots in n attempts if there is no such thing as a “hot hand.” Use the data given above to parameterize your model, and include a standard error for any parameter you estimate. (b) Develop a Markov chain model of Glenn Robinson’s shooting that could be used to predict his sequence of made and missed shots in n attempts if there is such thing as a “hot hand,” where the next shot depends on the last shot. Use the data given above to parameterize your model, and include a standard error for any parameter you estimate. (c) Develop a Markov chain model where the next shot depends on the last two shots. Use the data given above to parameterize your model, and include a standard error for any parameter you estimate. (d) In the Purdue vs. Ohio State game the longest run of shots Glenn Robinson missed was 4. How likely is a run of this length under each of your proposed models? Does this make you favor one model over the other? How might you test which model is best?  

 


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