PETERSON-MIDDLEBURY

I did not do as much with streaks in sports as I had originally planned. On the other hand, our general discussion of the Kahneman-Tversky ideas on representativeness, availability and anchoring was very popular.

As for runs, proper, I had a very successful in-class experiment based on the Schilling (1990) article in references. I left the room while half the class generated a sequence of 100 H's and T's by tossing a coin; the other half generated coin toss sequences mentally. When I returned I was able to distinguish all but one on the basis of the longest run of heads or tails (only one of the mental sequences contained a run of length at least 5).

Students found the statistical analyses in the Chance articles hard to get through (this was my experience with the journal in other aspects of the course as well, notably the DNA fingerprinting discussion). Of the Tversky-Gilovich statistical tests described in the preceding section, I was comfortable discussing only the first (conditional probability of hits following various hit-miss patterns).

**SOURCES**

**News Stories (chronological)**

Simon, Julian L. 'Batter's slump' and other illusions, *The Washington Post*, 9 August 1987.

Gleick, James . `Hot hands' phenomenon: a myth? *The New York Times*, April 19 1988, C1 &C8.

Callahan, Tim. Secrets of streaks and slumps. Time, June 6 1988, p74.

Peters, Barbara McGarry. How to balance reason and intuition. *The Washington Post*, 23
October, 1990.

Specter, Michael. Record hot readings in 1980's boost global-warming theory. *The
Washington Post*, January 13 1990.

Kerr, Richard A. ``Global temperature hits record again", *Science*, Vol 251, 18 January l991.

Kohn, Alfie. Folk wisdom is all wet. *The San Francisco Chronicle*, March 15 1992.

**Discussion articles**

Tversky, A. and Gilovich, T. (1989). ``The cold facts about the hot hand in basketball."
*Chance* **2 (1)**, 16-21.

Statistical evidence does not support fans', players' and commentators' description of the hot hand. Length and frequency of runs of successful shots do not exceed what would be expected under simple chance models of random sequences.

Gould, Stephen J. (1989) The streak of streaks. *Chance* **2 (2)**, 10-16.

Extols Joe DiMaggio's 56-game hitting streak in the 1941 baseball season as a transcendent phenomenon. Some discussion of general work of Kahneman and Tversky (Linda problem, etc.)

Larkey, Patrick D., Smith, Richard A. and Kadane, Joseph B. (1989). It's okay to believe
in the 'hot hand.' *Chance* **2 (4)**, 22-30.

A rebuttal of the Tversky-Gilovich Chance article.
Tversky, A. and Gilovich, T. (1989). ``The `hot hand': statistical reality or cognitive
illusion?" *Chance* **2 (4)**, 31-34.

Tversky and Gilovich's rejoinder. A spectacular revelation: Vinnie Johnson's magnificent ranking hinges on one 7 for 7 streak that, upon review of game videos turns out not to have happened-he missed once in the middle of his ``streak"!

Short and Wasserman (1989). Should we be surprised by the streak of streaks? *Chance*
**2 (2)**, 13.

Hooke, Robert (1989). ``Basketball, baseball and the null hypothesis." *Chance*
**2 (4)**, 35-37.

Argues that the null hypothesis should be that the hot hand phenomenon does exist.

What do economists know about the stock market? The Journal of Portfolio Management, Winter, 1991.

Case, Gene. DiMaggio's streak stricken? *The Nation*, August 26/September 2, 1991, p225.

Forthofer, Ronald N. (1991). Streak shooter - the sequel. *Chance*, **4 (2)**.

Albright, Christian (1992). Streaks and slumps (Take me out to the ball game: a statistical
analysis of major-league batting tendencies). *OR/MS Today*, April 1992, 94-95.

**Technical Articles**

Gilovich, T., Vallone, R. and Tversky, A. (1985). The hot hand in basketball: on the
misperception of random sequences. *Cognitive Psychology***17**, 295-314.

The original research article on basketball. Popular accounts of this fueled the controversy.

Gerber, Hans U. and Li, Robert S-Y. (1987) The occurrence of sequence patterns in repeated
experiments and hitting times in a Markov chain. *Stochastic Processes and Their Applications*,
101-108.

Li, Robert S.-Y. (1980). A martingale approach to the study of occurrence of sequence patterns
in repeated experiments. *Annals of Probability***8**, 1171-1176.

Schwager, Steven J. (1983). ``Run probabilities in sequences of Markov-dependent trials."
*Journal of the American Statistical Association* **78**, 168-175.

Schilling, Mark F. (1990). The longest run of heads. *The College Mathematics Journal***21**,
196-207.

The least technical article in this section. Provided idea for the ``classroom challenge" (in which instructor distinguishes toss sequences invented by students from those generated by actual coin-tossing). Recurrence relation approach to computing probabilities of runs of various lengths in sequences of tosses.

Tong, Y. L. (1985). A rearrangement inequality for the longest run, with an application to
network reliability. *Journal of Applied Probability* **22**, 386-393.

Zaleskas, Kristine Mary (1991). Where have you gone, Joe DiMaggio? A mathematical exploration of success runs in sports. Senior Thesis, Harvard University.

Introductory discussion of success runs in Bernoulli trials, generating functions. Modifies simple Bernoulli model to take into account the difficulty of each shot given where on the floor it was taken.

**General References**

Kahneman, D, Slovic, P. and Tversky, A. (Eds.) *Judgement Under Uncertainty: Heuristics and
Biases.* Cambridge University Press, 1982.

Feller, William. *An Introduction To Probability Theory and its Applications.*