Psychology 458/558
Judgment and Decision Making
Prof. Bertram Malle
Fall 1995

Lecture 10: Nov 2
Perception of risk and chance

Post-script to SDT

Many heuristics in human judgment have a lenient criterion (i.e., producing many hits but also many false alarms). For example, when making first impressions we are quick to arrive at a judgment about the other person ("she is smart," "he is nice"); even though we may thus achieve numerous "hits" (quick correct character assessments), we also accrue several false alarms. These false alarms can be flattering if the judgment is positive but very costly if the judgment is negative . We should therefore adopt a stricter criterion when making negative judgments. Lenient criteria are also the basis of the "fundamental attribution error," confirmation bias, the representativeness heuristic, and many more.

Risk perception

In prospect theory, risk was defined as a non-certain prospect (0 < p < 1); in research on people's risk perceptions, risk is vaguely defined as uncertain dangers. One purpose of this research is to find out exactly how people define and perceive risk; another purpose is to determine the consequences these perceptions have for the individual's quality of life as well as for social and economic decisions of companies and political institutions.

What do we already know?

People underestimate medium to high probabilities but overestimate small probabilities
People overestimate the probability of conjunctive events (e.g., worst-case scenarios in which a chain of unlikely events must develop) but underestimate the probability of disjunctive events (e.g., cumulative risks of unwanted pregnancies or car accidents over a long period of time)

These effects influence people's perceptions of statistics about risky events or activities. Other influences are controllability and familiarity, as described by Slovic (1987). With unknown, possibly dreadful risks, people have an extremely strict criterion of safety--they want to avoid "false alarms" at all costs (e.g., accepting an energy source that may not be completely safe). As with EUT, the multiplication of costs/benefits and probabilities does not describe people's feelings: a highly improbable but disastrous possible outcome influences people far more than a cold calculation of expected risks would suggest: A p = .00001 chance of 100,000 people dying is considered much worse than a p = 0.1 chance of 10 people dying. This is why airplanes, nuclear plants, genetic engineering, etc. are perceived as more risky than their expected fatalities suggest. Scenarios in which many people die at once (plane crash) or die a dreadful death (from radiation) are more feared than repeated scenarios in which a few people die (car accidents) or die quickly (electrocution).

Perception of chance and randomness

As the chapter in Plous (1991) describes nicely, people often see meaning in random patterns and consider patterns random only when they appear "chaotic" (which usually means deviating from true randomness because of more alterations and pattern changes). The ability to detect meaning in seemingly random patterns can be of great help--for empirical researchers who inspect their data, for FBI agents who study a serial murderer, for therapists who deal with a non-textbook case, or for politicians who have to understand public sentiments. Here, the cost/benefit ratios favor a lenient criterion of meaning detection, thus creating many hits but also several false alarms (which clever researchers know how to spot).

The "hot hand" myth. Even though your personal feelings may be very resistant to this finding, all available research indicates that "hot hands"--i.e., streak shooting deviating from chance runs--do not exist. Of course, this does not mean that athletes shoot randomly; it also does not mean that confidence does not improve performance. It only means that the hit streaks in basketball (or baseball) are perfectly normal and expected within the framework of random hit sequences given a certain hit rate.

In other words, hitting one, two or more in a row does not make it more likely that one hits the next one again; success does not breed success on such a local level. If a player feels he or she has a good day, this confidence may lead to a higher hit rate than usual; but the apparent confidence stemming from a few hits in a row does not lead to a higher likelihood of hitting the next one. The probability of hitting any given shot is always the same--namely, the athlete's hit rate.

What people "see" as streak shooting may just be a local random fluctuation (recall that coin tosses sometime look like this: hTTTTThThhh, which people perceive as non-random), or it may be bad coverage by the opponent's defense, or it may be an above-average hit rate for the day, etc.

All the data collected so far provide zero evidence for above-chance streak shooting. Three hypotheses, however, have not yet been tested:

Pros might be at the limit of their shooting capacity and may thus not benefit from success-breeds-success mechanisms; beginners or amateurs, however, might show streak shooting beyond chance because they are still susceptible to success-breeds-success. But why, then, do people "see" the hot hand in pros??
After hitting a few in a row, a player with p(hit) = .55 may attempt (due to confidence) more difficult shots than usual, for which the expected probability is not .55 but .35. Having gained confidence the player now hits these difficult ones with a probability of .55--which (in Gilovich & Tversky's analysis) looks like his average performance but is in fact above the expected performance for those difficult shots.
After hitting a few in a row, a player with p(hit) = .5 may attempt (due to confidence) more shots than usual; his absolute hit rate may be constant, such that he hits 2 out of his 4 attempts in the next two minutes. Without the confidence boost, however, he would have attempted only 2 in the same time span; in Gilovich & Tversky's analysis, no confidence effect would be found, but the team definitely benefits from the player's higher shooting rate--which produces four points rather than two points in two minutes. This mechanism would also explain why viewers "see" a streak--they perceive more shoots per time unit and it therefore appears as if the player hit more shots, which is only true in a relative sense (within a certain time period) but not in an absolute sense (hits per attempts).

Finally, even if hot hands are only in the eyes of the beholder and thus a myth, the cost of this myth is minimal--a lenient criterion may well be justified because it increases the joy of watching sports.