Hot Hand Effect and Gamblers Fallacy

Abstract

This study sought to investigate the possibility that causal belief and alternation rate are factors that affect a subject’s tendency to continue or end a run following a sequence. The sample consisted of 69 psychology students who were requested to determine whether they believed the run will continue (hot hand effect) or whether it will end (gamblers fallacy). Participants were assigned randomly to either a control, roulette or basketball group. We argue that the ‘hot hand effect’ could occur when sequences involve that of human performance e.g. basketball, but where subjects expect that outcomes are due to an inanimate mechanism and random causes e.g. a roulette game, we propose the gamblers fallacy. We also anticipated that a high alternation rate regardless of the belief was a contributing factor for the subjects to less likely continue the run than when given a low alternation rate. Our directional hypotheses were supported as it was found that long runs of success/sequences invoke the hot hand fallacy whereas chance mechanisms, which invokes the gamblers fallacy, as well as high alternation rates makes one less likely to continue the run.

Tendency to Continue the Run: A Product of Causal Belief, Alternation Rate or Both?

Almost every decision we make involves uncertainty in some way. The heuristic and biases approach to decision making outlined in the work of Tversky and Kahneman (e.g., Kahneman, Slovic, & Tversky, 1982; Gilovich, Griffin, & Kahneman, 2002) has focused on the validity of causal beliefs. Studies have shown that people are more likely to continue a sequence when, an event is not random and the outcome reflects human performance (Ayton & Fischer, 2004). The induction that the sequence should continue (positive recency) was observed by Gilovich, Vallone and Tversky (1985). They defined the “hot hand” in basketball as the belief that during a particular period a player's performance is significantly better than expected, on the basis of a player’s overall record and streak of hits (Burns & Corpus, 2004). However, when subjects are asked to identify sequences in random chance events e.g. roulette, the tendency is to predict the opposite of the last event (Ayton & Fischer, 2004). Kanheman and Tversky (1972) illustrate that people consistently judge the more representative event to be the more likely, whether it is or not. This notion of the representativeness heuristic has been utilised to explain trends in sequential alternation rates which has generated the central thesis of this experiment. This relates to the analysis of expectation and prediction of random events and the role of causal belief and sequence alternation rate upon prediction.

Analytical research conducted by Kahneman and Tversky (1972) examined the degree to which intuitive predictions caused important external factors to be ignored, resulting in the unjustified confidence of intuitive predictions. The study of representativeness heuristic and subjective randomness was continued by Ayton and Fischer (2004) who explored two opposing expectations of positive and negative recency. They concluded that the “hot handed fallacy” was driven by animate causes, while conversely, the “gambler’s fallacy” resulted out of inanimate causes.

The present study was undertaken using a sample of undergraduate psychology students. We sought to investigate the possibility that causal belief ...

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The present study was undertaken using a sample of undergraduate psychology students. We sought to investigate the possibility that causal belief and alternation rate are factors that affect the subject’s tendency to continue or end a run following a sequence. It was predicted that the hot hand effect (i.e., the likelihood to continue the run) would occur when sequences involved that of human performance. But where subjects expect that outcomes are due to an inanimate mechanism and random causes we hypothesise the gamblers fallacy. It was also anticipated that a high alternation rate, regardless of the participant’s causal belief, was a contributing factor for the subjects to less likely continue the run than when given a low alternation rate.

Method

Participants

The participants were undergraduate students studying a Bachelor of Psychology degree at the University of New South Wales. Seventy-five students, who were aged between 17 and 55 were used, M = 21.46 and SD = 6.724. Gender was not of even distribution, 48 females were used. The 72 students were split into three groups, (n = 24).

Design

The study examined the extent to which three different causal beliefs and several different alternation rates would affect one’s tendency to continue the run. The design of our experiment was 3 x (9) with causal beliefs being (basketball x roulette x control) and an alternation rate of (.1, .2, .3, .4, .5, .6, .7, .8, .9.) as the two independent variables. Our dependent variable was the tendency to continue the run which was measured by converting the number of times participants predicted whether the graph would go “up” or “down”. The results of all tests were analysed to draw final conclusions of what caused the tendency to continue the run and to demonstrate whether these assumptions have any grounds in regards to the basis of representation.

Materials

The experiment was undertaken on a computer based program designed to record the expectation and prediction of random events based on causal belief and alternation rate. Students assigned to the basketball and roulette groups were presented with a short cover story before commencing the experiment. The control group received no prior explanation. The program contained a series of 36 graphs, four of each alternation rate, which were presented in a random order and students were asked to predict the next result. Following this, they were instructed to respond to the graph patterns by indicating their prediction on a confidence bar scale from 1-10.

Procedure

Participants entered the computer laboratory and were randomly assigned to one of three groups (A, B or C). This divided the class into 3 different causal belief groups. All participants were first instructed to complete basic personal information (e.g. age, sex, etc) and the causal belief was displayed to each participant on their individual computers as they were given a cover story. Students were to indicate whether they thought the graph was going to continue “up” or “down”. They were to rate their confidence level on a bar scale of 1-10 inclusive, 1 representing the least confidence whilst 10 would measure as the most confident prediction.

Results

To analyse the present data an analysis of variance (ANOVA) was used. The data gathered revealed an overall tendency to continue the run when sequences involved that of human performance. The basketball causal belief group scored a mean of 0.51 and the random chance roulette group scored 0.41. These scores revealed a ‘real’ significant difference which supported our hypothesis as p<.05. This significant statistical difference between the groups can be seen on the graph below, thus the hot hand and gambler’s fallacy is made apparent. As Figure 1 indicates (see below) the tendency to continue the run in both the control and roulette groups were similar, with the control scoring a mean of 0.42, reflecting little significance between them.

Figure 1.

Figure 1. Mean and standard error of causal beliefs – basketball, roulette and control.

The ANOVA revealed that run length – alternation rate, was a significant determinant of the tendency to predict the same outcome as before i.e. tendency to continue the run regardless of the belief [F(1,69) = 269.07, p<.05]. As Figure 2 indicates, our hypotheses were directional as there is a significant descending linear trend due to alternation rate. The higher the alternation rate, the less likely subjects were to continue the run.

Figure 2.

Discussion

The results of the experiment confirmed our hypothesis in which the hot hand effect would occur when sequences involved that of human performance and when the task was nonrandom. Furthermore, the study confirmed the notion that the gambler’s fallacy was invoked due to an inanimate mechanism and random causes. Consistent with the hypothesis the study displayed that alternation rate was a significant contributing factor for subjects to less likely continue the run. Our hypothesis did not account for the close statistical difference, for the tendency to continue the run, between the mean of the control and roulette groups. It can only be speculated as to why both groups scored such similar means. Maybe the control group perceived the task as totally random hence generating outcomes similar to those produced by the random inanimate cause i.e. roulette.

Burns and Corpus’s 2004 research is consistent with our empirical findings. Burns and Corpus (2004) show that the hot hand fallacy and gambler’s fallacy appear to depend on how random/nonrandom the events are judged to be. Perhaps the findings presented in this study indicate that when presented with random sequences people tend to decide what the data is representative of, thus producing positive or negative recency. Ayton and Fischer (2004) propose that the hot hand and gambler’s fallacy are cued when subjects decide which previous life experience the data most likely resembles. Ayton and Fischer’s (2004) study revealed that subjects were more likely to continue a sequence when presented with low alternation rates. This supports and is consistent with our experiment as they attribute this continuation due to skilled human performance and conclude that sequences with high alternation rates are less likely to continue a sequence due to inanimate chance processes.

One limitation of our experiment was that the participants did not experience the actual events themselves in a real life situation. People’s reaction to sequences of events they experience live, does not only depend on how random and inanimate the generating mechanism is, but also on other factors such as previous experience and memory, learning and the environment (Burns & Corpus, 2004). For instance being amongst a crowd at a basketball game (due to the atmosphere of team support, clapping and overall mood) could strongly influence a person’s decision as to whether they think a player may continue the streak and score. These variables are not accounted for in our computer based experiment. Researchers therefore need to devise more effective means of measuring causal belief bias if we wish to further our knowledge and understanding of this phenomenon.

References

Ayton, P., & Fischer, I. (2004). The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness?. Memory & Cognition, 32 (8), 1369-1379.

Burns, B. D., & Corpus, B. (2004). Randomness and inductions from streaks: “Gamber’s fallacy” versus “hot hand”. Psychonomic Bulletic & Review, 11 (1), 179-184.

Gilovich, T., Griffin, D., & Kahneman, D. (2002). Heuristics and Biases: The Psychology of Intuitive Judgment. Cambridge University Press.

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

Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases, Cambridge University Press.

Kahneman, D., & Tversky, A. (1972). Subjective Probability: A Judgment of Representativeness. Cognitive Psychology, 3, 430-454.