Financial Fallacies Explained: The Hot Hand Fallacy and the Gambler’s Fallacy

February 2023 | By Vicki Bogan Investor Behavior Investor Insight

Making decisions based only upon recent information compared to all of the available data can often lead investors to think current trends are the best predictors of what will happen next.

When watching sports, particularly basketball, it is common to hear announcers and commentators talk about players having a "hot hand." And sports fans often assume that a particular player having a streak of successful shots has an increased probability of making the next shot, irrespective of the player's historical shooting percentage. However, studies have shown that a basketball player's probability of making a shot, conditional on him having made the previous shot, is not generally greater than usual. A paper published in Cognitive Psychology, found that the outcomes of consecutive basketball shots from professional NBA players are independent.¹ Further, they even found evidence that consecutive shots from these NBA players are slightly negatively related. When people unjustifiably form expectations about what is going to happen next based upon what has just happened, this is commonly called the hot hand fallacy. Economists refer to this fallacy as extrapolation bias.

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Despite evidence against the existence of the hot hand, research has repeatedly shown that individuals can be influenced by extrapolation bias. One study found that casino gamblers bet more after winning than after losing.² In other words, they bet more after winning because they believed that their chance of winning again was greater than before. Another study showed that basketball betting markets do indeed believe in the hot hand, and that the hot hand fallacy is also at play when people think about buying and selling in financial markets.³

Economists and financial analysts assess financial markets using what economists call "base rate information" — full historical stock market data. Everyday investors do not usually have access to such information, and instead base their judgments about risk and return on "singular information" — data which is more recent or more easily obtained. Making decisions based only upon recent information compared to all of the available data can often lead investors to think current trends are the best predictors of what will happen next.

For example, during a bull market, people will expect stocks to continue to earn high returns. In a bear market, they will think low returns will continue. This is extrapolation bias at work. You have probably experienced this countless times with clients a client calls during a bull market and wants to buy, or they call during a downturn and are anxious to sell. As a financial professional, it is important to recognize that extrapolation bias may be driving these clients to request exactly the opposite of what you would advise them to do.

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So what should you do as a financial professional? With respect to the hot hand fallacy, it is important to get clients to focus on the bigger market picture and not just what has been happening in markets recently. One tip would be to provide clients with a deeper historical perspective, using the base rate data. A few weeks, months, or quarters of statistics and price information may not be sufficient. Providing a fuller picture of the historical value of an asset can be helpful. In addition, reminding clients to plan and schedule rebalancing of their portfolios can also eliminate the opportunity for them want to buy or sell rashly based upon very recent market trends.

Financial professionals are generally not as susceptible to the hot hand fallacy with regard to financial markets. You are trained to monitor markets in order to provide the best possible advice to clients. However, this familiarity with historical market data can lead you to be influenced by another type of bias called the gambler's fallacy. The gambler's fallacy is the tendency to overweight the probability of an event because it has not recently occurred. The gambler's fallacy can lead individuals familiar with base rate market information to view long streaks as being unlikely. You may feel that a recent run-up in the price of a stock is not consistent with the actual historical distribution. Thus, you may be overly prone to predict reversals in stock prices.

Using brain mapping experiments, researchers have found neurological-based evidence of the gambler's fallacy. One study found that individuals evaluate random events such that they overweight the probability of an event, if it has not recently occurred.⁴ In field experiments, Croson and Sundali observed that casino roulette wheel gamblers bet in accordance with the gambler's fallacy.² For example, if black had not come up in a while on the roulette wheel, bettors would think that black was due to come up and would bet more on black. Making assessments based on a limited sample size like this leads to the gambler's fallacy. As a financial professional, when formulating investment advice, you need to keep the gambler's fallacy in mind so that you do not predict a trend reversal too quickly.

Both the hot hand fallacy and the gambler's fallacy belong to a group of biases that economists classify as "representative heuristics." (Heuristic is a fancy term for rule of thumb.) These heuristics involve making assessments based upon a small number of data points. Assuming that a small sample reflects the full distribution of outcomes in the same way that a large sample does, can lead to mistakes. In general, to avoid making these types of forecasting mistakes, it is important to take into account the size of the sample when drawing conclusions.

Key Takeaways

The hot hand fallacy or extrapolation bias is the unwarranted extrapolation of past trends in forming forecasts.
The gambler's fallacy is the tendency to overweight the probability of an event because it has not recently occurred.
While clients are often more influenced by the hot hand fallacy, financial professionals need to be more aware of the gambler's fallacy and its effects on their advice.
With respect to the hot hand fallacy, when advising clients it is important to get them to focus on more complete market data and not just recent market trends.
When developing investment advice for a client, keeping the gambler's fallacy in mind can decrease the tendency to overweight the probability of an event because it has not recently occurred.

¹Gilovich, Thomas, Vallone, Robert, & Tversky, Amos. (1985). "The Hot Hand in Basketball: On the Misperception of Random Sequences." Cognitive Psychology, 17, pp. 295-314.

²Croson, Rachel, & Sundali, James. (2005). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos" The Journal of Risk and Uncertainty, 30 (3), pp. 195-209.

³Camerer, Colin F. (1989). "Does the Basketball Market Believe in the 'Hot Hand'?" The American Economic Review, 79 (5), pp. 1257-1261.

⁴Xue, Gui, Lu, Zhonglin, Levin, Irwin P., & Bechara, Antoine. (2011). "An fMRI Study of Risk-Taking Following Wins and Losses: Implications for the Gambler's Fallacy?" Human Brain Mapping, 32, pp. 271-281.

The views and opinions expressed herein are those of the author, who is not affiliated with Hartford Funds. The information contained herein should not be construed as investment advice or a recommendation of any product or service nor should it be relied upon to, replace the advice of an investor's own professional legal, tax and financial advisors.

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About The Author

Dr. Vicki Bogan

Professor and Director of the Institute for Behavioral and Household Finance (IBHF) at Cornell University

The mission of the IBHF is research and education in the areas of behavioral finance and household finance with the goal of better understanding and modeling financial behavior.