Hot-hand Fallacy

The hot-hand fallacy is most commonly discussed within a context of sports or gambling. While making an incorrect prediction on the outcome of a sports game may not alone have negative consequences, often, people make bets based on the rationale influenced by the hot-hand fallacy. Once money becomes involved, the irrational and illogical belief of the hot-hand fallacy can begin to have more serious consequences.

If we make a bet on a sports game based on a successful run in the first ten minutes of the game, we are putting money down without considering all of the data. Just because a team or player is performing well in a short period of time does not counter their overall average statistics, but the hot-hand fallacy makes us believe it does. We are likely to make bets that reflect a logical fallacy and lose money as a result. 

Similarly, in gambling, when we have a winning streak, because of the hot-hand fallacy, we believe that our success will continue. In reality, most gambling games have to do with chance, and subsequent performance is completely independent from previous performance. We might get careless with our bets believing our good luck will continue and we can lose a lot of money in the process.

Fans are not the only people susceptible to the hot-hand fallacy when it comes to sports. Managers and coaches also often have to make decisions based on a small sample of observation, such as which players should be part of the starting line. Players need to decide which of their fellow teammates to pass to each game. The hot-hand fallacy affects not only those betting on the game, but may even impact the outcome of the game.

Moving away from sports and gambling, the hot-hand fallacy can come into play whenever we have to make assumptions or decisions based on a small sample of observations. For example, consider how politicians become delegates: they have to win a number of primaries. If a politician wins a few primaries in a row, we might be led to believe they will win the general election, even if this sample is not representative of the overall percentage of primaries they are likely to win. This can cause us to change our vote, or can perhaps even cause other candidates to drop out of the race, believing they don’t stand a chance.

If we are all impacted by the hot-hand fallacy, we are all making predictions about the future based on fallacious reasoning. We often behave according to other people’s predictions, such as deciding what to wear based on the weatherman’s forecast, or choose how to invest based on economists’ anticipated trends in the stock market, meaning that if those predictions are based on incorrect reasoning, we will find ourselves in sub-optimal outcomes. 

Since economic models are based on the belief that humans are rational, logical decision-makers, if we act according to the hot-hand fallacy, this model is inaccurate, and we have to revisit our assumptions about human behavior. 

As humans, we tend to try and find patterns and trends in order to make sense of the world. However, this tendency makes it difficult for us to understand chance because we pull together data into patterns that don’t necessarily exist. We are unable to properly understand randomness and chance, causing us to believe that independent events are actually dependent.¹

The hot-hand fallacy occurs in part because of the law of small numbers.² We often believe that small samples are representative of the larger samples that they are drawn from — that is in fact what all behavioral science experiments conclude, because it is too difficult to study the entire relevant population. However, these small samples often show patterns that don’t exist in large sequences.

Small numbers often don’t behave the way that large numbers behave. For example, it isn’t that unlikely that we would get five heads in a row in a coin toss when we only toss it five times. Yet, because we believe that there should have been more alterations, since there is a 50/50 chance of getting heads or tails, we think there is a hot streak. In fact, if we tossed the coin 100 times, we are likely to have an overall number of heads closer to 50%, but each smaller portion of the larger sequence will not necessarily reflect this.²

The hot-hand fallacy means we are making decisions based on faulty reasoning instead of logic and rationality. As a result, we find ourselves making sub-optimal decisions. We misidentify patterns and base following decisions on these made up trends.

Although the hot-hand fallacy is most commonly researched in sports and gambling contexts, it can impact day-to-day behavior as well. If we feel as though we have been lucky recently, we may think we’re on a lucky streak, and make decisions based on that feeling. We might buy a lottery ticket and pick numbers based on last week’s winning ticket, even though neither our past luck nor the past winning numbers actually affect our likelihood of winning the lottery.

The hot-hand fallacy can also impact decision-making when it comes to our consumer behavior, making it a dangerous heuristic. One study conducted by Joseph Johnson, professor of marketing, found that consumers are more likely to buy into a stock when it has been experiencing a positive earning trend.³ However, a previous trend is usually based on a small amount of data, such as the three-to-seven-day period in Johnson’s study and is not likely reflective of the overall pattern of stocks that involves many ups and downs. 

Since the hot-hand fallacy impacts so many of our decisions, by being aware of it, we might think twice before basing our decisions on a small amount of data like a winning streak.

However, it is difficult to overcome our instinctual cognitive heuristics, because we have to look somewhere for rationale when making decisions. To try to ensure that the hot-hand fallacy does not overshadow logical reasoning, we can try to look at larger sets of data when making predictions about future performance. 

For example, instead of placing a bet on a basketball game based on our favorite player’s three successful baskets in the first ten minutes of the game, we can remind ourselves that his average is much lower by looking at statistics that represent a much larger data set, like his season average, and make more intelligent predictions as a result. 

The hot-hand fallacy was first described by Amos Tversky, Thomas Gilovich and Robert Vallone, pioneers of behavioral science, in 1985.¹ The three behavioral scientists described the mistakes that we often make believing that we can make predictions about future outcomes based on a small sample of previously successful outcomes. They examined this heuristic with reference to the term “hot-hands” in basketball, where we believe a player that is making baskets will continue to do so.

As the researchers described, fans, coaches, and even players seem to believe that a player’s performance in a small period of time is a predictor for their performance in the rest of the game, and that it overshadows their overall performance statistics. For example, if a player makes their first three shots in a basketball game, but their average success rate is 75%, instead of realizing that the first three baskets were random successes, we are likely to think that player has “hot-hands” and will continue to be successful in subsequent shots. 

In order to try and understand what causes the hot-hand fallacy, Dr. Alan Castel, Professor of Psychology at UCLA, examined whether age impacted the likelihood that someone will fall victim to the hot-hand fallacy.⁴ 

There is a common belief that the older we get, the more we rely on heuristics for our decision-making. Castel therefore believed that older adults would be more likely to believe that a player is more likely to make a third successful shot after they had made two successful shots.

The study began by telling all participants ranging from 22-90 years old that usually, players in the NBA make around 50% of their shots. Next they were asked the following two questions:

1. Does a basketball player have a better chance of making a shot after having just made the last two or three shots than after having missed the last two or three shots?
2. Is it important to pass the ball to someone who has just made a few shots in a row?

Castel found that older participants were more likely to answer yes to both questions, suggesting they were influenced to a greater degree by the hot-hand fallacy.⁴ The study provides evidence that older people are more likely to rely on heuristic-based processing, even though their older age suggests that they are more likely to have more experience. This suggests awareness of the hot-hand fallacy might not be enough to counter it, as with age, we would assume people would have experienced more random sequence events.

As the hot-hand fallacy seems to lead to opposing beliefs to the gambler’s fallacy, Dr. Peter Ayton and Dr. Ilan Fischer, Professors of Psychology, wanted to better understand in what situations each one is more likely to occur.⁵

The researchers showed participants a computer-generated roulette wheel that would spin after a bet or prediction was made on what color the spinner would land on. When making their predictions, participants also had to rate their confidence levels as either “no confidence” or “strong confidence”. 

The researchers found that when there was a streak of a certain color, participants were likely to be influenced by the gambler’s fallacy and believe the next spin would result in the opposite color. However, the reports of confidence levels showed that a past run of successful predictions led to increased confidence levels in future predictions.⁵

From these results, Ayton and Fischer concluded that the hot-hand fallacy is more likely to influence decision-making when people are considering human performance, whereas gambler’s fallacy is more likely to impact gambling decisions that are based on inanimate mechanisms like the roulette wheel. 

However, the experiment does not reveal how likely we are to fall victim to the hot-hand fallacy in situations that involve inanimate mechanisms that we are not betting on. Participants in gambling situations may behave differently than people who are just trying to guess heads or tails in a coin toss.

What it is

The hot-hand fallacy describes our tendency to believe that a successful streak is likely to lead to further success. For example, if a basketball player has made three consecutive shots, we may believe he has a greater chance of making the fourth than is actually likely. 

Why it happens

The hot-hand fallacy occurs because we believe that small samples of data are representative of larger samples of data, when in reality, this is not the case. We often look for patterns in sequences and find it hard to properly understand randomness and chance, causing us to make predictions based on reasoning that is illogical. 

Example 1 - The hot-hand fallacy increases with age

Many psychologists believe that the older we get, the more we rely on heuristics in our decision-making processes. Supporting this theory, evidence has shown that older people are more likely to be misled by the hot-hand fallacy when it comes to predicting the future performance of basketball players when they’ve had a successful streak.  

Example 2 - The hot-hand fallacy has a stronger influence when people believe human skill impacts the outcome

The hot-hand fallacy is a heuristic that seems to contradict the gambler’s fallacy, because the hot-hand fallacy suggests future outcomes will be alike previous outcomes, whereas the gambler’s fallacy suggests future outcomes will be different to previous outcomes. The hot-hand fallacy may be caused due to increased confidence in our ability to predict what will happen when we have made a run of successful predictions. Alternatively, the gambler’s fallacy may be more likely to occur when we believe outcomes are only influenced by inanimate mechanisms, not human skill. 

How to avoid it

As the hot-hand fallacy is in part caused by the incorrect belief in the law of small numbers, we can try and make predictions based on larger data pools. By using more data, it is more difficult to ‘find’ a pattern that doesn’t actually exist, meaning that our decisions are less likely to be influenced by fallacious reasoning. 

Why We See Gambles as Certainties

In this article, our writer Stefan Kelly, who is pursuing a Master of Behavioral Science, explores the different biases that cause people to believe they can be confident in their gambling. He suggests people often mistake themselves as skilled gamblers, sometimes caused by the hot-hand fallacy. Kelly points out that awareness of gambling biases does little to deter gamblers or their habits, demonstrating that heuristics often overpower rationality.