sikwin: The Law of Small Numbers in Sports Betting

Sikwin argues that many people fall into the trap of making faulty judgments due to their belief in what’s known as the “law of small numbers.” Essentially, individuals tend to draw conclusions based on small sample sizes and incorrectly assume that the same patterns will hold true for larger samples. For instance, if a small sample shows random distribution, people may wrongly assume that a larger sample will also display random distribution.

Conversely, if a small sample displays a noticeable pattern (like getting 9 heads out of 10 coin tosses), observers might assume that this pattern will be replicated across the entire population. This assumption suggests a bias in the outcome of the coin toss, a phenomenon known as “associated disease.”

In uncertain situations, people often resort to opportunistic thinking, such as relying on the law of small numbers. Kahneman and Tversky refer to these as “opportunistic heuristics.” A common example is the representativeness heuristic, where individuals estimate the probability of an event based solely on similar events that have occurred in the past.

The gambler’s fallacy is another example of the representativeness heuristic. This stems from a deep-seated belief in the law of small numbers. Kahneman and Tversky note that at its core, the gambler’s fallacy reflects a misunderstanding of the fairness of chance. Those who fall prey to the gambler’s fallacy believe that if a random event deviates from its expected outcome, it will soon revert back to that outcome, thus evening out any discrepancies.

Sports bettors, in particular, are prone to these cognitive biases, often misinterpreting probabilities based on small samples of bets. This lack of understanding of event randomness and predictive skills often leads to long-term financial losses.