Why does a run of luck or misfortune look like fate?
In folk usage, a run of consecutive days of misfortune is often called "bad luck", and a run of consecutive favourable events is often called "good luck" . That way of speaking is not wrong as experience: the streak is real, and the feeling of being ruled by it is real. What psychology asks is different: does the streak need a cause behind it, or is it just what a random sequence normally produces.
The short answer is that people expect a random sequence to switch direction more often than it actually does. So when a coin comes up heads ten times in a row, we feel there is "something" to it, while in probability terms such runs lie within the normal expectation of a long sequence. The sense of a rule arises from the gap between the sequence we imagine and the sequence that occurs.
But this article does not stop there. There is a considerable surprise: the basketball "hot hand", treated as a textbook example of cognitive illusion for more than thirty years, turns out to be real once the measurement is re-examined.
Which judgement shortcuts make streaks look meaningful?
Amos Tversky and Daniel Kahneman published in Science in 1974 one of the most influential papers in cognitive psychology, describing three judgement shortcuts commonly used under uncertainty: representativeness, availability, and anchoring and adjustment. That paper sets out the gambler's fallacy as a consequence of judging probability by how "representative" a sample is of a typical pattern, rather than by its actual probability.
In short, representativeness makes us think a short run must look "random" according to our mental image: alternating, balanced, not too repetitive. Availability makes us remember and trust examples that are easy to recall: three accidents in a row hit harder than three accidents scattered over three months. The gambler's fallacy is the flip side of the same mechanism: after many reds, we think "it is time for black", as if the coin knew how to balance its own history.
Kind of knowledge: UnprovenNot enough evidence. Someone has claimed it, but no source or study is strong enough to confirm it. The five labelsThe two continued to dig into this topic in their paper on the "law of small numbers", published in Psychological Bulletin in 1971. The core point: people believe a small sample reflects the whole accurately, while in reality small samples fluctuate wildly. This is the missing piece in the story of luck: if we have only a few observations, we still read a rule into them, and we do not take into account that a few observations are not enough to conclude anything.
Why do long runs in one direction look more suspicious than we think?
A point easily overlooked: in a true random sequence, runs in the same direction appear more often than intuition suggests. With ten coin tosses, the probability of at least one run of three identical faces in a row is quite high, much higher than ordinary feeling. So when a person has three misfortunes in a week, that may just be such a run, without needing a "bad year" behind it.
Two different questions need to be distinguished. One is the statistical question: is the streak unusual compared with a random model. The other is the experiential question: does the streak mean something to the person inside it. Cognitive psychology answers the first; the second belongs to how people assign meaning to their lives, and no test can replace that part.
Another study shows these biases can be measured and are linked to thinking style. In a study published in 2015, the authors used a "bias and shortcut" questionnaire made of problems taken from Kahneman and Tversky, including the gambler's fallacy, and noted that this questionnaire had lower internal reliability than a reflective thinking test, perhaps because its items are more diverse. The authors also noted that scores on this questionnaire correlated with the ability to detect statements that sound profound but are empty.
This is worth noting because it shows that the tendency to read rules into random streaks is not an oddity of a few people, but a measurable dimension that varies across individuals.
The hot hand: from the 1985 conclusion to the 2018 correction
Kind of knowledge: Folk beliefFolk belief. What people believe, avoid or pass on by word of mouth, recorded as a belief, not as a checked fact. The five labelsThe "hot hand" is the belief of players and spectators that a player who has just scored repeatedly will have a higher than normal chance of scoring on the next shot. This belief is widespread in basketball, to the point that it becomes part of how games are commented on.
In 1985, Thomas Gilovich and colleagues published in Cognitive Psychology a study testing that belief with actual shooting data, and concluded that people see random streaks as rule-bound streaks: the probability of a hit after a hit is no higher than after a miss, so the "hot hand" is a cognitive illusion. This conclusion entered textbooks and became the standard example of the brain reading rules where there are none.
In 2018, Joshua B. Miller and Adam Sanjurjo published in Econometrica an analysis showing that the measurement in the 1985 study was biased. Specifically, the way the sample was selected and the way conditional probabilities were calculated in the shooting data created a systematic bias that concealed the true effect. Once that bias is corrected, the same old data show a hot hand effect.
This is the most important point of the article: a conclusion considered solid for more than thirty years had to be revised, not because someone wanted to believe in the hot hand, but because the measurement method was flawed. This offers a lesson in humility to both sides: the sceptical side can also be hasty, and "it is only an illusion" is not a claim exempt from testing.
The table below summarises the main milestones and the data scope of each study. Cells the source does not state are left blank.
| Study | Year | Journal | Data scope | Main conclusion |
|---|---|---|---|---|
| Tversky and Kahneman, Heuristics and Biases | 1974 | Science | Three judgement shortcuts, including the gambler's fallacy | |
| Tversky and Kahneman, Law of Small Numbers | 1971 | Psychological Bulletin | People believe small samples reflect the whole accurately | |
| Gilovich et al., Hot Hand | 1985 | Cognitive Psychology | Shooting data | Hot hand treated as cognitive illusion |
| Miller and Sanjurjo, Surprised by the Hot Hand Fallacy | 2018 | Econometrica | Reanalysis of shooting data | 1985 measurement was biased; correcting the bias reveals an effect |
Can a streak ever be real?
Yes, and this answer does not contradict the above. There are at least three situations where a run of luck or misfortune is no longer a matter of reading rules into randomness.
First, the streak may be caused by a real factor we have not seen. A person with a dull backache may sleep poorly, then work less effectively, then run into more trouble over a few weeks. The streak is real, and the cause is real, only it is not "fate" but an ordinary chain of cause and effect.
Second, the streak may be created by belief itself. In their hot hand research, Miller and Sanjurjo show the effect is real in the data after correcting the measurement error. To be clear: this is a statistical effect in shooting data, not evidence for a supernatural force. The effect may come from small changes in behaviour, focus, or how the opponent defends. Belief changes behaviour, behaviour changes outcomes: that is a real causal loop, neither the system predicting correctly nor the effect not existing.
Third, the streak may result from selecting the sample after knowing the outcome. If we only remember the times a streak appeared and forget the times it did not, we will see streaks everywhere. This is the flip side of availability mentioned above.
Where the evidence is still missing
Kind of knowledge: UnprovenNot enough evidence. Someone has claimed it, but no source or study is strong enough to confirm it. The five labelsTo date, no recorded study exists on how Vietnamese people interpret a run of misfortune as a "bad year" or "bad luck". The results cited in this article all come from research conducted abroad, mainly with English-speaking participants, in laboratory settings or sports data. There is no basis to infer that Vietnamese people read streaks in the same way, nor any basis to say the opposite.
Moreover, the fact that the hot hand effect is real in basketball data does not mean every run of luck or misfortune in life has a hidden cause. Each case needs separate examination, and most cases in life do not have enough data to test.
Reading streaks without jumping to conclusions
Reading a run of luck or misfortune carefully involves a few simple steps. First, ask whether the streak is unusual compared with a random sequence of the same length, rather than asking what it means. Next, check whether we are remembering the times the streak appeared and forgetting the times it did not. Finally, separate the statistical question from the question of meaning: a streak may be entirely normal in probability terms and still be a heavy experience for the person inside it.
The hot hand story reminds us of something uncomfortable for both sides. The sceptical side sometimes concludes too quickly that an effect is an illusion, then has to revise when the measurement method is examined more closely. The side that believes in fate also sometimes concludes too quickly that a streak is a sign, when the streak lies within the normal expectation of randomness. Both are doing the same thing: reading a short run of data and assigning it a long story.
Related article: Why people see rules where there are none: from faces in clouds to repeating numbers in life. That article deals with the general mechanism of rule recognition; this one focuses on streaks of luck and the hot hand case.
