A distinctive cluster of biases arises from misapplication of statistical reasoning. The gambler's fallacy holds that past random events affect future ones, so five reds in a row makes black feel "due," even though each trial is independent. The hot hand fallacy is its streak-positive cousin, often illusory though sometimes real in performance domains. Tversky and Kahneman's law of small numbers describes the broader error of treating small samples as representative of populations. Related is the disjunction fallacy, in which people underestimate the probability that one of several events will occur, the mirror image of the conjunction fallacy.
Regression to the mean is routinely misread as a causal effect: extreme observations naturally drift toward the average on subsequent measurement, so the "Sports Illustrated curse" (cover athletes performing worse after their appearance) is mostly regression, not a jinx. Similarly, regression to the mean makes punishment appear to "work" whenever it is applied after a peak performance, simply because the next performance is statistically likely to be lower regardless. Recognizing regression is essential for accurate causal inference.
The human mind is also an eager pattern-seeker. The cluster illusion, Texas sharpshooter fallacy, and apophenia all describe the tendency to see structure in randomness, drawing the target around the bullet holes or identifying a cancer cluster after the fact without a prior hypothesis. The narrative fallacy compounds this by weaving random events into a coherent story that overstates causal coherence, creating false confidence in future predictions. The illusion of explanatory depth reinforces this, with people believing they understand how things work in more detail than they do, until asked to explain. Statistical significance, hold-out test data, and asking "what would falsify the narrative?" are the standard counters.