According to Wikipedia, this is an informal fallacy known as the "Post hoc ergo propter hoc"
Latin for "after this, therefore because of this" (faulty cause/effect, coincidental correlation, correlation without causation) – X happened, then Y happened; therefore X caused Y.
This fallacy becomes the foundation of the anecdote described in the OP. Thus it creates a "regression fallacy"
Ascribing cause where none exists... failing to account for natural fluctuations.
Or perhaps you can apply the informal fallacy known as the "Gambler's fallacy"
the incorrect belief that separate, independent events can affect the likelihood of another random event. If a fair coin lands on heads 10 times in a row, the belief that it is "due to the number of times it had previously landed on tails" is incorrect.
This can be paired with the "hot hand fallacy" which uses the same flawed reasoning to say that the pattern of a series increases the likelihood of it continuing. In this case, "If a fair coin lands on heads 10 times in a row", the belief is that it will continue to land on heads again. Or the fact that a person has guessed correctly what face would be up 10 times, means that they are more likely to be correct the 11th time.