Conditional probability
How does knowing that something has already happened change the chance you assign to what happens next?
In plain words
Conditional probability is the chance of one event occurring given that another event has already occurred. It is read as the probability of the first event given the second, and it is estimated by counting only the cases in which the second event happened.
Why it matters
Markets carry history: a strong run, a volatility spike or the reaching of a level all narrow the set of past cases a trader is reasoning about. The relevant question is rarely how often an outcome occurs in general, but how often it occurs after this particular setup, which usually leaves a much smaller sample.
In a real week: BTC, week of 3 June 2019
BTC rose in each of the four prior weeks listed, by 20.68%, 16.94%, 5.73% and 1.32%, with prior_weeks_down at 0 and prior_weeks_up at 4. In the week of 3 June 2019 it fell 12.58%, closing at 7628.13, with a return percentile of 13.0 against 68 weeks of history. Conditioning on four straight up weeks did not prevent a large down week, and the number of such setups on record is too small to attach a stable rate to.
A common mistake
Assuming an outcome becomes likelier or less likelier purely because of the sequence before it. Conditioning narrows the comparison set; it does not point to a direction, and a handful of instances cannot measure the revised probability.