The binomial model provides a way to inspect binary outcome claims. Its independence and constant-probability assumptions must be stated.

What the source establishes

NIST’s binomial reference defines a model for counts of two-outcome trials with a fixed success probability. Applying that model to a trading record requires assumptions about the trials, including independence; those assumptions are not established by a platform’s win-rate label. NIST/SEMATECH — Binomial Distribution ↗

In an explicitly illustrative independent model with a 60% win probability on each trial, five specified consecutive losses have probability 0.4 to the fifth power, or 1.024%. This is a calculation under a model, not a measured frequency for a trading system.

What the distinction changes

The word specified is important. The chance of finding a five-loss run somewhere within a long record is different from the chance that the next five trials all lose. Treating these as the same event understates how many opportunities a long history creates for a cluster.

A loss cluster also does not imply that the next independent trial is due to win. Conversely, real trading outcomes may share market drivers and violate independence. Either error can turn a simple probability calculation into a misleading claim about a product.

Questions for the next review

State the event, observation horizon and assumptions before quoting a run probability. Compare the model with the complete dated record, including fees and omitted outcomes. Do not use a hypothetical percentage as evidence that a strategy has a verified edge.