streakiness

Streakiness refers to the tendency of events to occur in clusters, forming streaks of consecutive successes or failures, rather than being evenly dispersed. It is observed in sports performances, financial returns, and other time series where observations show runs longer than expected under a simple random process.

In probability terms, a streak is a run of identical outcomes in a sequence of trials. For a sequence of independent trials with probability p of a successful outcome, the length of a run of successes is described by a geometric distribution with parameter q = 1 − p, with expected run length 1/p. The same applies to runs of failures with parameter p. Longer runs can occur by chance, but their frequency can reveal serial dependence or changes in underlying probability.

Statistical methods such as the runs test or autocorrelation analysis are used to detect streakiness or clustering in data. Streakiness can be modeled with Markov chains, autoregressive processes, or bursty processes that allow overdispersion and clustering beyond what is expected under independence.

In practice, streakiness is discussed in sports when teams or players alternate between extended periods of success and droughts. It is also relevant in finance, quality control, and web analytics, where clustering of outcomes matters for risk assessment and forecasting. Interpreting streaks requires caution, as small samples and selection effects can exaggerate apparent clustering.

See also: runs, serial correlation, burstiness, clustering, persistence.