Recent theoretical research has shown that the assumptions that both laypeople and researchers make about random sequences can be erroneous. One strand of research showed that the probability of non-occurrence of streaks of repeated outcomes (e.g., HHHHHH) is much higher than that for a more irregular sequence (e.g., HTTHTH) in short series of coin flips. This tallies with human judgments of their likelihood of occurrence, which have conventionally been characterized as inaccurate and heuristic-driven. Another strand of research has shown that patterns of hits and misses in games like basketball, traditionally seen as evidence for the absence of a hot-hand effect, actually support the presence of the effect. I argue that a useful way of conceptualizing these two distinct phenomena is in terms of the distribution of different sequences of outcomes over time: Specifically, that streaks of a repeated outcome cluster whereas less regular patterns are more evenly distributed.