Numbers drawn at random look exactly like this

Every ball, against chance

bar — how many times the number has been drawn · tick — how many times chance expects. The tick sits in the same spot on every cell, and every bar ends near it. That is the whole finding.

The Powerball — its own drum, never mixed with the whites

Select any number for its record against chance.

The spread is what chance produces

The most-drawn white ball has come up 124 times and the least-drawn 75, against an expected 100.9 for every ball (SD 9.7). A spread of that size is not a property of the balls — it is what 1393 fair draws of 5-from-69 produce by themselves. The extremes below carry their expected values beside them, because a count without its expectation reads as a pattern that is not there.

Droughts, in this dataset

Every figure below counts draws present in this dataset, not draws held — the record has 5 disclosed fills (named in the methodology), and a drought is only as complete as the record it is measured in. A long absence says nothing about the next draw; past absence changes no probability.

The most frequent pair, honestly

White balls 21 and 32 have appeared together 15 times, against 5.9 expected for any one pair. That sounds remarkable until the maximum is put against its own null: across 2,346 competing pairs, a perfectly fair machine produces a top pair of 16 in the median run (95th percentile 18, 99th 20; 2,000 seeded replicates). 94% of fair runs reach or beat the pair observed here. The top of 2,346 counts is an artifact of taking a maximum, not a relationship between balls.