Understanding Powerball Statistical Analysis
The default analysis covers main Powerball draws under the 5/69 + 1/26 format first used on October 7, 2015. Earlier formats have different ball pools and appear in separate rule-era tables above. The included period and N describe the eligible records used, not a claim that every scheduled draw is present.
What Are Hot and Cold Numbers?
The hot list contains the ten most frequently drawn white numbers in the included period; the cold list contains the ten least frequent. Ties are ordered by number. These are historical rankings, not tests of statistical significance or predictions of the next draw.
Frequency Analysis and Expected Counts
N is the number of valid, unique included draws. Each contributes five distinct white balls and one red Powerball. For the current format, expected appearances per white number are N × 5/69, and expected appearances per red number are N/26. All numbers in each pool are included, even if their observed frequency is zero. Historical tables use the pool sizes applicable to their own periods.
The Powerball Number
The red Powerball comes from a separate pool. It can have the same number as a white ball. The current-format red chart contains numbers 1-26 only; older red pools belong in their historical era tables. Double Play is a separate drawing and is excluded from the default statistics.
Overdue Numbers and the Gambler's Fallacy
Gaps are calendar days from a number's last included appearance to the latest included draw date. The table ranks numbers with recorded appearances. A long absence does not make a number due: past results do not change the probabilities in the next independent draw.
Distribution Analysis: Odd/Even, High/Low and Sums
These charts use the same included draws as the frequency tables. Odd/even and high/low shares count individual white-ball appearances; the sum chart counts one five-ball sum per draw. They describe the observed sample and do not recommend a winning pattern.
How Draws Are Included
Results are selected by rule period and drawing type, checked for valid dates and ball values, then deduplicated before any frequencies are counted. Identical results count once regardless of white-ball order. Conflicting results for a draw date are excluded until resolved. Source coverage and any exclusions are shown beside the statistics.