Powerball — Statistical Analysis
Rigorous frequency tests across 2,061 recorded Powerball draws.
Per-Number Frequency vs. Expected
Each number should appear ~149.3× if the draw is perfectly uniform. Bars outside ±1.5σ are highlighted.
χ² Statistic
195.84
df = 68
p-value
<0.001
Strong signal (p < 0.001)
Expected / Number
149.3
across 2061 draws
Outliers (|z| > 1.5)
20
numbers outside 1.5σ
Overdue Numbers
The Powerball numbers that have gone longest without being drawn.
Gap Analysis
How many draws pass between consecutive appearances. A fair process follows a geometric distribution (dashed line).
Appearances
140
Observed mean gap
14.6 draws
Expected mean gap
13.8 draws
1 / (5/69)
Number 35's gap distribution closely matches the theoretical geometric curve — consistent with a fair draw.
Pair Co-occurrence
Expected ~8.8 times per pair by chance. Ratio = observed ÷ expected. Anything above ~1.5× warrants scrutiny.
Blue marker on each bar = expected frequency. Bar extending past the marker = above chance.
Jackpot Size Over Time
Amount per draw — resets to base after a winner.
Methodology
Hot & Cold NumbersHot and cold rankings compare each ball’s actual draw count against pure chance.
For each ball we compare its appearance count across every recorded draw in our archive against the count you would expect if every ball were drawn equally often, and express the difference as a z-score — the further from zero, the hotter or colder the number.
The chi-square test at the top of this page checks whether the frequency spread across all numbers is larger than random chance would produce. In a fair lottery you should usually see “no significant bias detected” — hot and cold streaks are exactly what randomness looks like over a few hundred draws.
Remember that every drawing is independent: a cold number is not “due,” and a hot number is not on a roll. These statistics describe history; they cannot predict the next draw.
Key Terms
- Hot Number
- Drawn more often than the all-ball average across recorded history.
- Cold Number
- Drawn less often than the all-ball average across recorded history.
- Z-Score
- How many standard deviations a ball’s draw count sits above or below the expected count.
- Chi-Square
- A test of whether the overall frequency spread differs from what randomness would produce.