Powerball — Statistical Analysis

Rigorous frequency tests across 2,036 recorded Powerball draws.

Per-Number Frequency vs. Expected

Each number should appear ~147.5× if the draw is perfectly uniform. Bars outside ±1.5σ are highlighted.

χ² Statistic

202.14

df = 68

p-value

<0.001

Strong signal (p < 0.001)

Expected / Number

147.5

across 2036 draws

Outliers (|z| > 1.5)

20

numbers outside 1.5σ

z > +1.5σ (above expected)
z < −1.5σ (below expected)
within ±1.5σ

Gap Analysis

How many draws pass between consecutive appearances. A fair process follows a geometric distribution (dashed line).

Number:

Appearances

139

Observed mean gap

14.5 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 ~8.7 times per pair by chance. Ratio = observed ÷ expected. Anything above ~1.5× warrants scrutiny.

1
32
49
21 observed2.42×
2
22
32
21 observed2.42×
3
37
39
21 observed2.42×
4
41
59
20 observed2.30×
5
37
44
20 observed2.30×
6
20
39
19 observed2.19×
7
3
16
19 observed2.19×
8
23
47
19 observed2.19×
9
30
48
19 observed2.19×
10
21
32
19 observed2.19×
11
30
59
19 observed2.19×
12
37
53
18 observed2.07×
13
19
21
18 observed2.07×
14
5
28
18 observed2.07×
15
7
24
18 observed2.07×
16
6
36
17 observed1.96×

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.