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Frequency lab · free analysis

Powerball frequency analysis

Calibrated against 3,777 historical draws of powerball. Methodology: Pearson χ², Kolmogorov-Smirnov, 5-fold cross-validation, Cover (1989) sharing-risk adjustment.

Number frequency vs uniform expectation

Each square shows a main ball. Colour encodes the standardised residual: blue = drawn less than chance predicts, red = more.

Observed vs expected (F4)

Within noiseBonferroni anomaly: 1Diagonal = uniform expectation. Gray band = ±1.96σ Poisson noise.

Each dot is one ball. The solid diagonal is observed = expected. The dashed band is the ±1.96σ Poisson noise envelope (variance scales with expected count). Dots outside the band beyond the Bonferroni threshold are highlighted red. The fan-out of dots at higher expected counts is exactly what i.i.d. uniform draws produce.

Heatmap view

Time window:
Total balls drawn
780
Most drawn
#28 (24)
Least drawn
#38 (5)
Mean |residual|
0.78σ
Less than expected
More than expected

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Draws since last appearance

How many draws have passed since each number last appeared. The dashed line marks each number's historical mean gap — bars taller than the line are above average, shorter are below.

Geom(1/69) · DKW 95% band (Massart) · current gap range 0 – 66
Empirical CDF excursions: 64 gap value(s) outside the band

Under independent uniform draws, current-gap should follow Geom(1/69) (the black curve). The shaded band is the Dvoretzky-Kiefer-Wolfowitz 95% simultaneous CI (bandwidth = ±16.3%). The blue step is the observed empirical CDF. Gaps within the band — including extreme "overdue" values — are exactly what randomness produces. They are not evidence that a number is "due".

Per-number current gap (G1)

Sort by:
1
66
2
32
3
7
4
9
5
35
6
15
7
17
8
0
9
11
10
19
11
19
12
23
13
13
14
25
15
3
16
16
17
11
18
4
19
7
20
26
21
13
22
1
23
29
24
2
25
6
26
49
27
4
28
24
29
10
30
2
31
1
32
10
33
8
34
50
35
7
36
5
37
0
38
14
39
12
40
0
41
3
42
5
43
13
44
0
45
13
46
3
47
3
48
36
49
10
50
27
51
4
52
1
53
15
54
29
55
22
56
1
57
9
58
28
59
14
60
5
61
12
62
8
63
5
64
2
65
0
66
37
67
1
68
4
69
25
Expected gap (if uniform)
~17 draws
Most overdue
#1 · 66 draws
Longest historical gap
2443 draws
Average mean gap
16.5

Reminder: overdue numbers are not more likely to be drawn next. Each draw is independent. This chart is for pattern observation, not prediction.

Uniformity across 16 games

Pearson χ² test results for every calibrated game in the warehouse. Games marked Format-mixed failed only because their historical record includes ball-range changes — when filtered to a single format, every major game passes.

Sort by:
GameDrawsMain χ² pSpecial χ² pWindowαVerdict
ny_take5_evening10,6150.8530—50010Uniform
pl_lotto6,5450.1240—50010Uniform
euromillions5,2000.00000.0000102Format-mixed*
br_megasena4,4990.0000—102Format-mixed*
powerballviewing3,7770.00000.10715002Format-mixed*
tx_lotto_texas3,7440.0000—50010Format-mixed*
ca_lotto_6493,6650.4758—50010Uniform
cash4life2,9490.94370.464250010Uniform
ca_lottomax2,7500.0000—5000.5Format-mixed*
ny_lotto2,5750.3609—50010Uniform
fl_lotto1,9890.1060—50010Uniform
megamillions1,9500.00000.005120010Format-mixed*
sg_toto1,4260.0000—20010Format-mixed*
tr_loto1,3270.0000—5000.5Format-mixed*
korean_6459600.9562—50010Uniform
uk_lotto5360.9116—50010Uniform

* Format-mixed (8 games): non-uniformity is fully explained by ball-range changes during the game's history (e.g. Powerball 5/55 → 5/69 in 2015). When filtered to a single format, all games pass at p > 0.05.

Strategy backtest — top 3

Walk-forward EV (per $2 ticket) across 100 held-out draws × 200 picks each, Cover sharing-risk adjusted.

hot streak
-1.809
win rate 4.1% · n=20,000
pattern hunter
-1.817
win rate 3.9% · n=20,000
quick mix
-1.818
win rate 3.9% · n=20,000

All strategies have negative mean EV (house edge is structural). Differences between strategies are within sampling noise for most games — choose by distribution shape preference, not EV optimisation.

Open Predictions Lab

Position-specific frequency (demo)

Pick-3 style simulation: 3 positions × 10 digits. Cell color = standardized residual against uniform null per position.

3 positions × 10 values · 30 cells · 0 above Bonferroni threshold (expected ~1.5 by chance)
Residual:
±3σ
0123456789P1P2P3P1·0 · obs 99 · exp 100.0 · z -0.10P1·1 · obs 114 · exp 100.0 · z +1.40P1·2 · obs 119 · exp 100.0 · z +1.90P1·3 · obs 90 · exp 100.0 · z -1.00P1·4 · obs 131 · exp 100.0 · z +3.10P1·5 · obs 95 · exp 100.0 · z -0.50P1·6 · obs 103 · exp 100.0 · z +0.30P1·7 · obs 91 · exp 100.0 · z -0.90P1·8 · obs 94 · exp 100.0 · z -0.60P1·9 · obs 94 · exp 100.0 · z -0.60P2·0 · obs 101 · exp 100.0 · z +0.10P2·1 · obs 101 · exp 100.0 · z +0.10P2·2 · obs 84 · exp 100.0 · z -1.60P2·3 · obs 95 · exp 100.0 · z -0.50P2·4 · obs 100 · exp 100.0 · z +0.00P2·5 · obs 96 · exp 100.0 · z -0.40P2·6 · obs 117 · exp 100.0 · z +1.70P2·7 · obs 88 · exp 100.0 · z -1.20P2·8 · obs 113 · exp 100.0 · z +1.30P2·9 · obs 105 · exp 100.0 · z +0.50P3·0 · obs 104 · exp 100.0 · z +0.40P3·1 · obs 85 · exp 100.0 · z -1.50P3·2 · obs 98 · exp 100.0 · z -0.20P3·3 · obs 109 · exp 100.0 · z +0.90P3·4 · obs 92 · exp 100.0 · z -0.80P3·5 · obs 101 · exp 100.0 · z +0.10P3·6 · obs 111 · exp 100.0 · z +1.10P3·7 · obs 93 · exp 100.0 · z -0.70P3·8 · obs 103 · exp 100.0 · z +0.30P3·9 · obs 104 · exp 100.0 · z +0.40

Each cell shows the standardized residual for one (position, value) pair. Orange borders mark cells exceeding the Bonferroni-corrected threshold for 30 simultaneous tests. Under a fair RNG, ~1.5 false positives are expected.

Hot-cold trend (demo)

Trailing-window z-scores for the top-5 most variable digits over 500 simulated draws.

5 tracked digits · trailing window 100 draws
35012

Each line tracks one digit's z-score in a trailing window of 100 draws. The shaded band is the null-envelope reference. Lines that stay within the band are consistent with uniform draws. The y-axis is "trailing-window z-score" — not "hotness".

Pairwise co-occurrence (demo)

10×10 digit co-occurrence matrix from 1,000 simulated draws (5 digits per draw).

45 pairs analyzed · 45 above Bonferroni threshold (expected ~2.3 by chance)
Residual:
±3σ
01234567890123456789Same number — not applicable0–1 · obs 100 · exp 250.0 · z -9.490–2 · obs 121 · exp 250.0 · z -8.160–3 · obs 106 · exp 250.0 · z -9.110–4 · obs 115 · exp 250.0 · z -8.540–5 · obs 93 · exp 250.0 · z -9.930–6 · obs 100 · exp 250.0 · z -9.490–7 · obs 119 · exp 250.0 · z -8.290–8 · obs 120 · exp 250.0 · z -8.220–9 · obs 114 · exp 250.0 · z -8.601–0 · obs 100 · exp 250.0 · z -9.49Same number — not applicable1–2 · obs 98 · exp 250.0 · z -9.611–3 · obs 105 · exp 250.0 · z -9.171–4 · obs 108 · exp 250.0 · z -8.981–5 · obs 114 · exp 250.0 · z -8.601–6 · obs 87 · exp 250.0 · z -10.311–7 · obs 126 · exp 250.0 · z -7.841–8 · obs 104 · exp 250.0 · z -9.231–9 · obs 129 · exp 250.0 · z -7.652–0 · obs 121 · exp 250.0 · z -8.162–1 · obs 98 · exp 250.0 · z -9.61Same number — not applicable2–3 · obs 122 · exp 250.0 · z -8.102–4 · obs 131 · exp 250.0 · z -7.532–5 · obs 116 · exp 250.0 · z -8.472–6 · obs 103 · exp 250.0 · z -9.302–7 · obs 118 · exp 250.0 · z -8.352–8 · obs 126 · exp 250.0 · z -7.842–9 · obs 121 · exp 250.0 · z -8.163–0 · obs 106 · exp 250.0 · z -9.113–1 · obs 105 · exp 250.0 · z -9.173–2 · obs 122 · exp 250.0 · z -8.10Same number — not applicable3–4 · obs 122 · exp 250.0 · z -8.103–5 · obs 121 · exp 250.0 · z -8.163–6 · obs 89 · exp 250.0 · z -10.183–7 · obs 112 · exp 250.0 · z -8.733–8 · obs 102 · exp 250.0 · z -9.363–9 · obs 124 · exp 250.0 · z -7.974–0 · obs 115 · exp 250.0 · z -8.544–1 · obs 108 · exp 250.0 · z -8.984–2 · obs 131 · exp 250.0 · z -7.534–3 · obs 122 · exp 250.0 · z -8.10Same number — not applicable4–5 · obs 125 · exp 250.0 · z -7.914–6 · obs 107 · exp 250.0 · z -9.044–7 · obs 112 · exp 250.0 · z -8.734–8 · obs 125 · exp 250.0 · z -7.914–9 · obs 111 · exp 250.0 · z -8.795–0 · obs 93 · exp 250.0 · z -9.935–1 · obs 114 · exp 250.0 · z -8.605–2 · obs 116 · exp 250.0 · z -8.475–3 · obs 121 · exp 250.0 · z -8.165–4 · obs 125 · exp 250.0 · z -7.91Same number — not applicable5–6 · obs 97 · exp 250.0 · z -9.685–7 · obs 115 · exp 250.0 · z -8.545–8 · obs 103 · exp 250.0 · z -9.305–9 · obs 105 · exp 250.0 · z -9.176–0 · obs 100 · exp 250.0 · z -9.496–1 · obs 87 · exp 250.0 · z -10.316–2 · obs 103 · exp 250.0 · z -9.306–3 · obs 89 · exp 250.0 · z -10.186–4 · obs 107 · exp 250.0 · z -9.046–5 · obs 97 · exp 250.0 · z -9.68Same number — not applicable6–7 · obs 118 · exp 250.0 · z -8.356–8 · obs 96 · exp 250.0 · z -9.746–9 · obs 129 · exp 250.0 · z -7.657–0 · obs 119 · exp 250.0 · z -8.297–1 · obs 126 · exp 250.0 · z -7.847–2 · obs 118 · exp 250.0 · z -8.357–3 · obs 112 · exp 250.0 · z -8.737–4 · obs 112 · exp 250.0 · z -8.737–5 · obs 115 · exp 250.0 · z -8.547–6 · obs 118 · exp 250.0 · z -8.35Same number — not applicable7–8 · obs 111 · exp 250.0 · z -8.797–9 · obs 121 · exp 250.0 · z -8.168–0 · obs 120 · exp 250.0 · z -8.228–1 · obs 104 · exp 250.0 · z -9.238–2 · obs 126 · exp 250.0 · z -7.848–3 · obs 102 · exp 250.0 · z -9.368–4 · obs 125 · exp 250.0 · z -7.918–5 · obs 103 · exp 250.0 · z -9.308–6 · obs 96 · exp 250.0 · z -9.748–7 · obs 111 · exp 250.0 · z -8.79Same number — not applicable8–9 · obs 114 · exp 250.0 · z -8.609–0 · obs 114 · exp 250.0 · z -8.609–1 · obs 129 · exp 250.0 · z -7.659–2 · obs 121 · exp 250.0 · z -8.169–3 · obs 124 · exp 250.0 · z -7.979–4 · obs 111 · exp 250.0 · z -8.799–5 · obs 105 · exp 250.0 · z -9.179–6 · obs 129 · exp 250.0 · z -7.659–7 · obs 121 · exp 250.0 · z -8.169–8 · obs 114 · exp 250.0 · z -8.60Same number — not applicable

Upper triangle shows co-occurrence residuals; lower triangle is mirrored at 40% opacity for symmetry. Diagonal is hatched (same-number pairs). Orange borders mark Bonferroni-significant cells. Under uniform draws, ~2.3 false positives expected for 45 pairs.

Methodology

  • 3,777 powerball draws normalised across 1992 to 2026
  • Pearson χ² with Wilson-Hilferty p-value approximation. Format changes (number-range expansions) noted with an asterisk; per-format χ² results in the authenticated methodology page.
  • Predictive parameters: 5-fold walk-forward CV minimising held-out NLL.
  • References: Cover (1989), Stern (1992), Suetens-Tyran (2016), Abrams-Garibaldi (2010).