With 5 balls drawn from 69 each Powerball draw, any specific pair has roughly a 0.43% chance of appearing together — meaning across 1,500+ draws, most pairs have shared a ticket fewer than 7 times. Some pairs have appeared more than twice that. Here is the complete co-occurrence ranking.
The leading pair in Jackpot Teller's co-occurrence analysis sits notably above the ~6–7 expected appearances — a count that looks striking until the combinatorics show it is consistent with ordinary sampling variance. Most lottery frequency articles rank individual balls by solo draw count. This analysis goes one layer deeper: for every possible pair of white balls, how many draws contained both? With 2,346 possible pairs and exactly 10 new pair observations per draw, the dataset builds fast. The conclusion the data delivers is the conclusion the math predicts before you look at a single draw.
Which Powerball numbers appear together most often?
The top-ranked pairs in the full co-occurrence table sit noticeably above the ~6–7 expected appearances — elevated by the natural variance of a random draw process applied to a large combination space. The next two pairs cluster close behind. A chi-square analysis with Bonferroni correction across all 2,346 pairs, covered in full below, finds none above the corrected significance threshold: the observed spread is consistent with what random sampling produces. The complete ranked table of all 2,346 possible white-ball pairs — with observed count, expected count, and observed/expected ratio — is available at Jackpot Teller's draw history tool, updated through the current draw date.
What the distribution looks like structurally: most pairs cluster near the 6–7 expected-appearance mark. A thin right tail contains the elevated pairs. A thin left tail holds pairs that ran below expectation. A small number may show zero observed appearances — a statistically plausible outcome given the probability math below.
How often should any two Powerball numbers appear together?
This is a combinatorics question with a clean answer. Powerball draws 5 white balls from a pool of 69 (the current matrix, in effect since October 2015). For a specific pair to appear in a given draw, both balls must be selected, plus 3 more from the remaining 67.
- Ways to complete a draw containing a specific pair: C(67, 3) = 47,905
- Total possible draws: C(69, 5) = 11,238,513
- Probability that pair appears in one draw: 47,905 ÷ 11,238,513 ≈ 0.426%
In 1,500 draws, the expected number of appearances for any specific pair:
1,500 × 0.00426 ≈ 6.4 appearances
A pair appearing 7 times sits right on the expected line. A pair appearing 13 times looks striking — until you note it is roughly twice the baseline over a decade-plus window, a deviation entirely consistent with normal sampling variance across a large pool of combinations. On the low end: the probability of a specific pair going completely undrawn across 1,500 draws is (1 − 0.00426)1500 ≈ 0.17%. Small — but with 2,346 pairs in the pool, a handful of zero-count pairs is a plausible outcome.
What does the full Powerball pair frequency table show?
The co-occurrence table at Jackpot Teller ranks all 2,346 possible white-ball pairs by observed appearances. Each row shows:
- Pair: the two ball numbers, sorted ascending
- Observed: total draws in which both balls appeared together
- Expected: draw count × 0.00426, the combinatorics baseline
- Ratio: observed ÷ expected — 1.0 means exactly average; values above 1.0 indicate above-baseline frequency
Every draw contributes exactly C(5, 2) = 10 pair observations to the table — all unique combinations among the 5 drawn balls. Over 1,500 draws, that is 15,000 total observations distributed across 2,346 possible pairs, at an average of ~6.4 observations per pair. The full table, sortable by any column and filterable by number range, is live and free at jackpotteller.com/w/data.
Are any Powerball number pairs statistically significant?
Testing every pair against the null hypothesis — that each pair appears with probability p ≈ 0.426% per draw — is straightforward. The multiple-comparisons problem is what makes the significance bar far higher than intuition suggests.
The test setup:
- H₀: pair (a, b) appears in any draw with probability p = C(67,3) / C(69,5) ≈ 0.00426
- Test: binomial goodness-of-fit, approximated by chi-square with 1 degree of freedom for large n
- Statistic: χ² = (k − μ)² / μ, where k is observed count and μ is expected count
Bonferroni correction: With 2,346 simultaneous tests, the per-test threshold is α = 0.05 / 2,346 ≈ 0.0000213 — corresponding to a z-score of approximately 4.30 standard deviations above the mean.
What that requires in raw count: Given μ ≈ 6.4 and σ = √(n × p × (1 − p)) ≈ 2.52, a pair would need approximately 6.4 + (4.30 × 2.52) ≈ 17 or more appearances to clear the corrected significance threshold.
The verdict: The chi-square analysis — with full values for all 2,346 pairs available in the Jackpot Teller tool — returns no pair above the Bonferroni-corrected threshold. The top co-occurring pairs show elevated ratios, but their χ² statistics do not approach the corrected cutoff. The observed spread across all 2,346 pairs is consistent with what random sampling produces when you apply a low-probability event to a large combination space. This is the honest result, and it is the result the math predicts before you look at a single draw.
Does playing top pairs improve your odds?
No — and the structure of the problem explains why before statistics do.
Powerball draws are independent. The balls drawn on Saturday carry no memory of Tuesday's result. A pair that has appeared 13 times in history carries the exact same probability for the next draw as a pair that has appeared 4 times: approximately 0.43%.
Historical co-occurrence frequency is backward-looking data. It describes what happened across the draw record. It carries zero predictive weight for what happens in the next independent random draw. Using historical pair frequency as a picking strategy is a dressed-up version of the gambler's fallacy — the belief that a random process has memory it does not have. Lotteries are random; pair rankings do not change that.
The data is analytically interesting. It is not a picking strategy.
How was this analysis done?
The draw history comes from the official Powerball record maintained by the Multi-State Lottery Association (MUSL). The analysis tracks the full draw history with particular attention to the October 2015 matrix change, when the white-ball pool expanded from 59 to 69 numbers.
Why era boundaries matter: Before October 4, 2015, Powerball used a 59-ball matrix. Ball numbers 60–69 did not exist. Mixing pre- and post-2015 draws would artificially suppress co-occurrence counts for any pair containing a number above 59, and distort the probability baseline for the pre-2015 pool. The pair analysis covers the post-2015 matrix era specifically; the methodology section of the Jackpot Teller tool documents era handling in full.
Pair extraction: For each draw, all C(5, 2) = 10 white-ball pairs are enumerated and tallied. Expected counts use p = C(67,3) / C(69,5). Chi-square statistics are computed per pair; Bonferroni correction is applied across all 2,346 pairs when assessing significance.
Frequently asked questions
What are the most common Powerball number pairs?
The top-ranked white-ball pair in Jackpot Teller's co-occurrence analysis sits notably above the ~6–7 expected baseline across 1,500+ draws — the kind of gap that looks striking but falls within normal sampling variance. The full ranked list, with observed counts, expected counts, and ratios for all 2,346 possible pairs, is available free at jackpotteller.com.
Do number pairs repeat in Powerball?
Yes. With approximately 6.4 expected appearances per pair across 1,500 draws, repeated co-occurrences are the statistical norm, not the exception. Every pair should appear roughly 6–7 times by chance alone over that span. What varies is whether a specific pair lands slightly above, at, or below that expectation.
What is the probability two Powerball numbers are drawn together?
The probability that any specific pair of white balls appears together in a single Powerball draw is C(67,3) ÷ C(69,5), which equals approximately 0.43%. That means roughly 6–7 expected co-appearances across 1,500 draws for every one of the 2,346 possible pairs — concentrated within a tight range by chance alone.
Has any Powerball pair never appeared together?
With 2,346 possible white-ball pairs and an expected frequency of about 6.4 appearances per pair across 1,500 draws, the probability of any specific pair going completely undrawn is roughly 0.17% — small but nonzero. By chance, a handful of pairs may have zero-count records. Check the complete ranking at Jackpot Teller to see the current zero-count list.
How many possible Powerball pairs are there?
There are C(69, 2) = 2,346 possible white-ball pairs across the current 69-ball pool. Each draw of 5 balls produces C(5, 2) = 10 unique pairs simultaneously, meaning every draw adds exactly 10 data points to the co-occurrence table — covering a different slice of the 2,346 possible combinations each time.
See the full co-occurrence ranking
The complete ranked table of all 2,346 Powerball white-ball pairs — observed counts, expected counts, ratios, and chi-square values for every combination — is live at Jackpot Teller. Signup is free.
View the full Powerball pair frequency table at Jackpot Teller →