For the most current and up-to-date results, this article has been replaced with a continuously updating website where the statistics are recalculated after each new drawing. For information on how the analysis was conducted, please continue reading the original article below. Rather than debunk any of these theories of lottery fraud or rigging, this article reveals the trends and patterns of winning lottery numbers for public scrutiny using basic data analysis.
Recently, MegaMillions drew the largest jackpot ever recorded at $370 million, exceeding the previous record held by PowerBall.2 The prizes were not always so large, nor did the participants span the United States. A single dollar in MegaMillions purchases a 1 in 175,711,536 chance of landing the jackpot.
As a first step, it was necessary to obtain a collection of MegaMillions’ lottery numbers. When the BigGame debuted, players were allowed to choose numbers between 1 and 50 with a MegaBall ranging from 1 to 25. The BigGame was changed on January 13, 1999 to increase the number of available MegaBalls from pool of 25 to 36. On May 15, 2002 the MegaMillions drawing expanded the pool of numbers available to players to range from 1 through 52. After looking at the behavior of the numbers in aggregate, the occurrence of numbers respective to their position was analyzed.
It is important to recognize the four variations of the lottery’s number pool has an impact on the ratio of occurrence for each number.
Green bars represent the current version of MegaMillions where players choose from numbers 1 through 56 and a MegaBall number of 1 through 46. Blue bars represent the weighted aggregation of a number’s winning percentage from all MegaMillions drawing variations since 1996.
The red line represents a five variable polynomial trend line to the winning percentage of the current MegaMillions drawing pool. Ignoring the version differences in number pooling across the lottery’s lifetime, the first ball has ranged between 1 and 37 with an average winning number of 8. Ignoring the version differences in number pooling across the lottery’s lifetime, the second ball has ranged between 2 and 46 with an average winning number of 17. Ignoring the version differences in number pooling across the lottery’s lifetime, the third ball has ranged between 5 and 54 with an average winning number of 29. Ignoring the version differences in number pooling across the lottery’s lifetime, the fourth ball has ranged between 5 and 55 with an average winning number of 35.


Ignoring the version differences in number pooling across the lottery’s lifetime, the fifth ball has ranged between 13 and 56 with an average winning number of 44.
Ignoring the version differences in number pooling across the lottery’s lifetime, the MegaBall has ranged between 1 and 52 with an average winning number of 20. The graph at right shows that in the current version of MegaMillions, pairs of numbers win repeatedly quite often. There have been many repeat winning combinations of three numbers in the lifetime of the lottery, although it is a less frequent phenomenon in the current version.
In the graph to the right, there have been many repeat winning combinations of three numbers in the lifetime of the lottery, although it is a less frequent phenomenon in the current version. A natural extension of analyzing number groups was to identify the trends by which numbers differ from one another.
Analyzing the distribution of numbers over time only provided half the picture in terms of any given number’s propensity towards winning. This graph depicts the numbers with the shortest, average time between appearance since version four of MegaMillions began in 2005.
The six month graph replicates the logic found above on the lifetime graph, only this time restricted to winning numbers over the past six months. Interesting as these trends may be, they will not assist in making the odds of winning the MegaMillions lottery any better if the system is truly fair and random.
Each number has been drawn at least eight times as compared with the most frequent winners that occurred twenty-seven times.
Looking at the current version of MegaMillions, the first ball shows a steeper trend curve with nearly twice the drawings on winning numbers as any other ball. Looking at the current version of MegaMillions, the second ball shows a shallower trend curve. Looking at the current version of MegaMillions, the third ball shows the shallowest trend curve. Looking at the current version of MegaMillions, the fourth ball’s trend curve begins to steepen. Looking at the current version of MegaMillions, the fifth ball’s trend curve steepens sharply. Looking at the current version of MegaMillions, the MegaBall’s trend curve is relatively flat. Using the MegaMillions data, there are 10,780 possible pairs of which 1503 are unique over the lottery’s lifetime.


There are 10,780 possible triples of which 8675 are unique over the lottery’s lifetime. There are 5390 possible quadruplets of which 5328 are unique over the lottery’s lifetime. Only one set of five numbers has ever repeated twice in the history of MegaMillions: (11, 14, 18, 33, 48).
Simply having a low average, however, is not a good indicator that a number occurs frequently. MegaMillions winning numbers ranged from 1 through 37 with an average winning ball of 17 since 2002. MegaMillions winning numbers ranged from 2 through 43 with an average winning ball of 22 since 2002.
MegaMillions winning numbers ranged from 3 through 54 with an average winning ball of 26 since 2002. MegaMillions winning numbers ranged from 7 through 55 with an average winning ball of 35 since 2002. MegaMillions winning numbers ranged from 26 through 56 with an average winning ball of 41 since 2002.
MegaBall winning numbers ranged from 1 through 46 with an average winning ball of 23 since 2002.
The numbers 13, 12, 17, 25, 10, 18, 20, 14 and 21 represent 40.77% of the winning numbers on the second ball.
The numbers 20, 35, 31, 25, 37, 26, 32, 24, 23 and 38 represent 39.06% of the winning numbers on the third ball.
The numbers 51, 42, 46, 36, 48, 40, 38, 39 and 49 represent 40.77% of the winning numbers on the fourth ball. The numbers 53, 54, 56, 52 and 55 represent 42.92% of the winning numbers on the fifth ball.
Although the linear trend line rises modestly, the primary numbers have a relatively even distribution over time.
The numbers 2 and 3 were drawn the most as MegaBalls at fifteen times apiece while 11 was drawn the fewest at four times.



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