Mega Millions Lotto Picks for the Week

Have you ever wondered if the Mega Millions lottery is really random? Does it seem to you that some of the numbers come out more than others? You may be surprised to find out that this is true, to a degree. This site will show you how the balls have been drawn since the beginning of the lottery in 2002, so that you can pick your next lottery numbers using a logical, statistical approach. Good luck, you will need it,... enjoy.

Frequency matrix: First, we download all of the 970 mega millions results since it's inception to Dec 20,2011 and count how many times each of the 56 regular balls was drawn, in any order. 0 1 2 3 4 5 6 7 8 9 10 0+ 76 95 77 85 88 82 90 81 87 100 10+ 80 94 92 103 81 91 95 93 85 93 20+ 89 92 73 93 91 85 92 91 92 84 30+ 100 98 76 73 87 92 78 86 101 89 40+ 73 88 81 90 90 98 76 97 86 98 50+ 108 99 66 56 51 58

modal frequency is: 86.6071428571 times sigma is: 4850 sigbar is : 1

Chi-square goodness of fit test: Then, we test the Null Hypothesis that the lottery is a good fit to the perfectly random model. The closer a value is to zero, the more perfecly random is that ball. You can look up the Chi-square value for the table for the significance level at 55 degrees of freedom here. 0 1 2 3 4 5 6 7 8 9 10 0+ 1.30 0.81 1.07 0.03 0.02 0.25 0.13 0.36 0.00 2.07 10+ 0.50 0.63 0.34 3.10 0.36 0.22 0.81 0.47 0.03 0.47 20+ 0.07 0.34 2.14 0.47 0.22 0.03 0.34 0.22 0.34 0.08 30+ 2.07 1.50 1.30 2.14 0.00 0.34 0.86 0.00 2.39 0.07 40+ 2.14 0.02 0.36 0.13 0.13 1.50 1.30 1.25 0.00 1.50 50+ 5.28 1.77 4.90 10.82 14.64 9.45

the chi-square is: 83.0927835052 with 55 degrees of freedom

Variance matrix: Next, we compute the variance between the actual results and the average results as a matrix of the difference of the squares between the actual results and the results divided by the sample size, in this case 970 0 1 2 3 4 5 6 7 8 9 10 0+ 5770 9016 5923 7218 7736 6717 8092 6554 7561 9990 10+ 6393 8827 8455 10598 6554 8272 9016 8640 7218 8640 20+ 7913 8455 5324 8640 8272 7218 8455 8272 8455 7049 30+ 9990 9594 5770 5324 7561 8455 6078 7388 10190 7913 40+ 5324 7736 6554 8092 8092 9594 5770 9399 7388 9594 50+ 11652 9791 4352 3133 2598 3361

A perfectly random lottery would yield: 7493.06441327 in each cell

Covariance matrix: Finaly, we compute a matrix to determine the degree of covariance between the actual results and the perfect lottery. This is equivalent to a correlation matrix between the two scenarios. Here, a high correlation coefficient indicates a lower level of randomness. 0 1 2 3 4 5 6 7 8 9 10 0+ 1.36 1.70 1.38 1.52 1.57 1.46 1.61 1.45 1.55 1.79 10+ 1.43 1.68 1.64 1.84 1.45 1.62 1.70 1.66 1.52 1.66 20+ 1.59 1.64 1.30 1.66 1.62 1.52 1.64 1.62 1.64 1.50 30+ 1.79 1.75 1.36 1.30 1.55 1.64 1.39 1.54 1.80 1.59 40+ 1.30 1.57 1.45 1.61 1.61 1.75 1.36 1.73 1.54 1.75 50+ 1.93 1.77 1.18 1.00 0.91 1.04

The coefficient of covariance is: 86.5178571429

Best fit statistical picks for the " . $lotto . " lottery Using the covariance matrix as a correlation coefficient between the actual and the perfect lottery, we can select those numbers that have shown the highest correlation with the Null hypothesis of randomness, in that the higher the covariance for that ball, the higher the probability is that that ball will be drawn. color codes: best... better... good..... average poor.... worst... 0 1 2 3 4 5 6 7 8 9 10 0+ [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] 10+ [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] 20+ [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] 30+ [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] 40+ [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] 50+ [51] [52] [53] [54] [55] [56] Sponsors