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# FAQ: Statistical Analysis

Lottery Insight uses statistical analysis of the historic draws to determine its target numbers. We do not use other popular systems such as “Lucky Numbers”, nor astronomic data like the phases of the moon or planetary alignments.

Cyclical Patterns
If there could be a cyclical pattern hidden in the draw data, then this might be found by using Fourier analysis. This method hunts for a principle harmonic in the data: if this is found its calculated values are extracted from the data and the process repeated until the resulting data is a flat line. In truely random data there should be no cyclical patterns.

Probability
Are all possible sets of drawn numbers equally likely to happen? If that is the case, then {1,2,3,4,5,6} and {1,10,19,28,37,46} and {5,7,11,30,44,49} are all equally probable random selections of six numbers from 49.

Special Cases
just looking at the three examples in the previous item, the equal probability clause seems wrong. This is because you are taking the gaps between numbers into account: the first two sets have exactly equal gaps: this is a what mathematicians call a “special case”.

Variance
with {1,10,19,28,37,46} and {5,7,11,30,44,49} the mean gap between their pairs of numbers are 9.0 and 8.8 but the variances (or what mathematicians call the “standard deviation”) are 0.0 and 6.6 ... so a small variance could point to a lack of randomness and a variance larger than the mean gap might be an indicator of good randomness. The size of the variance is not proof of randomness or otherwise, it may only be an indicator.

False Logic
Imagine that “number 18 has been drawn in every draw the last three weeks” (that is, the last six draws):

1. ... so it must happen again this time: it's a definite pattern.
2. ... so it cannot happen again this time: it's just impossible.
3. ... so it is probably unlikely to happen again this draw: it's a vanishingly small possibility.
Each statement has a logic of it's own. The random chance is 1 in 2,422,779 ... so if you are prepared to try twice every week for 23,296 years any one ball coming up seven draws in a row could happen.

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