# STATISTICS (UPDATED 7/30/2009)

NOT EVERYTHING THAT LOOKS IMPRESSIVE IS IMPRESSIVE

*ROFFMAN SKIP FORMULA.

The number of ways that a term (either forwards, backwards, or diagonal) can fit into a matrix is determined as follows:

(1) Let the number of skips possible in a forward direction on a row of length (r), where r = the number of columns in the matrix, be equal to "Sr."

(2) Likewise, let the number of skips possible in a vertical direction on a column of length (c), where c = the number of rows in the matrix, be equal to "Sc."

(3) The Roffman Skip Formula for total skips is as follows:

Skips = 2(Sr + Sc + 2[Sr][Sc]) = 2Sr + 2Sc + 4SrSc.

An example of skip value determined through use of the above tables and formula follows:   Find the number of skips possible for a 4-letter word in a Matrix 28 columns by 11 rows.

SolutionSkip Tables for words ranging between 3 and 8 letters are posted on this site.  For a 4-letter word use Table 1B.  On it find that 28 columns = 9 possible skips forward.  Thus Sr = 9.  Now note that 11 rows = 3 possible skips vertically.  Thus Sc = 3.  Now apply the formula which is Skips = 2(Sr + Sc + 2[Sr][Sc])    2(9 + 3 + 2(9)) = 2(12 + 54) = 2(66) = 132 SKIPS.  Now, let us suppose that the 4-letter term occurred at skip 100.  To get an idea of how likely such a term is to be found at an ELS, search a range of 132 skips, such as from skip 101 to skip 232.  The number of "hits" for this term is then divided by letters in the Control (if this is scrambled Torah the number of letters in the Control is the same as in Torah, i.e., 304,805).  The quotient is the Word Frequency Per Letter. This is multiplied by the number of letters on each matrix to reveal Word Expectancy Per Matrix.  It is inherent in this procedure that the larger the number of letters in the matrix, the larger the number of placements possible for any given key word at any ELS.   After determining Word Frequency Per Plot we apply the  Poisson Equation to see the probability that they are present at least once. This is necessary to determine a true probability for each word. Just because a word is likely to appear once per plot does not imply it will always be there. Words may average out to many times per plot area without actually being in a given plot of that area. Of course, if the expected frequency is sufficiently high we eventually reach a probability like .9999999 which we simply round off as 1.0.

HOW TO FIND THE CHANCE OF A TERM APPEARING AT LEAST ONCE*

1.  FIND PROBABILITY IT DOES NOT OCCUR BY POISSON EQUATION.

x (-lambda)
f(x) = Lambda e                   x = 0; lambda = expected frequency per matrix
x!

2.   1 ‑ f(0) = THE PROBABILITY OF OCCURRING AT LEAST ONCE.

(where f(0) = the probability it will not occur)

3.  On an Excel or Works spreadsheet, head columns as follows:  A: Whatever identifies the calculation; B: Skips Used on the Matrix, C: Number of hits (on CodeFinder or similar software) in Skip Range; D: Divide by 304,805 Letters in Torah or Control; E: The Quotient Equals Frequency Per letter; F: E Quotient Multiplied by Letters on Matrix = Word Expectancy; G:  Poisson Equation = 1-EXP(-F#) where # equals the row number of the item in Column F in question on the spreadsheet.  If you want to know the chance for the item to be on the matrix, head Column H accordingly. The value of Column H will be the reciprocal of the value found in Column G by Poisson Equation.

* Note: While this author (Barry S. Roffman) discovered the Roffman Skip Formula, my son (an MIT geophysics graduate), Rabbi Robert Roffman, is the author of the spreadsheets and the man who first introduced use of the Poisson Equation into my research.

ROW SPLIT AND WRAPPED MATRICES

There is some indication that when a row skip or row split function for the axis term is employed, that the true value of an open text match must be the value computed by standard means divided by the row spit.  The lowest ELS of Ark of the Covenant at skip -306 (cylinder circumference 306 letters) had about one chance in 2,931 of being in a 104-letter matrix with Egyptians were burying.  At skip -306 there was no row split function enabled on CodeFinder.  Had it been enabled and a row split of 2 were used (with a cylinder circumference of 153 letters), if the matrix size  (area) were the same, I would have divided 2,931 by 2  to arrive at a value of 1 chance in 1,465.  In this case however, the matrix with circumference 153 would have been larger because the match on the matrix with circumference 306 was already about as tight as it could be with the row skip function disabled.  There is also a discussion about dividing the value of a matrix by the number of passes through the Torah made by CodeFinder on a wrapped (rounded torus) search before acquiring an axis term.  See the permutation experiment

SPECIAL CASE SKIPS

Finally, when computing the value of a-priori open text terms on a matrix, it is my practice to only employ the frequency of this term at Skip +1 (in unwrapped Torah) on my spreadsheet in column C.  However, if the a priori term appears at skip -1, N (parallel to, in the same direction, and at the skip of the axis term), or -N (parallel to, in the opposite direction, and at the skip of the  term) in column C, I list the frequency (number of hits) as the total hits at skips +1, -1, N, and -N (with wrapped Torah allowed if that was required to find the axis term.  These skips are considered  special because they seem to leap out at the eye of the researcher and make the case for deliberate encoding seem more plausible.