Generalized Average Rate of Reoccurrence

Generalized Average Rate of Reoccurrence

    Reference - Combinatorial Distribution, Average Rate of Reoccurrence Distribution

    Generalized Average Rate of Reoccurrence - Ag = n / r

      n - number of items
      r - number of items in a combinatorial set

The generalized average rate of reoccurrence was derived from the combinatorial distribution function. The generalized average rate of reoccurrence is the same average rate for all items or numbers drawn in a combinatorial random selection. In example, the generalized average rate of reoccurrence for all numbers in a 6/49 lottery is about 49 / 6 = 8.167 draws. Looking at the column total in the combinatorial distribution, the total is the same for all items or numbers. Item/number 1 in column 1 for the combinatorial distribution function can be used to describe the column total for all items/numbers. Setting c = 1 and z = 1, the generalized average rate of reoccurrence can derive for all items/numbers.

    c = 1 and z = 1, also for reference  a! / (a - 1)! = a

    Ag = Ar(n,r,1,1)

    Ag = C(n,r) / D(n,r,1,1)

    Ag = C(n,r) / (C(1 - 1,1 - 1) * C(n - 1, r - 1))

    Ag = C(n,r) / ( 1 * C(n - 1, r - 1))

    Ag = C(n,r) / C(n - 1, r - 1)

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * ((n - 1) - (r - 1))!))

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * (n - 1 - r + 1)!))

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * (n - r)!))

    Ag = (n! / (r! * (n - r)!)) * ((r - 1)! * (n - r)! / (n - 1)!)

    Ag = (n! / (n - 1)!) * ((r - 1)! / r!) * ((n - r)! / (n - r)!)

    Ag = (n! / (n - 1)!) * ((r - 1)! / r!) * 1

    Ag = (n! / (n - 1)!) * (1 / (r! / (r - 1)!)

    Ag = n * (1 / r)

    Ag = n / r

Some various generalized average rates for Pick 5, Pick 6 and Pick 1 of Powerball and Mega Millions: