Probability?

[nave]

Is there any formula to calculate the probability or odds of a set o
numbers. For example if you have 10 numbers that represent lets sa
horses, ranked in descending order and want to figure out the odds o
the top number winning the race and the odds of the remaining
contenders can that be done

 

[Jerry W. Lewis]

Ignoring the possibility of ties, there are 10! ways to order the 10
horses. If the horses are interchangeable, then the probability of a
particular order finish would be 1/(10!). In reality, the horses in a
race are rarely interchangeable; there are differences in ability,
health, motivation, riders, etc.

Jerry

 

[nave]

Jerry

The Numbers I have are after all factors that I consider important and
each factor is weighed differently. Then my program spits out a final
number on each horse... lets say horse #1 is 11.457 and horse #2 is
11.320 and so on. The higher the number the better the horse. Now I
want to make the odds or probability on each horse winning the race.
Can I do that with any excel formula??
Any suggestions from anyone

thanks

 

[Jerry W. Lewis]

Assuming that your rating numbers are linearly proportional to the
probability of winning and that ties cannot occur, then the probability
that horse x wins is
rating_x / SUM(ratings)

If you further assume that these ratings fully define the probability
structure (including an assumption of independence), then we can also
calculate the probability of the entire finish.

To calculate the probability of a particular finish in a 10-horse race,
put the ratings in A1:A10 sorted in finish order (A1 contains the rating
of the winner, ...). In B1 calculate the probability of the winner
=A1/SUM(A1:A$10)
In B2 calculate the probability of the ordered 1-2 finish
=A2/SUM(A2:A$10)*B1
Copy the formula in B2 down through B10. The ith row of b then contains
the probability of the top i ordered finishers, and B10 contains the
probability of the entire finish order.

If all of your rating numbers are equal, then B10 will contain 1/10! as
previously noted.

Jerry