Figuring % chance A will be larger than B

eric.wikman@gmail.com · science forum beginner Joined: 05 Oct 2005 Posts: 3

I have two completely independent numbers and the mean and standard
deviation for each. I'd like to figure out what percent chance one has
of being larger than the other. I cannot say for sure if it follows the
normal distribution or some other distribution, because I have a small
sample size. For example:

Team A has a mean of 80.375 and a StDev of 13.02
Team B has a mean of 70.875 and a StDev of 25.20

I did a Monte Carlo simulation (and I assumed it was a normal
distribution) and found that Team A has a 63.26% chance of winning
after 100,000 simulations.

Each team can only effect the number of points they score, they cannot
effect the number of points the opposing team can score, that's why I
say the numbers are independent. Team A and B are both fantasy
football teams.

What is a better way to come up with 63.26% (or some more accurate
number) using math instead of brute force?

Eric

iandjmsmith@aol.com · science forum beginner Joined: 13 Sep 2005 Posts: 15

eric.wikman@gmail.com wrote:

eric.wikman@gmail.com · science forum beginner Joined: 05 Oct 2005 Posts: 3

Thank you Ian. That works great, I tried it with the other 4 matchups,
and it was always within 1% of the number I got from simulation.

Do you know of any web references or books that could help me learn
more about why this works, and hopefully dive into a tougher discussion
on how to handle it when there are dependencies (therefor not
independent variables)?

iandjmsmith@aol.com · science forum beginner Joined: 13 Sep 2005 Posts: 15

eric.wikman@gmail.com wrote:

Google