Jim, I have asked Dan Tandberg if he might be able to help

From:

rcse@googlegroups.com [mailto:rcse@googlegroups.com] On Behalf Of Jim

Monaco

Sent: Thursday, September 29, 2011 11:16 AM

To:

rcse@googlegroups.com
Subject: [RCSE] F3J Flight Matrix Calculations

As many of you know I regularly run F3J events and handle all the matrix and

scoring tasks. In the past I have always generated the flight matrix using

a random assignment and rarely have any complaints. However, I am now

looking at generating the fairest possible matrix for the US F3J Team

Selections and have run a number of tests and often see anomalies in the

matrix where a pilot flies against another an inordinate number of times or

very few times. I ain't the sharpest pencil in the box, so I could use some

suggestions on how to improve the matrix from some of the smart math people

in the group. I am a programmer so if I understand the algorithm I can

program it.. :)

Here are the constraints:

1. There are 10 teams

2. Each team consists of 4 pilots (if there are less than 4 pilots a

BYE will fill the empty slots).

3. Each pilot will fly once in a round (so there are 4 groups in a

round)

4. Pilots on the same team are protected and will never fly against

another team member.

5. We will schedule 24 total rounds in the matrix

Here is what I have attempted so far:

1. Pure random - for each round I process each team. On each team

every pilot has a fixed pilot number between 1 and 4 (including BYES). I

then compute a random sequence of the position numbers 1-4 and assign the

flight group based on that sequence. Repeat for each team. When all teams

have been computed for a round I go on to compute the next round.

2. Random with statistical preference - I do the above, but I

calculate a factor to use in determining the variance in the matrix and run

1000 trials and select the one with the least variance. To do this I

compute and record how many time each pilot flies against the other pilots.

For each pilot I compute the standard deviation of these numbers. I then

add all the pilots standard deviations together and compute the average

standard deviation for the entire matrix. I pick the matrix that generates

the lowest standard deviation in 1000 trials. Generally I see a minimum

standard deviation of about 1.28. Some individual matrix SDs are 1.9 or so.

3. Random with statistical preference and permutiations - for this

approach I calculate all the possible permutations of the sequence 1-4.

Then for each team I generate a random sequence of those permutations

(1-24). I then assign the group position for each pilot in a round based on

that teams random set of permutations. I then do the same as #2 and

calculate the minimum SD of all the matrixes and select the lowest.

Interestingly this approach was nearly identical in minimum SD as the #2

approach.

It just feels to me like there should be a better way to get a more even

distribution - I'm hoping one of you math heads out there can help me

improve the matrix.

If not - it is what it is and I did my best.

Jim

--

You received this message because you are subscribed to the Google Groups

"RCSE" group.

To post to this group, send email to

rcse@googlegroups.com.

To unsubscribe from this group, send email to

rcse+unsubscribe@googlegroups.com.

For more options, visit this group at

http://groups.google.com/group/rcse?hl=en.

--

You received this message because you are subscribed to the Google Groups "RCSE" group.

To post to this group, send email to

rcse@googlegroups.com.

To unsubscribe from this group, send email to

rcse+unsubscribe@googlegroups.com.

For more options, visit this group at

http://groups.google.com/group/rcse?hl=en.