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Old Sep 29, 2011, 12:22 PM
Dave Jensen
Dave Jensen
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Re: F3J Flight Matrix Calculations

Nevermind on the when/where.... I just remembered it's next month in
FL.



On Thu, 29 Sep 2011 11:15:45 -0600, Jim Monaco wrote:

> 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
>
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