Sep 29, 2011, 12:15 PM Jim Monaco Jim Monaco Guest n/a Posts 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.