*5 J's* wrote:We only have 50 cubs in our pack, with 80% participation, I anticipate 40 entrants. I may run subgroups to award 1-3 ribbons to each age group, but I want all to run against each other for the top four positions as we need to send the top four to district competition.
Racing "everybody against everybody" (head to head) on a 2 lane track takes a lot of heats (40*39/2 = 780 heats, I think). However, you probably have time (2 to 3 hours) for 6 heats apiece (3*40 = 120 heats total) and can run with times. A good starting gate (spring open) will avoid most of the timing issues that I described. Still to avoid embarrassing errors, the results need to be "sanity checked" and the track operators need to be trained and have some practice before they start.
*5 J's* wrote:
Stan Pope wrote:As I understand, "Phase shift" is equivalent to the underlying heat generation process of PPN. The difference is that the racer number delta between lanes starts out larger than the current PPN deltas. If you use "phase shift", you may unintentionally produce greater variance in opponent equity and, as a result, loose the points ranking - times ranking correlation.
Okay looking at a sample 40-2 (3 round) PPN which produces 120 heats, I see that you start with a 1-12 generator for the first 28 heats, then go to a 28-1 generator, then 1-11, 29-1, 1-10, 30-1.
Are you saying that the difference is that "Phase Shift" would start with a generator with a larger delta such as a 1-18? Can you explain in the simplest terms how this "may unintentionally produce greater variance in opponent equity and, as a result, loose the points ranking - times ranking correlation".
Both use "modulus arithmetic" in generating heats. Modulus arithmetic gets its result using the remainder after division. It is equivalent (and simpler in this case) to just observe that when adding two numbers that are in the range 1-40 that if the sum exceeds 40, then subtract 40 (the number of racers) from the result. If a difference is less than one, add 40 to the result.
The example that you showed (1-12, 28-1 generators) are actually just one generator (12), i.e. the number of the lane 2 racer is 12 greater than the number of the lane 1 racer modulus 40. When, for instance, racer 29 races in lane 1, racer 1 (=29 + 13 - 40) races in lane 2.
Note that if I chose a generator of 20, in heat 1 racer 1 races against racer 21, and in heat 21 racer 1 races again against racer 21 but with lanes swapped. This creates an unsatisfactory imabalance in opponents: racing some twice while not racing others at all.
Those combinations are easy to avoid on 2 lanes, but are increasingly harder to avoid on 3, 4, and 5 lane tracks. The reason is that every two lane matchup presents the same problem. A 40 car 3 lane chart (generator = x,y) needs to avoid x = 20, y=20, and x+y=20. In addition, the generator needs to avoid x=y and x=-y. A 40 car 4 lane chart (generator = x,y,z) needs to avoid x=20, y=20, z=20, x+y=20, y+z=20, z+x=20, and x+y+z=20. In addition, the generator needs to avoid x=y, x=-y, x=z, x=-z, y=z, y=-z, x+y=y+z, x+y=-y-z, z+x=x+y, z+x=-x-y, (All "equals" relations interpreted using modulus arithmetic.)