I have a 5 person team in a 24 hour relay race. Each loop of the course will take approx 1.5-2hrs so we expect to complete between 12 and 16 loops. The easiest way to organize the team would be to run through the riders (A-B-C-D-E-A-B-C-D-E- …). However, I don’t think this is fair for E. “E” has to wait 6-8 hours for his first ride, and also, E has the lowest probability of getting the same number of rides as everyone else. Of course I realize that someone has to go last (there is no way to avoid this) but this person should be compensated in some way.
So, what’s a fairer way to do this ?
First, some restrictions:
at no time should any rider have completed 2 more loops than any other rider, so: a system where “A” does 3 loops, before everyone else has done their 2nd loop is not valid.
a rider must have a rest of at least 2 loops, before riding again. So, A-B-C-D-E-C is okay since 2 riders do loops before 'C’s 2nd loop. A-B-C-D-E-D is not okay since D has only a 1-rider rest.
a rider should a rest of no more than 6 loops before the next ride. So, A-B-C-D-E-B-C-A is okay, since A has to wait for 6 loops.
all else being equal, try to reduce the number of 6-rider waits, and then, try to reduce the number of 2-rider waits. These cannot be avoided, but it would be good to try to minimize these.
My current idea is:
1st Ride: A B C D E
2nd Ride: A D B E C
3rd Ride: D E A C B
4th Ride: E D C B A
Notes:
D and E each have a 2-rider wait
A and B and C each have a 6-rider wait
If we only manage to complete 12 loops, D and E get the extra rides. If we manage to complete 16 loops, E gets the extra ride.
If you determine the running order by lot, I don’t see how ABCDE… is unfair. Everyone gets within one run of anyone else, and that’s the best that can be done. And everyone gets the maximum rest between runs. Where’s the problem?
The "problem " is that whoever is “E” has to both: wait the longest for their first ride, and, also, is less likely to get the same number of rides as everyone else. Maybe my solution is worse than the problem, but that’s why I’m looking for a better solution.
How about this: you win? Basically, poor little E’s entry fee be damned, you put your fastest riders out on the course as often as possible and only have another rider go in when they are exhausted beyond the speed that a typically “slower” rider could accomplish. Do you have access to the course right now? Have people go out, do trials, and then see how fast everyone is. Time every lap from everybody to decide when to substitute oter riders.
Share in the prize money equally, go to Mexico, party.
That doesn’t increase D’s waiting time the first cycle and reduces everybodies
thereafter. It also appears to increase the chances everyone will have the
same number of rides:D
And if this race lasts for 24 hours, do you really want the racers to go in a strict ABCDEAB… rotation? Everybody would get between six and eight hours rest between their shifts, which isn’t really going to be enough for a good, sound sleep. Why not give a few people an extra shift or two early, while others are resting to pull extra shifts overnight while the others are sleeping. Let people know the schedule in advance (maybe even ask them how they’d prefer to do it), so some can adjust their sleep schedules to be ready for when they’re needed the most.
The first issue of your “problem”, is unavoidable, someone is going to be, at best, in fifth position as their first ride.
For your second issue, again, I think it’s unavoidable, that if you don’t end after 10 or 15, then someone will get screwed out of the extra rides.
Maybe the best way is to run 2 sets (A,B,C,D,E) and then see who’s best off or fastest between A,B, and C, and then when that person finishes (say it’s C), see who’s best off between A, B and D. Just keep an eye on the no more than 6 between riders. To continue my example, say D goes again, then A has to go after, and B has to follow.
I think it’s going to be easiest to just use the same order every round and assigning order by random, like Hoodoo Ulove says.
Also, does ‘E’ have to be awake/there when ‘A’ starts? Can’t ‘E’ just show up later fixing your first issue?