2-Lane Round Robin

This is a total rework of the previously described procedure and simplifies and expands the process. (Stan 2/21/97)

Generating a Full Round Robin for a 2-lane Track

Count the cars.
Let N be the Number of cars.

Round 1: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 2 through N, then continue, starting with 1. Each car races twice, once in each lane.

Round 2: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 3 through N, then continue, starting with 1. Each car races twice, once in each lane.

Repeat until (N X (N-1)) / 2 heats (i.e. (N-1)/2 columns) have been scheduled.

The numbers listed are the numbers that will be randomly assigned to the Cubs/Cars.

The left number in each column is the number of the car which will race in the left lane of that heat.

Improvement, to (mostly) avoid a Scout racing two successive heats: Move the even numbered heats of the first column (in order) to the bottom and renumber them.

Example: 8 cars

N = 8
Number of heats to schedule: (8 X 7) /2 = 28
Number of columns to schedule: (8-1)/2 = 3.5

Round:   1       2       3       4
Heats  -----   -----   -----   -----
1:   1 - 2   1 - 3   1 - 4   1 - 5
2:   2 - 3   2 - 4   2 - 5   2 - 6
3:   3 - 4   3 - 5   3 - 6   3 - 7
4:   4 - 5   4 - 6   4 - 7   4 - 8
5:   5 - 6   5 - 7   5 - 8
6:   6 - 7   6 - 8   6 - 1
7:   7 - 8   7 - 1   7 - 2
8:   8 - 1   8 - 2   8 - 3
Improvement:
Round:   1       2       3       4
Heats  -----   -----   -----   -----
1:   1 - 2   1 - 3   1 - 4   1 - 5
2:   3 - 4   2 - 4   2 - 5   2 - 6
3:   5 - 6   3 - 5   3 - 6   3 - 7
4:   7 - 8   4 - 6   4 - 7   4 - 8
5:   2 - 3   5 - 7   5 - 8
6:   4 - 5   6 - 8   6 - 1
7:   6 - 7   7 - 1   7 - 2
8:   8 - 1   8 - 2   8 - 3
In Column 1, Car 1 races in the left lane against Car 2, Car 3 races in the left lane against Car 4, etc.

Generating a Partial Round Robin for a 2-lane Track

The disadvantage of a Partial Round Robin is that some cars do not race against each other. This will erode the accuracy of the results. It is "fair" if the racer numbers are assigned "by lot", but "not as accurate" as a Full Round Robin. For instance, this could cause the 3rd fastest car to race both of the faster cars, but the 4th fastest car to race neither of them, which would probably cause the 4th fastest car to "finish 3rd," and vice versa.

I do not recommend this particular alternative... but it might be the only alternative if you must race a large number of cars. If it is used, it might be used as a way of qualifying cars for a "finals" race in which the qualifying cars race a Full Round Robin.

Count the cars.
Let N be the Number of cars.

If N is "odd", set K to (C - 1)/2.
If N is "even", set K to C/2.

Decide how many rounds you will have time to run. The number of rounds must be no greater than K.

Round 1: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 2 through N, then continue, starting with 1. Each car races twice, once in each lane.

Round 2: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 3 through N, then continue, starting with 1. Each car races twice, once in each lane.

Repeat until the desired number of rounds has been completed.

The numbers listed are the numbers that will be randomly assigned to the Cubs/Cars.

The left number in each column is the number of the car which will race in the left lane of that heat.

Improvement, to (mostly) avoid a Scout racing two successive heats: Move the even numbered heats in Column 1 (in order) to the bottom and renumber them.

Example: 9 cars

N = 9
K = (9-1)/2 = 4

Desire to run 3 rounds (27 heats).

Round:   1       2       3
Heats  -----   -----   -----
1:   1 - 2   1 - 3   1 - 4
2:   2 - 3   2 - 4   2 - 5
3:   3 - 4   3 - 5   3 - 6
4:   4 - 5   4 - 6   4 - 7
5:   5 - 6   5 - 7   5 - 8
6:   6 - 7   6 - 8   6 - 9
7:   7 - 8   7 - 9   7 - 1
8:   8 - 9   8 - 1   8 - 2
9:   9 - 1   9 - 2   9 - 3

Improvement:

Round:   1       2       3
Heats  -----   -----   -----
1:   1 - 2   1 - 3   1 - 4
2:   3 - 4   2 - 4   2 - 5
3:   5 - 6   3 - 5   3 - 6
4:   7 - 8   4 - 6   4 - 7
5:   9 - 1   5 - 7   5 - 8
6:   2 - 3   6 - 8   6 - 9
7:   4 - 5   7 - 9   7 - 1
8:   6 - 7   8 - 1   8 - 2
9:   8 - 9   9 - 2   9 - 3

Car 1 races in the left lane against Car 2, etc.

Generating a Double Round Robin for a 2-lane Track

The advantage of a Double Round Robin is that no car gains an advantage by racing against a slightly better car while having a better lane. The disadvantage (?) is that it takes more heats! And more racing!!!

Count the cars.
Let N be the Number of cars.

Round 1: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 2 through N, then continue, starting with 1. Each car races twice, once in each lane.

Round 2: List the positive integers vertically, 1 thru N. Next to them, list the positive integers 3 through N, then continue, starting with 1. Each car races twice, once in each lane.

Repeat until (N X (N-1)) heats (i.e. (N-1) columns) have been scheduled.

The numbers listed are the numbers that will be randomly assigned to the Cubs/Cars.

The left number in each column is the number of the car which will race in the left lane of that heat.

Improvement, to (mostly) avoid a Scout racing two successive heats: Move the even numbered heats of the first and last columns (in order) to the bottom and renumber them.

Example: 8 cars

N = 8
Number of heats to schedule: (8 X 7) = 57
Number of columns to schedule: (8-1) = 7

Round:   1       2       3       4       5       6       7
Heats  -----   -----   -----   -----   -----   -----   -----
1:   1 - 2   1 - 3   1 - 4   1 - 5   1 - 6   1 - 7   1 - 8
2:   2 - 3   2 - 4   2 - 5   2 - 6   2 - 7   2 - 8   2 - 1
3:   3 - 4   3 - 5   3 - 6   3 - 7   3 - 8   3 - 1   3 - 2
4:   4 - 5   4 - 6   4 - 7   4 - 8   4 - 1   4 - 2   4 - 3
5:   5 - 6   5 - 7   5 - 8   5 - 1   5 - 2   5 - 3   5 - 4
6:   6 - 7   6 - 8   6 - 1   6 - 2   6 - 3   6 - 4   6 - 5
7:   7 - 8   7 - 1   7 - 2   7 - 3   7 - 4   7 - 5   7 - 6
8:   8 - 1   8 - 2   8 - 3   8 - 4   8 - 5   8 - 6   8 - 7
Improvement:
Round:   1       2       3       4       5       6       7
Heats  -----   -----   -----   -----   -----   -----   -----
1:   1 - 2   1 - 3   1 - 4   1 - 5   1 - 6   1 - 7   1 - 8
2:   3 - 4   2 - 4   2 - 5   2 - 6   2 - 7   2 - 8   3 - 2
3:   5 - 6   3 - 5   3 - 6   3 - 7   3 - 8   3 - 1   5 - 4
4:   7 - 8   4 - 6   4 - 7   4 - 8   4 - 1   4 - 2   7 - 6
5:   2 - 3   5 - 7   5 - 8   5 - 1   5 - 2   5 - 3   2 - 1
6:   4 - 5   6 - 8   6 - 1   6 - 2   6 - 3   6 - 4   4 - 3
7:   6 - 7   7 - 1   7 - 2   7 - 3   7 - 4   7 - 5   6 - 5
8:   8 - 1   8 - 2   8 - 3   8 - 4   8 - 5   8 - 6   8 - 7
In Column 1, Car 1 races in the left lane against Car 2, Car 3 races in the left lane against Car 4, etc.

Scoring, Identifying the Winners, Breaking ties!

For each heat, award the first place car 2 points, and award the second place car 1 point. (This is more work than awarding the second place car 0 points, but it is worth it to avoid any Cub from having a "Goose Egg" total score!) At the end of the racing, add up each racers points! (Hint: For quicker results, just count and compare, but don't post, the number of 2-point scores!)

If there are 2-way ties that must be broken, race the tied cars on alternating lanes until one racer wins 2 consequetive races.

If there are multi-way ties to break, use a double Round Robin among the tied cars. This is generated the same way as a full Round Robin, then use the same chart again with the lanes swapped.

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Latest update: 02/21/97