Charts - Perfect-N Type

Perfect-N Type Scheduling

General

This chart generator interface uses a driver to produce racing charts which satisfy the Partial Perfect-N (PPN) criteria. Where numbers permit, the charts also satisfy the Perfect-N criteria or the Complimentary Perfect-N criteria.

PPN Charts are a concept expounded to Stan Pope by Cory Young, under the name "Enhanced Lane Rotation". They are "final standing" charts, which span the gaps in Perfect-N charts. They satisfy most of the Perfect-N criteria.

A PPN chart is one which satisfies these conditions:

1. Each vehicle races the same number of times in each lane (which implies that the number of heats is a multiple of the number of vehicles)
2. Equality of opposition is optimized, i.e., no head-to-head match up count exceeds another by more than 1.

Note: There are no known PPN (or better) charts for the following cases: 5 lanes: 20 and 22 vehicles; 6 lanes: 16, 17, 29, 30, 32, 33, and 34 vehicles. (Many of these cases fall near Perfect-N charts ... which seems to be a complicating factor.) Lower quality charts, labeled "Miscellaneous", are produced for these options. Whether the chart is used for awarding trophies or screening for a more accurate finals, more accurate results will be accomplished by running byes in a PPN chart constructed for a slightly larger number of vehicles.

Note: Accuracy of the PPN charts ranks below Perfect-N and above Stearns and Double Elimination.

Note: This chart generator produces Perfect-N and Complementary Perfect-N charts when the chart selection parameters allow. Otherwise, it generates Partial Perfect-N charts or, as a last resort "Miscellaneous" charts. The title above the generated chart tells the type.

Advantages/Disadvantages

PPN Charts have their advantages and disadvantages that you should be aware of, so you should examine them before deciding on this type of scheduling for your race.

• Advantages:
  1. Race in Each Track Lane - This is one of the criteria that PPN charts must meet. Each racer has the same advantage/disadvantage when it comes to the lane assignments, so "slow" or "fast" lanes will not determine the outcome of the race.
  2. Equal Number of Heats - This is one of the other criteria that PPN charts must meet. The race is made more fair by allowing the racers an equal chance to compete by racing an equal number of times.
  3. High Number of Opponents - PPN Charts do a good job of maximizing the number of opponents for each racer without yielding as many heats as some other scheduling methods like the Stearns Method do. These charts are suitable for use when scoring by points due to the high number of opponents.
  4. Heats Spread Out for Each Racer - Though it is possible for a racer to race in back to back heats, PPN charts generally spread out the heats for each racer. This will keep the racers more into the race and less likely to get into mischief.
• Disadvantages:
  1. Heat Randomness - Though there are mathematical algorithms that determine when the racers will race, it can appear to be random to the lay person. This can be a bit confusing since racers can be unsure when they will be racing and in which lane. This confusion can slow down a race unless countermeasures are put in place (posting schedules, displaying On Deck racers) to make sure that the appropriate racers get to the start gate when they should.
  2. Some Charts Cannot be Generated - It is not possible to generate charts for all possible combinations of lanes, racers and number of runs per lane since the mathematical algorithms to create them have not yet been found. This problem increases with higher numbers of lanes and number of runs per lane.