Racing Rules of Sailing (RRS), Appendices E and A. A copy of the RRS may be downloaded from: The Racing Rules of Sailing
Problem Statement Background Radio control sailboat races are scored on a “low point” system as defined by the official Racing Rules of Sailing (RRS), Appendices E and A. A copy of the RRS may be downloaded from: The Racing Rules of Sailing 2013-2016 An event is called a race and consists of multiple heats. Contestants are awarded points equal to their finishing position in a heat: 1 for first, 2 for second, and so forth. Depending on the number of heats run, contestants may discard one or more high scores. The remaining scores for the heats are summed and the low score wins. A typical race scoring matrix can be found here: http://www.unm.edu/~eschman/dcmyc/2013_R5_S1M.pdf There are times when the entry list is too large to compete in a single heat. At least two systems have been devised to handle such events. These systems divide heats into what we will call subheats and combine the results in a “fair” way to determine winners. An overview of such systems can be found here: http://www.theamya.org/resources/prorelsys.php Note that the linked document uses the term “heat” for what we call here a “subheat.” Heat Management System The dominant system is Heat Management System (HMS) 2007. In its simplest form, each heat is run as two subheats, called A and B. Contestants are initially assigned to the subheats either through a “seeding competition” or arbitrarily by the race committee. The better contestants are placed in the A subheat and the contestants of lower ability are placed in the B subheat. For example, consider a field of 20 contestants. This would be split evenly into subheats of 10 contestants each. The B subheat is run first. The top 4 finishers are not scored but are marked for promotion. The remaining finishers are assigned scores of 10 through 16. Then the A subheat is run. The finishers are assigned scores of 1 through 10. The bottom 4 finishers are then relegated to the next B subheat and the B subheat contestants marked for promotion are promoted to the next A subheat. Note that this system maps (in our example) the possible range of scores from 1-20 if all sail together to 1-16 owing to the unscored contestants who are promoted from the B subheat.
A detailed description of an HMS variant called the Equal Opportunity Racing System (EORS) can be found here: http://bit.ly/17mEyGV As before, this document uses “heat” where we use “subheat.” A simulation model and analysis of the HMS/EORS system can be found here: http://www.onemetre.net/OtherTopics/EventSim/Eventsim.htm The HMS/EORS systems have been criticized on three grounds: complexity, consequences of scoring errors, and the “bubble phenomenon.” The last refers to a situation in which mid-range competitors are repeatedly promoted and relegated so that they are forced to compete in multiple sequential subheats, a situation which can lead to fatigue and equipment failures. Subheat Shuffling A competing system for combining subheats into heat scores is called Odd/Even. This is a member of a family of possible systems which we will call subheat shuffling. In “pure” Odd/Even the contestants are initially assigned randomly to A and B subheats. The subheats are run independently, usually A first and then B. Contestants are scored in finishing order; following our example, this means that the A heat contestants are awarded 1 to 10 points and the B heat contestants are awarded 1 to 10 points. The scores are entered in a scoring matrix as if the whole group raced as one. The difference is that two contestants will be awarded 1 point (the winners of A and B), two contestants 2 points, and so forth. An example of such a scoring matrix can be found here: http://www.unm.edu/~eschman/dcmyc/2013_RGCup.pdf Note that this system maps (in our example) the possible range of scores from 1-20 to 1-10. After each pair of subheats is run, the membership is shuffled in the following fashion: all contestants who received an odd number of points are placed in the next A subheat. All contestants who received an even number of points are placed in the next B subheat. The process is then repeated. The criticism of Odd/Even is that the top competitors may not be in the same subheat enough times to produce a “fair” result. This problem has been addressed by assigning contestants to A and B heat based on perceived ability to begin with, and then reassigning based on partial results at periodic intervals. Another criticism is that the reduced range of scores increases the probability of ties.
Other forms of subheat shuffling are possible, including simply randomly assigning competitors to subheats each cycle. We are not aware of any simulation models or analyses that have been produced for Odd/Even or other possible subheat shuffling system. Tasks and Possible Results The principal tasks would be to construct simulation models of full fleet racing, HMS/ EORS and a variety of subheat shuffling systems. These models would have to capture intuitively satisfactory notions of competitiveness and “fair” results. The existing simulation model of HMS (linked to above) can be used as inspiration. The next task would be to form a series of interesting questions to be examined using the simulation model. Some possible questions are: Is the scoring system defined in the RRS “fair” by your definition? If not, why not? To what degree are the various systems “fair?” Is there a point where the systems converge on “equivalent” results? Can you draw interesting conclusions about when the “bubble phenomenon” in HMS/ RRS is likely to occur? Can you model the effects of fatigue and equipment stress? And so forth, limited only by your imagination. Contact If you have questions I may be reached at:
[email protected] Good luck, Earl Boebert (Senior Scientist, Sandia National Laboratories, Retired)
