Modelling boat ability
The simulation offers five different ability models as standard (but it is simple to add others). The graph illustrates these models using a 48-boat fleet.
The two linear models spread boat ability evenly, the difference being the tight linear model packs the abilities closer together, while the wide model spreads them out as much as possible.
The two "J" shaped models have the top boats more separated in ability, while the also-rans are more tightly packed. The 'hard' J models a situation where the top boat is much better than the second boat, which is much better than the third, and so on, such that the top four boats enjoy the top half of the ability range. By the time we reach the 8th boat or thereabouts the boat abilities are packed together into the lowest one-third of the ability range. The 'soft' J model similarly gives the top boats proportionately more difference between them and the rest of the fleet, but this is not as marked as in the 'hard' J. In the 'soft' J, the top 13 or 14 boats of the 48 in the fleet take up the front half of the ability spread. We might imagine that the 'hard' J model applies to a club event, where there are generally a few very good sailors plus the rest, and the 'soft' J model would apply for a regional or national event where there are more good sailors but there is also a sizeable tail of also-rans.
The cosine 'S' model provides for a group of closely matched sailors at the top end of the fleet, and a similar group of, erm, closely-matched sailors at the bottom of the fleet, with the middle of the fleet spread between these two extremes. This might serve as a model for an international event.
The weighting parameter determines how heavily the simulation emphasises any boats out of position, and has (obviously!) a profound effect upon the results. Five weighting methods are available (and again, it is very simple to add others).
The 'egalitarian' weighting method weights all boats equally. That the boat with the bottom ability might place third-last is assigned equal importance to the boat with top ability which places third. This weighting method would be appropriate if the simulation was used to explore the quality of an event from the point of view of any competitor.
The 'linear' method gives a straight-line decreasing weighting in accordance with the boat's ability. The top boats are weighted more than the bottom boats, but not very strongly. As with the 'egalitarian' method, this would be used to assess the internal quality of the event from a competitor's point of view.
There are three 'J' methods which seek to weight the top boats, and these methods are appropriate if the simulation is used to explore questions such as, "Did the top boats come top?"
The third graph shows the discrepancy scores resulting from every combination of boat ability profile and discrepancy weighting method, for a 'standard' event of 20 races. This should help with the interpretation of a particular discrepancy score from a specific simulation run.
©2023 Lester Gilbert