by David Lussier
When multihulls race using the PHRF or NEMA handicap systems, they are inevitably unfairly rated, except in mid-range wind conditions. In general, if the wind is light, faster boats with the lower handicap numbers will win the race. On the contrary, if the wind is heavy, slower boats with larger handicap numbers will usually win the race. There is a simple mathematical explanation for this, which apparently, not many racers stop to consider. This is evident by the continued use of Time-On-Distance (TOD) mathematics for sailboat race handicapping as well as the future development by many organizations of more refined TOD mathematics, in lieu of Time-On-Time (TOT) mathematics. The objective of handicapping is to take the variables associated with different boats out of the equation thereby determining the winner based solely on the skipper/crew expertise. This paper serves to explain the mathematical differences between TOD and TOT handicap systems and offer an alternative system for rating all multihull events, regardless of boat size from beach catamarans to large cats and tris.
For a light air race using NEMA (or PHRF) TOD handicapping, consider two boats, A and B, where boat A (faster boat) has a NEMA# of 25 and boat B (slower boat) has a NEMA# of 190. These are realistic NEMA handicaps for a Formula 40 and an F-27, respectively. The difference between the two boats NEMA#'s is 190-25=165 which translates into 165 seconds/mile or 2 ¾ minutes/mile. For an 8 mile race, that means boat A has to beat boat B by at least 22 minutes (2 ¾ minutes/mile x 8 miles) to win on corrected time. In light air, let's assume the course will enable boat A to average 6 knots, which means boat A will take a total of (60*D=S*T or T=60*D/S) 60*8/6=80 minutes to complete the course. Let's assume boat B will average 4.5 knots which will take a total of 60*8/4.5=107 minutes. The difference in corrected times will be:
Boat A: CT=ET-D*N#/60=80-8*25/60=77 minutes
Boat B: CT=ET=D*N#/60=107-8*190/60=81 minutes
In this light air race, Boat A wins by a 6% margin. It took both boats a longer time to complete the course due to light air. In heavier air, the time to complete the course will be less for both boats. In the lighter air, the race for both boats is longer in duration allowing more time for Boat A to put more time between the two boat's finishing times.
Based on NEMA handicap ratings, the margin for Boat A to beat boat B is a fixed number of 2 ¾ minutes/mile, regardless of how long the course is, no matter how hard the wind blows, and no matter how long it takes either boat to complete the course.
For a heavier air race, consider the same two boats. Let's assume the same 8 mile course is raced, but with the heavy air, assume boat A will average 16 knots and boat B will average 12 knots. Boat A will take a total of 60*8/16=30 minutes and boat B will take a total of 60*8/12=40 minutes to complete the 8 mile course. The difference in corrected times will be:
Boat A: CT=ET-D*N#/60=30-8*25/60=27 minutes
Boat B: CT=ET-D*N#/60=40-8*190/60=15 minutes
In this heavy air race example, Boat B (the slower boat with the larger handicap number) wins on corrected time by a large margin (45%). The numbers are fictional for discussion purposes, but are not far off of performances of past NEMA regattas.
For a medium air race, the TOD handicapping system works fairly well, especially after years of data collection are accumulated to refine the handicaps for each boat. The problem with light air races is that the faster boats have a longer race time period to put a fixed number of seconds between them and the slower boats. The problem with heavy air races is the faster boats do not have a long enough race time period to put those same fixed quantity of seconds (once the course length is determined) between them and the slower boats.
No matter how long the race distance is, no matter how long the race takes to complete, or how hard the wind blows, two differently rated boats have a fixed handicap time difference between them for each mile to be sailed. This translation means that the handicap process is not linear in fairness for varying wind conditions.
Monohull sailors have encountered this same dilemma, but the problem is not as pronounced as it is for multihulls due to the general average boat speed differences between monohulls and multihulls. Although there is a large boat speed differences between boat A and boat B for multihulls, the boat speed difference between two monohulls with a similar PHRF comparison as boat A and B would be far less than that discussed above (i.e. 3 knots in light air and 7 knots in heavy air vice 6 and 16).
A more accurate way to handicap racing multihulls (as well as monohulls) is to consider that two boats are handicapped on a relative percentage, as the existing US Sailing Portsmouth System does, and small beach catamaran sailors have been doing for many years.