SORC 1998

by David Lussier dlussier@seacorp.com

Introduction

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.

Definitions and Formulas

In order to discuss this subject matter, the following defined variables are provided as reference:

T=Time (Minutes)

CT=Corrected Time (Minutes)

ET=Elapsed Time (Minutes)

D=Course Distance (Nautical Miles)

S=Speed (Knots = Nautical Miles/Hour)

N#=NEMA Handicap Number (Seconds/Mile)

PH#=PHRF Handicap Number (Seconds/Mile)

DPN=Designated Portsmouth Number (Unitless Factor)

TOD=Time-On-Distance (formula reference)

TOT-Time-On-Time (formula reference)

Both NEMA and PHRF handicap mathematics contain essentially the same formulas which are:

NEMA formula:

CT=ET-(D*N#/60)

PHRF formula:

CT=ET-(D*PH#/60)

Portsmouth mathematics utilize a more simple formula, then refine the DPN with for wind velocity and boat modifications. The basic formula is:

Portsmouth formula:

CT=ET/DPN

TOD Examples

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.

TOD Conclusion

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.

A translation of the TOD (NEMA or PHRF) formulas in words would be:

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. Look at the table below to visualize this non-linearity, by examining the "Difference %" in the bottom line. That value is the percentage difference in CT between the two boats for three different race wind conditions. As illustrated in the table, the fast boat (A) wins in light air, but loses in heavy air with a difference between the boats that signifies there is some wind speed between light and medium where the two boats are accurately handicapped.

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).

TOT Concept

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. The Portsmouth system ignores the course distance, but does consider the wind speed in a simple formula:

Portsmouth Math:

CT=ET/DPN

In addition to this formula, the DPN can be altered for all boats based on different wind conditions. For example, boat A mentioned in the previous examples has a DPN for general use in all conditions, but also has specific refined DPN’s for various wind speeds as follows:

Let’s assume the same race conditions in the previous light and heavy air races with the same two boats, A and B. The two boats mentioned have DPN’s of 0.545 for Boat A and 0.720 for Boat B. In the light air race, the CT’s would be:

Boat A: CT=80/0.545=147 minutes

Boat B: CT=107/0.720=148 minutes

In the heavy air race, the CT’s would be:

Boat A: CT=30/0.545=55 minutes

Boat B: CT=40/0.720=56 minutes

The table below illustrates the example race results using NEMA mathematics as well as Portsmouth mathematics for easy comparison. As you can see from these results, the same ET race results from the same boats would yield a Portsmouth CT which has a solid linearity in all wind conditions, even without using specific DPN’s for variable wind conditions. It clearly shows that as the wind conditions change, the Portsmouth mathematical approach provides for a difference in CT of only 1% for all conditions, while the NEMA mathematics for the same race conditions of boat speed and elapsed times shows a gross mismatch as the wind speed increases.

The results in the table also illustrate that while the refined DPN’s for variable wind conditions are available for many boats (Portsmouth Math with WIND HC), the Difference % in results between the boats remains relatively constant in different conditions, making them less desirable to utilize. However, the refined DPN’s are based on actual race results collected over time by US Sailing and are generally more accurate, especially when mixing larger fleets of different boat types.

In addition to the refined DPN’s for various wind conditions, the Portsmouth handicap system also has modification factors for boat and/or crew modifications, which could be expanded to include modifications to any boat, one design or home built. The current list of Portsmouth modification factors and potential additions for Corsair trimarans are discussed later in the Corsair section of this paper.

NEMA Considerations

NEMA is comprised of over 40 registered racers per year, including of home built catamarans and trimarans as well as one design factory built boats. As of the 1996 racing roster, over 60% of NEMA registered racers were factory built boats and already have a Portsmouth number (DPN) maintained by the US Sailing organization. If NEMA decided to utilize the Portsmouth system for handicapping, most of the boats handicaps would be a simple look up in the annually published listing, while the remaining minority would require a simple interpolation or conversion process to extrapolate DPN’s for the home built boats. As race result data is collected over the years in the future, refinements to both home builts and factory one designs handicaps could be performed to establish and maintain fair ratings for all.

In addition to the various boats registered as racers in NEMA, the organization also handicaps skippers, similar to a bowling or golf league. As you improve yourself, your handicap changes to keep the less skilled competition equally competitive with you in the remaining or follow on racing season. This approach was intended to attract members and racers, so that beginners could compete with the "pros" and still have a chance at a trophy. When you mix this with the continual handicap updates due to people learning about their boats and boat improvements, the NEMA handicaps are extremely variable and do not represent an accurate rating for a particular boat type, but are specific to the boat, the skipper, and how they interact with the current NEMA racing fleet. Obviously, this system is not transportable to other parts of the country.

The F-27 Class Association President Don Wigston had a couple of good quotes on this topic. "I don’t want a trophy, I want to become a good sailor. Racing would be rather pointless if the best skippers were handicapped. Aren’t we out there trying to figure out who is the best?"

I personally consider it a challenge and honor when racing against great sailors like Bob Gleason or Randy Smyth and do well against them, win or lose, with an even handicap based on boat characteristics only. Unlike basketball, we can’t play one on one with Michael Jordan, but we can sail against the best in the US on a fairly regular basis. What a great opportunity! If we really had so many novice sailors that really wanted to race, but were not participating due to intimidation by the pros, separate A and B classes could easily be established on a regatta basis to allow them to participate with the same handicap system against sailors of similar skill levels. My experiences indicates that the vast majority of prospective offshore multihull race participants are generally not novice racers anyhow.

Regattas Etceteras

A lot of multihull race organizers fear continuing to use NEMA, PHRF TOT, MASF, or Portsmouth systems since they are not clearly recognized by many monohull regatta organizers who usually use PHRF TOD handicapping. The fear stems from their pursuit to get multihulls invited to traditionally monohull regattas, and the presumption that the monohull organizers will use the different handicapping system as a reason or excuse to not invite a multihull class.

First, the monohull regattas should accept multihulls regardless of the handicap system differences. A multihull racer or volunteer organizer for the multihull fleet should take the burden off of the traditional monohull race committee and utilize whatever system the multihulls want to use and only require the race committee to record sail numbers and finish times.

Second, if the Portsmouth system were utilized by multihull fleets, the following situation would present itself. For every race where multihulls tell the race committee that a Portsmouth system must be used in lieu of PHRF, and they shrug their shoulders and don’t let the multihulls participate, there are at least two other regattas organized by beach catamarans that would love to have the larger multihulls participate. The beach catamaran clubs (lots of em) generally have a Portsmouth class in their regattas already, so the larger multihulls would fit right into the scoring system. In addition, many of them are prospective big boat owners and would love to race with/against the larger boats, on separate or same circles, just to see the boats perform. This would help multihull racing growth in the future as the generally younger racers see the more comfortable sport boats racing with a cruising option style boat. There is no issue with the smaller boats with respect to scary high boat speed at the starts or mark roundings since many of them (Mystere 6.0, NACRA 6.0, etc.) are faster than many of the larger multihulls anyhow. The largest regattas of non-one design multihulls in New England has been events such as Cat ’88 and the old Unlimited Regattas where the beach cats were invited along with the big multihulls, not multihulls participating in traditional monohull regattas.

In the 12/96 issue of American Sailor, Russ Cardoza, the chief handicapper for the Narragansett Bay PHRF, discusses the future as the monohull fleets in this area as they begin to transition from TOD to TOT handicapping. They have recognized the inaccuracy of TOD and are moving forward with competitive racing. One of the interesting points he brings out is that the PHRF system has trained many racers to easily calculate where they stand in the middle of a race by timing competitors at marks or the finish. With TOT mathematics, this computation during the race is no longer trivial since the difference between boats is not a simple seconds/mile calculation. However, Russ does offer some elaborate TOT cheat sheet methodology for figuring your standing with competitors.

"PHRF TOT"

MASF and other organizations have begun to use the PHRF TOT system which basically takes the PHRF TOD handicap system and converts each boat type handicap, exclusive of skipper skills, to a PHRF TOT handicap. This process ignores race course distance, taking most of the error out of the PHRF TOD system. The conversion formula is:

PHRF(TOT)=650/(550+PHRF(TOD))

This system is much more accurate than the PHRF(TOD) and NEMA systems, but still has a flaw in the mathematical process. There are various handicap corrections for sails, hull extensions, and other boat modifications that are accounted for in seconds/mile (TOD) to the basic PHRF(TOD) handicap. These corrections are made to the PHRF(TOD) number before the conversion process which implies that a correction for an improvement is equal to a value that is constant across all wind conditions, which is obviously not true. For example, if 6 seconds/mile were the correction factor for a an additional screecher sail, the correction should be 6 seconds/mile for medium air, but likely a different value for light as well as heavy air conditions.

Also, the resultant PHRF(TOT) handicap is not compatible in any way with the Portsmouth TOT system. The end number is in fact a TOT handicap used in a ET/CT formula similar to Portsmouth, but the end number is not in a range compatible with the existing Portsmouth system which already has hundreds of boats handicaps documented.

Measurement System

The measurement system puts forth design constraints for one-design fleets, but requires extensive and laborious efforts to ensure the designers, owners, and race participants are all in compliance with the specifications. However, in order to integrate both one designs and home built multihulls into a common Portsmouth system, home built boats may require measurement of their current designs to establish a Portsmouth handicap. Alternatively, race results and existing TOD handicaps for home built boats could be converted to a Portsmouth handicap by relatively simple interpolation process.

Corsair Trimarans

The Corsair line of Trimarans has a national organization of members striving to establish a common handicap system for all races involving Corsair boats in the USA. They can be contacted on an Internet list server via email address: f_boats-1@mail.unm.edu or the organization President Don Wigston at email address: meddjw@emory.edu or you can visit the handicaps web site at internet address: http://userwww.service.emory.edu/~meddjw/handicaps.html .

This organization is in hot pursuit of establishing a national handicap system for mixing Corsair Trimarans amongst themselves as well as with other multihulls and monohulls. The group actively communicates on the internet and exchanges technical findings from various multihull clubs nationwide.

Last year, the 1996 Corsair Nationals used handicap ratings assembled by a Committee consisting of Trey Ritter, Paul Koch, Alan Tate, Ian Farrier, Gino Morrelli, John Teloh, Bob Gleason, and Randy Smyth. They put together a list of as many different ratings they could find that included the F-24, F-27, and F-31, and compared the time differences. The result was a table of PHRF TOD style handicaps for those boats as well as interpolated handicaps for other regatta participants including the F-24 Mk II, F-27 Formula, and F-25C. In addition, a conversion from TOD to TOT was developed and utilized to more accurately handicap the boats. No handicap was employed for skipper skill.

The table below illustrates, in lines 1 and 2, the TOD and TOT handicaps established for the mix of boats at the 1996 Corsair Nationals.

The handicaps used on line 2 adequately represented the fleet for the regatta with the exeptions noted earlier in "PHRF TOT". Taking this process one step further, lines 3 and 4 of the table utilize the PHRF TOT handicap and convert them into equivalent Portsmouth handicaps. Line 3 takes this handicap and inverses the number (1/X) so that the smaller number is the faster boats and the larger number is the slower boats, just as the Portsmouth system. This step does not degrade the relativity of each number to the other boats handicap from a percentage standpoint.

Line 4 is where the magic happens. Using the Stock F-27 as a baseline boat with a relatively known Portsmouth number, the handicaps in line 3 are converted into Portsmouth ratings in line 4 by taking ratios against the Stock F-27 Portsmouth number of 0.720. Although US Sailing lists the F-27 as 0.755, six years of personal experience and peer concurrence has shown that the Stock F-27 (with symmetrical spinnaker and no bow sprit) is about as performance equivalent as a Hobie 18 without a spinnaker, which has a well established Portsmouth number of 0.720.

Line 4 reflects proposed handicaps for all of the Corsair line of boats that could be refined based on changing class rules or a more definitive rating for the baseline Stock F-27. This simple process could also be used to establish Portsmouth numbers for all the boats in NEMA, MASF or any multihull organization. If that were done, Corsairs could travel nationwide and participate in races knowing their rating with little doubt. In addition, the potential to participate in the multitude of small boat regattas that use the Portsmouth system could be realized.

Another consideration that the Corsair folks are studying is how to handicap boats that meet the class rules for one of their classes, but deviate in some small fashion by particular boat modifications. The Portsmouth system already has a system for modifying DPN’s due to boat and/or crew modifications, although only the boat modification factors would apply to the Corsair group. The table below illustrates the 1995 list of modification factors (MF) for US Sailing multihulls. If using the DPN, the new DPN would be calculated by:

DPN(modified)=DPN*MF

If using the specific DPN for a wind speed category as shown in the last four columns, the formula would be the same, but using the appropriate MF based on wind speed. The numbers in the four wind columns represent wind speeds represented by the Beaufort scale (top) and knots (bottom).

The existing Corsair fleet has a list of modifications and respective handicaps expressed in seconds/mile. The table below lists those modifications and the applicable handicaps. In addition, the table shows the calculated adjustment to the DPN in two formats. First, the DPN Adj is an adjustment to the DPN which is a value that would be subtracted from the DPN. Second, the DPN MF is a multiplication factor which could be used to yield a new DPN by multiplying the base DPN by the DPN MF.

Just as in existing DPN MF’s, if multiple MF’s were applicable, the final DPN would be:

DPN(final)=DPN*(DPN MF1)*(DPN MF2)…

Summary

Use TOT mathematics, not TOD.

Use the Portsmouth TOT system.

Don’t penalize good skippers by changing their handicap.

Establish a National and eventually global scoring system for all multihull handicap sail races.

Copyright MASF 2/3/97  Last updated:  01/15/98,  Click here to send mail to web administrator.
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