by Paul and Kathy Mathews, J35 Whitehawk, 41322

Grand River Sailing Club

PO Box 607, Grand River, Ohio 44045

e-mail: pmathews@apk.net

Introduction

People have complained for years about the PHRF handicapping system. PHRF has endured because of its simplicity, low cost, ease of administration, and inertia. Yet most people agree that PHRF fails under certain conditions. When the wind is extreme it’s often possible to accurately predict the day’s winners and losers before ever leaving the dock. Now an alternative system, Americap, has been developed and appears to offer significant improvements over PHRF while preserving most of PHRF’s advantages. Numerous articles have been published describing the Americap system but none of them have attempted to explain how Americap ratings are derived. The purpose of this article is three-fold: first, to review the PHRF, IMS, and Americap handicapping systems; second, to identify the key flaws of the PHRF system; third, to outline the theory behind the Americap system.

The data we used in this article is old and limited. We had access to the 1991 IMS Master File which gives limited information on IMS time allowances, 1994 IMS certificates for a J35 and a C&C 38, and a 1997 Americap certificate for a J35. Even though IMS has changed considerably since 1991 we feel that our conclusions will remain qualitatively the same for current data. Throughout the article we’ve used IMS as the benchmark for evaluating other handicapping systems since it provides the best model of true boat performance.

Every handicapping system specifies at least one coefficient that comprises a boat’s rating. This rating is used in an algorithm to convert elapsed time into corrected time. A boat’s corrected time corresponds to the amount of time a reference boat (RB) would have taken to complete the course under the same conditions. Comparing corrected times to determine who won a race is like pretending that everyone’s sailing a RB. In some systems the RB is the fleet scratch boat, in others the RB may be hypothetical. Of course the boat with the shortest corrected time, corresponding to the fastest RB, wins.

PHRF uses a single rating coefficient to correct elapsed times based on course length. This is commonly referred to as a time on distance correction. PHRF corrected times are calculated using the following equation:

t_corrected = t_elapsed - (R * d) (1)

where R is the PHRF rating of the boat in seconds per nautical mile (sec/nm) and d (for distance) is the straight line length of the course in nautical miles. For example, suppose that a J35 with PHRF rating
R = 69 sec/nm completes a 10nm course in 7200 seconds (2 hours). The J35’s corrected time would be:

t_corrected = 7200sec - (69sec/nm*10nm) = 6510 seconds

This means that the PHRF RB, with a PHRF rating R = 0, would have taken 6510 seconds to complete the course if it was sailed in place of the J35.

IMS represents the complicated end of the handicapping system spectrum. IMS uses a computer program called a velocity prediction program (VPP) to predict boat performance. The VPP predictions are based on fundamental physics so IMS is not a performance based handicapping system like PHRF. The inputs to the VPP are measurements of boat hull shape, rig, displacement, ballast, etc., and assumptions about the number of crew and their placement on the boat. The output of the VPP is predicted boat velocity (v) for different true wind speeds (TWS) and true wind angles (TWA). The VPP also gives optimum beat and optimum run boat velocity and TWA. The VPP outputs are presented in tabular form but they are often summarized in a velocity polar plot. If you do not have an IMS certificate for your boat, or one from a sister boat, consider obtaining one from US Sailing. An IMS certificate provides an excellent benchmark for boat performance such as how high you should point on a beat and what your gybe angles should be.

Since boats perform differently on different points of sail, IMS uses the VPP predictions weighted by the beat, reach, and run fractions of a course to determine ratings. IMS gives ratings for common course configurations: Windward-Leeward, 6 Leg Olympic Triangle, Linear Random, and Circular Random. These ratings are reciprocal velocities (1/v or v^-1), also referred to as time allowances (TA), and are reported in seconds per nautical mile. A TA is the amount of time that a boat should take to sail one nautical mile under certain conditions of TWS and course configuration. (To convert a TA to a velocity use v = 3600/TA where v is in knots and TA is in sec/nm.) The IMS VPP gives TAs for seven values of TWS: 6, 8, 10, 12, 14, 16, and 20 knots for each course. The TAs from an IMS certificate for a J35 are given in Table 1. The Table shows, for example, that a J35 should complete each mile of a 6 Leg Olympic Triangle in 731 seconds when sailing in 10 knots of wind.

The four standard IMS courses were carefully designed to cover a broad spectrum of course configuration. One way of comparing the courses is by their beat content, the percentage of the course distance devoted to beats. The beat content of the Windward-Leeward and 6 leg Olympic triangle are 50% and 55%, respectively. The Linear Random course corresponds to a straight line course with the wind blowing for equal amounts of time from all TWA. This rating is recommended for point to point racing when no information about the prevailing wind direction is available. The beat content of the Linear Random course is about 16% of total distance. The Circular Random course corresponds to sailing around a perfect circular island while the wind blows from a fixed direction. The beat content of this course is about 25% of total distance. IMS recommends that nonstandard courses be scored using the ratings for the standard course with the closest beat content. IMS is capable of custom scoring any course but this is usually not necessary.

There are several methods used to score races under IMS. One of the simplest methods involves using the IMS rating for the TWS closest to the observed TWS for the race. Suppose that in the J35 scoring example the race committee called a Circular Random course and observed an average TWS of 8 knots. The J35’s rating for the race, from Table 1, is 683.6sec/nm. The J35’s corrected time will be:

t_corrected = 7200sec - (683.6sec/nm*10nm) = 364sec

This corrected time suggests that the J35 took 364 seconds longer to complete the course than IMS predicted, that is, the J35 was slow by 364 seconds.

Another method of scoring, essentially the same as the previous method, involves correcting time to a scratch boat or RB. Suppose that the scratch boat in the example was a Frers 45. At 8 knots TWS on the Circular Random course IMS predicts that the TA difference between the J35 and Frers 45 is about 50sec/nm (data are from 1991 IMS Master File) so the J35’s corrected time will be:

t_corrected = 7200sec - (50sec/nm*10nm) = 6700sec

This corresponds to the amount of time that the scratch boat would have taken to complete the course if it had been sailed in place of the J35. This example shows that the TA difference between two boats is like a PHRF rating; it indicates how much time one boat should give the other.

A more accurate method of scoring under IMS uses a boat’s performance on the course and its TAs to determine an implied TWS. The RB’s performance at the implied TWS determines the corrected time. This method eliminates the need for the race committee to have to pick a TWS for scoring. To see how this works, consider the J35 example again with the Frers 45 as the scratch boat (RB). Figure 1 shows TA versus TWS for the two boats. Since the J35 completed the 10nm course in 7200 seconds, its average reciprocal velocity over the course was v^-1 = (t_elapsed/d) = 7200sec/10nm = 720sec/nm. The graph shows that to complete the course at this rate the J35 must have effectively sailed in 7.8 knots of true wind. Under the same conditions the RB would have sailed at 667sec/nm and so would have completed the course in 667sec/nm*10nm = 6670 seconds. 6670 seconds is the corrected time for the J35. In practice this calculation is done by an appropriate scoring program or spreadsheet package.

Americap is a compromise between PHRF and IMS. It’s like a PHRF system with different ratings for different wind speeds and courses. The Americap rating coefficients for a J35 are shown in Table 2. Americap uses only two coefficients, called A and B, to determine a boat’s rating on a course. These coefficients are picked to approximate the predictions of a VPP over all wind speeds. US Sailing plans to keep the Americap VPP secret to prevent designers from building boats that beat their rating, but the Americap and IMS VPP must be very similar.

Americap corrected time is calculated from:

t_corrected = (A*t_elapsed) - (B*d) (2)

The first term, (A*t_elapsed), is a time on time correction and the second term, (B*d), is a time on distance correction. The Americap corrected time for the J35 in the example would be:

t_corrected = (0.9574*7200) - (75.4*10) = 6140 sec

where A=0.9574 and B=75.4 came from Table 2 for the All Purpose Closed Course. This corrected time implies that the Americap RB, sailed under the same conditions as the J35, would have completed the course in 6140s.

Don’t be concerned that the three handicapping systems yielded different corrected times in the example calculations. It’s inappropriate to compare corrected times from different handicapping systems since each system has a different RB. Only corrected time differences between boats scored under the same handicapping system are meaningful.

The level racing format used at large regattas also deserves mention. Boats racing level are scored as if they are all rated the same so finish order determines place. In this format there are no handicapping coefficients since corrected times are unnecessary. This puts the different handicapping systems into perspective according to their complexity as shown in Table 3.

0 1 2 7 Number of factors in rating

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Level PHRF Americap IMS Handicapping System

PHRF operates under two flawed physical assumptions: first, that the TA difference between two boats does not change with TWS, and second, that the TA difference between two boats does not change on different courses. Both of these assumptions are wrong and lead to very large PHRF scoring errors. Any alternative handicapping system seeking to improve on PHRF will have to take both factors into account.

The first PHRF assumption is tested in Figure 2 which shows the TA difference between an Express 27 and a J35 versus TWS for IMS and PHRF. PHRF says the J35 gives the Express 27 66sec/nm for all TWS. IMS suggests a very different picture, that the J35 should give the Express 27 about 90sec/nm when TWS = 6 knots and about 40sec/nm when TWS = 20 knots. This means that when the wind is less than 6 knots or greater than 20 knots PHRF is in error by at least 25sec/nm. On a 12nm course this is a 5 minute error! Scoring with PHRF at 6 and 20 knots TWS is like setting your spinnaker at the right time on average, but always too early or too late. In both cases the result is exactly the same: pissed off racers.

The second PHRF assumption is tested in Figure 3 which shows the TA difference between a C&C 38 and a J35 versus beat content at TWS = 10 knots. The beat content data comes from the predetermined IMS courses. Figure 3 shows that the TA difference between the boats increases significantly as beat content increases. Apparently when the beat content is high the J35’s upwind ability gives it a significant advantage over the C&C 38. The same effect is seen at other true wind speeds. IMS says that in a race with high beat content (55%) the J35 should give the C&C 38 about 25sec/nm more than in a race with low (16%) beat content. In a 12nm race this is a 5 minute difference. PHRF misses all of this completely and assigns a 45sec/nm difference between the C&C 38 and J35 for all courses.

The Americap system uses a fixed RB to determine corrected times. The Americap RB has rating coefficients A = 1 and B = 0. We used the 1991 IMS Circular Random course TAs and the 1997 J35 Americap All Purpose Closed Course rating to approximate the Americap RB TAs. As best we can tell from our limited data, the Americap RB is comparable to a Swan 65 or a loaded MacGregor 65. The actual RB performance is under lock and key at US Sailing, but these boats give a useful benchmark for understanding the Americap system.

where a is the numerical slope of the line and B is the TA Difference axis intercept. The statistically fitted line in Figure 5 has the equation:

and provides an excellent fit to the IMS data.

If we put equations 3 and 4 together we get:

TA - TA_RB = aTA + B (5)

Solving this equation for TA_RB we get:

TA_RB = (1-a)TA - B (6)

or, by expressing the TA values in terms of time divided by distance:

(t_RB/d) = (1-a)(t_elapsed/d) - B (7)

where d is the course length. Finally, by multiplying this result through by d:

t_RB = (1-a)t_elapsed - Bd (8)

Recognizing that t_RB is the corrected time and letting A=(1-a) we get:

t_corrected = At_elapsed - Bd (9)

The data in Figure 6 help drive the TWS nail into the PHRF coffin. Consider the 13 boats in the Figure to constitute a racing fleet. Note that when the TA is low, which corresponds to high TWS (boats go fast in heavy air), the TA Difference across the fleet is small, that is, in heavy air all boats go nearly the same speed: fast. When TA is high, which corresponds to low TWS (boats go slow in light air), the TA Difference across the fleet is large, that is, the fleet spreads out on the course. The TA Difference between the slowest and fastest boats in the fleet is about 100sec/nm when TWS is high and about 200sec/nm when TWS is low. PHRF assigns a fixed difference of about 150sec/nm between these boats, so in extreme wind conditions PHRF is in error by +/-50sec/nm. If PHRF was correct the IMS data and Americap lines in the Figure would all be horizontal.

While researching for this paper we discovered that yet another new handicapping system is in the works. This one comes from the ISAF ORC (Offshore Racing Council) and will be administered by US Sailing in the United States. This new system, called ORC Club, is a collection of three different types of ratings. The first rating is called Performance Line Scoring (PLS) and is very similar to Americap. PLS has an A and B coefficient like Americap and corrected times are determined the same way as Americap (see Equation 2). PLS does not take different course types into consideration so only one pair of A and B values are given. The second ORC Club rating is a Time on Distance (ToD) rating like PHRF and the third rating is a Time on Time (ToT) rating. Both the ToD and ToT ratings use one handicapping coefficient. Corrected time under the ToD rating is calculated the same way as PHRF (see Equation 1). Corrected time under ToT is calculated by:

t_corrected = C*t_elapsed (10)

where C is the ToT handicapping coefficient. The value of C for the ORC Club ToT RB is 1.0, so all boats will have C values of about 1.0.

The ORC Club ratings are being marketed as a "VPP Inside" rating system, that is, the three ORC Club ratings are determined from the IMS VPP. The feature that ORC Club provides over IMS and Americap is that ORC Club does not require the measurement of IMS hull lines to determine a rating. Only a subset of the IMS input data is necessary and all other measurement data are determined from a database of default values. These default values are chosen to put a minor penalty on boats with ORC Club certificates compared to boats with full IMS certificates. The intent is to put some pressure on boat owners to upgrade their ratings to full IMS.

We see several problems with ORC Club. Regarding the PLS scoring method, ORC Club ignores the significant performance difference between boats on different courses. PLS does take TWS into account though and this is a tremendous improvement over any single coefficient handicap like PHRF. In PLS’s favor is 100% availability for all boats who want a rating. The failure of PLS to account for course differences might be a small price to pay if Americap can’t provide a rating for every boat. The ToD and ToT handicaps may actually be worse than what PHRF is currently doing. The intent of PHRF is to have PHRF locals adjust boat ratings to reflect their normal sailing conditions. This gives the PHRF locals a chance to fine tune the ratings. The ORC Club ToD and ToT ratings eliminate this opportunity since they’re under control of an international organization. Of course the reason for offering these ratings is to remove the political pressures on PHRF committees and replace the subjective PHRF handicaps with objective handicaps derived from the IMS VPP. In the end we think that the ORC Club ToD and ToT ratings have little to offer.

We’ve seen that there are substantial performance differences between boats at different wind speeds and on different courses. PHRF fails to account for either of these factors and consequently commits substantial scoring errors, on the order of several minutes of corrected time. Both IMS and Americap take wind speed and course content into account. This will be a requirement of any serious handicapping system of quality. It’s unavoidable.

IMS and Americap both depend on a VPP. This presents advantages and disadvantages. On the plus side, VPP based systems avoid many of the political issues of a committee driven system like PHRF. The ratings derived by a VPP are objective and likely to be fair, to a point. As long as the IMS VPP is for sale boat designers will build boats to beat their IMS rating. This is the motivation of US Sailing in keeping the Americap VPP secret and they threaten to change the VPP if designers do figure it out which is inevitable. On the minus side of VPP based systems is the barrier that the VPP represents. Right now both IMS and Americap probably use the same input information to rate a boat and that means that any boat to be rated must be measured. The cost to measure one-off boats or some of the older boats that actively race but haven’t been measured is prohibitive. PHRF will always offer a rating at a reasonable cost for any boat that requests it. This must be a goal for Americap if it is to be universally adopted.

Recently PHRF National has developed a plan to limit the number of crew a boat can carry. While this might be appropriate for a one design class, it is a bad course of action for PHRF. PHRF has much bigger problems than weight limits. It’s like trying to improve the gas mileage of a badly tuned car by limiting the number of people who can ride in it. (For a scathing editorial on PHRF weight limits see Bill Schanen’s article "PHRF to Big Crews: Stay Home" in the January 1998 issue of Sailing.)

Americap’s designers were very clever. They have come up with a scoring system which is very simple to use and yet has comparable, if not the same, quality of scoring as IMS. This new handicapping system deserves serious consideration and offers an excellent alternative to PHRF provided the access barriers to getting a rating are removed.

Until US Sailing can get Americap together and achieve 100% availability for all boats that request ratings, Americap will suffer the same trouble as IMS. The ORC Club Performance Line Scoring system is appealing for this reason and it may become the rating that replaces PHRF until Americap is ready. Furthermore, ORC Club removes some of the issues of administrating Americap for race committees, specifically the necessity for the race committee to select from the limited list of Americap courses available when none of them are clearly correct or when a significant wind shift occurs during a race and changes the beat, reach, and run content of the course. The simplicity of ORC Club makes it an important alternative for PHRF locals to consider.

Hits counter was reset in Nov 2002. Total hits is ~2000. This paper has been on this site since 1999 after sailing magazines refused its publication because it was too technical.