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The Fallacy of Time-On-Distance

An Unenlightened Discussion

by

Joe Siudzinski

I wrote and published (August 22, 1991) this somewhat tongue-in-cheek tirade during my stint as Ratings Chair of the Bay Area Multihull Association (BAMA). I subsequently updated it to include reference to the 1992 DoubleHanded Farallones Race which further demonstrated the inadequacy of Time-On-Distance. I'm making this available here on my website in response to several requests, the only changes being a rather crude re-formatting into html and a few minor edits. JoeS.

The purpose of this discussion is to air my thoughts on the concept of PHRF. After being involved with the rating of small multihull sailboats for over 20 years using the Portsmouth Yardstick system, I am baffled as to why PHRF is even considered as a valid approach to handicapping sailboats. It appears to me that the fixed time-on-distance approach to handicapping sailboats is a significantly less accurate first-order approximation than time-on-time.

Attempts at mathematically equating sailboats of varying sizes and shapes in order to allow them to race together has been the playground of many dedicated people over at least the last century. An unbelievable amount of effort has gone into establishing rating rules utilizing measurable boat parameters, with IMS being the latest solution to this non-crisis.

I'm not going to touch that arena with a 10-foot whisker pole; instead, I'd like to discuss ratings based upon empirically-derived performance data, i.e., ratings resulting from race results. Two such performance-data-derived popular rating techniques have evolved: PHRF and Portsmouth Yardstick. Both of these first-order-of-magnitude approximations are used to 'correct' the finish times of racing sailboats to determine who won.

The PHRF system is extensively used throughout the United States for running multi-clsss sailboat races. It is a time-on-distance approach to handicapping sailboats. Time-on-distance means that boats are rated as being a certain number of seconds per mile slower or faster than a predetermined 'scratch' boat. One advantage of time-on-distance is that a person can easily calculate how many seconds are needed to beat rivals in a given sailboat race.

Portsmouth Yardstick is also an empirically-derived rating scheme which is popular in Europe and in the US with dinghy classes and small multihulls, but which uses time-on-time as a criteria; i.e., boats are rated relative to each other using a multiplier (actually, a divisor) of the time it took to finish a race. One advantage for users of this system is that race course distances need not be known, and only race elapsed time is needed in order to score an event.

I totally agree with the performance-data-derived aspect of PHRF, provided someone is staying on top of the race results and is continuously refining the individual boat handicaps. In formal USYRU (now US Sailing) PHRF, one evidently has to pay money to a committee in order to petition to have one's rating changed - this analysis is not routinely done after each race. Getting protested also gets one's rating re-examined. In this modern day and age, I don't understand why the PHRF committee doesn't get automatic computer downloads of all races and automatically perform "Rating Sailed" calculations on every boat in every race, with an every-expanding database to support its ratings.

My bone of contention is the use of time-on-distance, since I believe that handicapping using seconds per mile is a flawed concept.

PHRF is a system which works reasonably well when applied to boats which get up to a certain hull speed and basically stay approximately at that speed no matter what happens - i.e., displacement keelboats. When the wind picks up, all the boats get going a little faster and the incremental speed increase will yield a time differential which ends up having a fairly small overall effect, especially if the boats are separated into divisions of comparably-performing characteristics.

Let's contrast three boats (let's call them A, B, and C) which travel one nautical mile in three different windspeeds at the speeds shown below - you'll note that I've purposely left the percentage speed difference amongst them the same. Here's how long they take to cover that nautical mile:

LIGHT | MEDIUM | HEAVY | |||||||
---|---|---|---|---|---|---|---|---|---|

BOAT | Speed | Sec | Sec/Mi | Speed | Sec | Sec/Mi | Speed | Sec | Sec/Mi |

A | 2.00 kts | 1800 | 360 | 4.00 kts | 600 | 120 | 8.00 kts | 490 | 90 |

B | 2.25 kts | 1600 | 160 | 4.50 kts | 533 | 53 | 9.00 kts | 400 | 40 |

C | 2.50 kts | 1440 | 0 | 5.00 kts | 480 | 0 | 10.00 kts | 360 | 0 |

The Sec/Mi figure would be their PHRF rating, with boat 'C' being the scratch boat. Notice the tremendous disparity! If the medium wind performance determined the boats' basic ratings, then boat C (the fastest) would always win in light airs and lose in heavy winds on corrected time.

I know, I know, you're saying that I assumed that the percentage difference in speed amongst those boats is the same for the two conditions -- where did that come from? Well, here's where I become a name dropper and refer to Marchaj's Aero-Hydrodynamics of Sailing, pages 88 & 89. He says that the speed ratio for a given boat, expressed as boat speed divided by true wind velocity, is largely independent of windspeed. If this ratio is constant and boats are sailing in the same windspeed, then one boat's speed relative to another is also constant and can thus be converted into a rating -- Britain's Portsmouth Yardstick and Holland's Texel Ratings are two popular rating systems which reflect this approximation.

From a practical standpoint, simply look at the results of this year's DoubleHanded Farallones race where, despite breaking all elapsed time records, Tom Cat (Formula 40 catamaran with a current PHRF of -150) came in close to last on PHRF but would have been second multihull under the Portsmouth Numbers - its percentage difference was in line with its rating, whereas under PHRF it would have needed to cover the course at an average speed of 30 knots!! Similarly, Aotea (currently rated at PHRF -140) significantly beat this rating on a number of occasions in the last six months in light airs, and yet was in the same boat (smile) as Tom Cat in that DoubleHanded Farallones screaming reacher.

Once again, the fundamental flaw in the time on distance concept is that it inherently is saying that it takes each boat a fixed number of seconds to cover one mile, and everything is thus based on this premise.

Boats which have significant speed variations (such as ULDB's and multihulls) simply don't conform to the time-on-distance concept of PHRF; nevertheless, if a race is held in medium to light air, everybody just lumbers around the course at an average speed of four or five knots and the results of the races can appear real because they do, indeed, fall into the range where the PHRF ratings are established (I think). I believe that the success of PHRF is based on exactly this point: that most races average out to a medium-to-light air event.

If we were to accept that all boats do indeed cover a given distance in a predetermined amount of time, then we had darn well better be careful about what we call distance. A race out to the Lightbucket and back may well be ten miles out and ten miles back, but going out everybody is tacking so their distance sailed is probably closer to 14miles, for a total distance of 14+10=24. If the race scoring is based on 20 miles, somebody's going to be shortchanged (and I didn't even consider tide effects)! What I think happens is that everybody's calculated average speed over this rhumb line distance ends up being artificially low and gets us back to that medium-light air range where the ratings seem to work. This one needs some more thought put into it.

How is point-of-sail accounted for in time-on-distance? Certainly, broad reaching produces significantly higher speeds which yield differing absolute numbers in terms of the number of seconds it takes to cover that mile - even in the lumbering monohull world! As best I can figure out, we always presume that we are dealing with average courses which give us average ratings, and thus any individual race course weirdness will probably favor a particular type of boat for that race.

Refering back again to Marchaj's text, percentage differences of speed between boats are somewhat constant over relatively large variations of boat and windspeed, and thus can produce a more accurate first-order approximation for race scoring. A basic inequity will undoubtedly still exist if boats with wildly varying speed potential are scored against each other (e.g., ULDB or multihull vs. heavy keelboat), but perhaps this inequity is not as great as under PHRF - I don't know, and the only way to answer this is to grab a handful of polar diagrams based on measured data, set up some hypothetical courses, and play with the computer (sorry, but I'd rather go sailing).

I said I wouldn't touch this, but I can't resist a tirade: I personally believe that attempting to assess boat performance using measurable boat design parameters yielding rating 'rules' is a fantastic ploy which keeps boat designers, boat builders, and their arch-rivals, the statisticians, employed. The concept of having the boat become 'obsolete' because an equation doesn't accurately characterize its performance is mind-boggling! It's the formula, not the boat, which is flawed, and I contend that they should thus get rid of the bloomin' equation and quit trying to design a boat around it! Enough digression, ... we should strive to have ratings so that everyone can race their toy with some possibility of winning.

We've been talking about first order of magnitude approximations for all this rating business: give the Race Committe one simple number to plug into the formula and calculate the results. Never mind that sailed course lengths vary, that different windspeeds, tides, and wave conditions are experienced at different times by different boats all over the course. Heck, we could put sensors on every boat and feed it all to a computer which would tell us that a green hull with pink polkadots is worth a penalty of 0.000276 seconds/mile.

All I'm saying is that it's more accurate to treat boats for racing purposes by saying that one is "x% faster" than the other instead of saying it's "x seconds per mile faster". Sailboat racing is fun and we'll continue doing it, but perhaps we should consider something a little less fundamentally inaccurate than time-on-distance for scoring our races.

After I came down off my soapbox it occurred to me that I've probably missed some fundamental concept which does, indeed, make time-on-distance really work better than I think it does. I welcome all comments anyone reading this may have.