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PHRF Fallacy Revisited - a Glimmer of Reason
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December 2008 Introductory note:
I think I wrote this around 1993 although my last computer file copy was dated 1998. This is a follow-up to the original PHRF Fallacy discussion, a somewhat tongue-in-cheek tirade against the Time-On-Distance rating system used by PHRF during my stint as Ratings Chair of the Bay Area Multihull Association (BAMA). 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.
The other day I received a phone call from Mississippi I understand you have some PHRF ratings for multihulls which Id like to obtain. We use Portsmouth around here and it sucks!
Needless to say, it piqued my interest, because I still had not received a rebuttal to my ranting and raving treatise condemning the time-on-distance aspects of PHRF. So I asked What in the world makes you desire PHRF? (actually, what I said isnt printable).
Its very simple, he said, on our long distance overnight races the wind dies at sundown and doesnt come up until the morning. If youre racing under Portsmouth and you have a fast boat, youre screwed; in fact, the slowest (rated) boats will usually win!
Wow! Finally I had someone give me a possible reason for validity of Time-On-Distance. I decided to set up a hypothetical race and see what happens, so bear with me...
Lets say we have a ten-mile race with only two boats: an F-27 with a Portsmouth Number of 75 and a PHRF rating of 20 competing against the high-speed Antrim 40 trimaran Aotea with a Portsmouth Number of 60 and a PHRF rating of -100. (2008 Note: rating numbers for example only and probably close to actual ratings once upon a time...)
Now, lets say we have conditions whereby the F-27 maintains an average speed of exactly 6.000 knots while Aotea travels at exactly 7.500 knots. The time it took the boats to cover the race course was 6000 seconds (one hour and forty minutes) for the F-27 and 4800 seconds (one hour and twenty minutes) for Aotea.
Since I rigged the race, heres what happened:
Using PHRF, the corrected time of both boats was 5800 seconds, a tie!
Using Portsmouth, the corrected time of both boats was 8000 seconds, also a tie! Amazing!
Now, lets change the scenario: lets say that after exactly one hour into the race the wind dies completely for exactly one hour, and then picks back up to allow the boats to continue at their previous speeds. During that one hour of dead time, lets assume that the boats make zero progress towards their destination.
As they finish, the elapsed time is now 9600 seconds (6000 + 3600) for the F-27 and 8400 seconds for Aotea. The corrected time under PHRF is 9400 seconds for the F-27 and 9400 seconds for Aotea, a tie! The corrected time under Portsmouth is 12800 seconds for the F-27 and 15667 seconds for Aotea. No question, the faster boat is guaranteed a loss under Portsmouth!
For races which may well be subjected to significant periods of no wind, a Time-on-Distance rating system such as PHRF offers an adequate solution; nevertheless, for most race conditions I believe that Time-on-Time still offers a less-inaccurate system for calculating results. (Dec.2008 comment - gee, I wasn't biased, was I?). June 2009 further thoughts: my previous statement was biased by my own experience, as in San Francisco Bay summer conditions we almost always have good winds; however, having recently experienced winter races with many long zero-wind intervals, I'm slowly coming around to the concept that TOD may indeed have a place in this world... the penalty of a boat not moving at all with the clock still ticking is often insurmountable in TOT.
I very carefully rigged the first example above because it is the only boat velocity combination which produces a tie in both systems. To show you how invalid Time-On Distance (PHRF) is, if the F-27 were averaging 15 knots, then in order for the boats to tie under Portsmouth Aotea would need to travel at 18.75 knots (a reasonable speed) whereas to tie under PHRF Aotea would need to go at 30.00 knots!!! This scenario indeed took place in the 1992 DoubleHanded Farallones Race whereby the two hottest boat corrected out (PHRF) way down in the pack despite breaking all sorts of elapsed time records! Conversely, in light airs, the faster boat needs a negligibly higher average speed (e.g., 1.03 vs. 1.00) and can thus stomp the slower boats.