I believe you fundamentally misunderstand the conversion of ToD handicap
ratings to ToT time correction factors.
The basic assumption is that you have ToD handicaps that are accurate
for some wind strength and you want to convert them to ToT (if you don't
have accurate ToD handicaps then you have to fix those first!). You want
the ToD and ToT results to be the same at the wind strength at which you
think your ToD handicaps are most accurate. That dictates the B factor
in the standard conversion formula: TCF = A/(B+PHRF), where TCF is the
time correction factor for each boat and PHRF is the boat's standard
handicap. The A factor has no impact on the order of boats and it is
recommended to use an A factor that is the same as the B factor so that
a boat with a 0(zero) handicap has a TCF of 1.000. Anything else will
probably be confusing to the sailors but you are free to use whatever
number you want as it has no impact on the positions of boats.
So, what should the B factor be? Consider two boats, one with a handicap
of zero and another with a handicap of 90. At your specified wind
strength you want the ToT results to be the same as the ToD results. The
way you do that is to use a B factor that is equal to the time (in
seconds per mile) that the 0-rated boat would sail a typical one-mile
course in that wind. In a perfect world, the 90-rated boat will be
exactly 90 seconds per mile slower and so the corrected times of ToD and
ToT scoring will be identical. [Some quick noodling with elementary
algebra should prove that to your satisfaction.]
So, the ToD to ToT conversion formula is a single one for all wind
speeds and conditions but needs to be chosen for the wind speeds and
conditions that are most accurate for the locale where the ToD handicaps
were assigned. You don't want your ToT results to be less accurate than
your ToD results!
A good number for the B factor when converting ToD handicaps for
windward/leeward buoy racing in 10-12 kts of wind is 625. So, if the
general consensus would be that your ratings are accurate for that wind
speed and course configuration then that is the B factor to use.
Conversely, if you live in San Francisco and "light" is anything <15 kts
then you would want to use a much faster speed, say 550-560, or maybe
even faster. Random leg courses are sailed at a much faster pace so 575
might be a good number to use for 10-12 kts.
I'm not sure where you heard about the concept of changing the
conversion formula based on the actual wind strength in the race.
However, consider what that would mean - since the B factor is defined
such that the ToD and ToT results are identical with that wind then if
you were to change the B factor based on the wind strength then you
would be ensuring that the ToD and ToT results were the same at all wind
speeds. Obviously, if that were true you'd get the same results
regardless of whether you used standard PHRF handicaps or TCFs and so
there would be no benefit to using ToT instead of ToD.
There are two benefits to using TCFs and ToT scoring:
1. Standard seconds per mile handicaps assume you can accurately
determine the course length that all boats must sail. When there is
current that is with or against the course direction then the distance
sailed can be significantly different from that measured "over the
ground." TCFs and ToT can be more accurate (which is why the usage of
TCFs and ToT increases in direct proportion to the distance from the
equator, in other words, as tidal effects get larger). Once upon a time
measure course distances "over the ground" was hard but with modern GPS
that problem is a thing of the past. But, current (whether by tides or
in a river) can still be a significant problem depending on where your
race is held.
2. Naval architects have determined that for similar style boats, the
speed difference between two differently sized boats varies based on
wind speed closer to a percentage than a fixed amount. TCFs and ToT
assume each boat is slower or faster than the base boat (with a TCF of
1.000) by a fixed percentage while standard PHRF handicaps assume each
boat is slower or faster than the base boat (with a PHRF handicap of 0)
by a fixed amount per mile. Neither is accurate but the "percentage"
assumption is slightly more accurate when the boats are of a similar
type AND the wind speed varies from the average by a significant amount.
TCFs and ToT can have a significant impact when the average wind speed
is 10-12 kts but the race is run in 5-6 kts. But, it will have virtually
no impact for races run in the 10-12 kt conditions. If you live
somewhere that has fairly consistent winds day after day (as is
generally true where I live) then ToT probably won't be much better than
ToD. But, if you live somewhere that has summer winds that are
significantly lighter than spring and fall winds (as is true where I was
born and grew up) then ToT might be a good option to consider.
Hope this helps.
Art
PS - I've been asked to write a paper on ToD vs ToT scoring to better
explain the underlying concepts. I've never got around to finishing the
paper but it does mean I've thought a lot about how to explain the
concepts. I apologize if as a result the length of my reply seems
somewhat daunting.
···
On 8/12/2015 9:23 AM, plb1937@gmail.com [sailwave] wrote:
We are attempting to change our scoring system to PHRF ToT. Ran into a problem that hopefully has a simple solution.
Just had a small regatta, 2 days, 24 boats in 3 classes. Saturday's 3 races had the first in light winds, the other two in very strong winds. Sunday's had a regular race first, around the marks and back in average winds, then an all upwind race in average winds, then an all downwind race in strong wind.
It is my understanding that the B factor in the denominator varies according to conditions. But I cannot figure out how to change it for each race; it seems to set for the whole series.
I would also like to be able to set the A factor by fleet, so that the boat with the lowest PHRF in that fleet becomes the "scratch boat" with no correction, all others correct.
Can this be done?
M G Laurin, SYC, Okanagan Lake, BC