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[Q]

Sailor_man, I sent you the spreadsheet I use.  Let me know if you find it of any use.  As you have noted, the formula to calculate the TOT multiplier reduces to the simple form when the constants (such as "scratch boat rating") are set and combined. The PHRF-LO formula form is identical to what is shown on the USSailing website.  The original formula is given in the report so that guys like you and me can remember 15 or 20 years down the road where the numbers actually came from.

I totally agree that other factors cause the majority of variability in the performance data.  Personally I think rating adjustments of less than 6 sec./mile are a waste of time since I'm sure that there is an inherent inaccuracy in our predictions of at least that amount.  That being said however I still think the system works very well.

Steve,

Thanks for the spreadsheet. I've taken it and input races from my local summer series for this year. I saw that you had input races from your club, which helped get me going in the right direction.

I agree that +/- 6 sec per mile is probably about as good as one can expect for accuracy of TOD ratings. That type of variation has some impact on results but not much at the end of the day. Other stuff, such as windshifts, new sails, crew skill, etc., is more important and worth far more than +/- 6 sec per mi. In the same vein, I also think that the choice of a Q Factor probably has less impact than +/- 6 sec per mile and so although it clearly has some impact on results one shouldn't make it more important than it is. I find the Q Factor analysis interesting as an intellectual matter as much as anything.

Q Factor Analysis of Local Fleets

As I said, to get a handle on the Q Factor analysis, I input the races from our local summer series. I input three different classes sailing in 18 races for a total of 53 races (one class had no boats finish one race). The results were interesting. What I found was:

1. Of the 53 races I entered, it was impossible to calculate a Q factor for 10 of the races, almost 20%. In all 10 cases, positive infinity wouldn't compensate for the "bias" toward higher-rated (i.e., slower) boats. [I used 99,999 instead of infinity in my calculations.]

That a "Q Factor analysis" wouldn't work for almost 20% of the races I looked at raises a troubling question as to whether it is a valid method of analyzing bias in TOD ratings. As a check I did a similar type of analysis on the TOD ratings directly - plotting TOD corrected time vs. TOD rating and adjusting a "fudge" factor until the slope of the linear regression line was zero (I used the formula CT = ET - (Fudge * TOD * DIST). Using that method I was able to analyze all 53 races - in other words, whereas I could not come up with an "optimum" Q factor for 10 of the 53 races I was able to come up with an optimum TOD "fudge" factor for all 53 races. That suggests to me that the TOD "fudge" factor analysis is more valid than the Q factor analysis, even if in the end you come up with the same conclusion of bias toward lower-rated boats.

2. One of the classes (PH-B) that I analyzed has most of the talent at the faster end of the class. That class did indeed show a heavy bias toward lower-rated (i.e., faster) boats, as you would expect with most of the better-sailed boats at the lower end of the rating band. The optimum Q factor for that class for the 2010 season was -0.0246 average, -0.0523 median. The rating band was 36 sec/mi and the class averaged 12 boats per race.

3. The other two classes (PH-C and PH-D) have the talent spread fairly equally across the rating band (42 and 64 sec/mi, respectively; averaging 14 and 7 boats per race). Both classes showed a marked bias toward the higher-rated (i.e., slower) boats, which presumably shows that talent is weighted slightly toward the slower end of those classes even though it might not appear that way on inspection. For PH-C the optimum Q was 38,889 average and 1.258 median; for PH-D the optimum Q was 17,649 average and 0.457 median.

4. Combining all 53 races, I came up with an overall optimum Q of 18,869 average and 0.180 median. That translates into a fairly significant overall bias in favor of slower (i.e., higher-rated) boats (a Q factor showing no "bias" would be close to 0.09).

5. For the record, the "average" Q factors don't have much meaning and I include them only to show that the distribution is nothing like a "normal" distribution where the average and median are fairly close together. I did some histograms of my results for all 53 races, as shown below:



One thing to note is that my third histogram (showing the results of just 40 of the 53 races I analyzed) looks somewhat similar to the histogram from the November 2008 Report of the PHRF-LO Technical Advisory Committee, the so-called Time on Time Study (posted on the PHRF-LO website at http://www.phrf-lo.org/images/Documents/tot_q_study.pdf), in that it shows a long "tail" to the right:





PRELIMINARY CONCLUSIONS

It is a bit early yet but it seems to me that the Q Factor analysis is extremely sensitive to the makeup of the classes/races being analyzed. The classes I looked at had rating bands of 36, 42 and 84 sec/mi for an average of 54 sec/mi. That is very similar to the 60 sec/mi average rating band found in the 2008 Time on Time Study. So, from that perspective the classes I looked at seem to be the same kind as those from the Study.

In the class where all the talent was obviously concentrated at the lower end of the rating band, the Q Factor analysis showed bias for the lower-rated boats. That hardly seems surprising and may have nothing to do with "rating bias." I haven't yet thought of a way to try and separate the "rating bias" from the talent factor. The other two classes showed a bias toward the higher-rated boats, which is the opposite of what the PHRF-LO Time on Time Study showed. However, that may simply be a reflection of the fact that although the talent seems equally spread across the rating bands for those classes it actually is concentrated slightly with the higher-rated boats.

Overall, I am not yet convinced that this so-called "rating bias" is real. It very well may be. I have heard about it for years and have always kind of assumed it was real but now I am not so sure. In any evernt, the Q Factor analysis doesn't seem to be a very good way to prove that such bias actually exists as it seems to be incredibly sensitive to the makeup of the classes being analyzed. I analyzed as a single "race" only those boats that started together because for our evening races the wind does die and that could have a significant impact on the analysis. I wonder if there might be other systematic errors that I should be considering.

I think I might put in at least one more year of results and see if the Q Factor analysis shows something different.

sailor_man

[Update - After initially posting this I rechecked all of my calculations and I found that there was an optimum Q Factor for the case where I had found no solution using negative infinity. I have updated my histogram and the wording above to reflect that correction.]

Not so Dumb as Hell:

"Except to say that the first premise of PHRF is to create a rating for the first place boat not the middle boat in a class."

I disagree, I think that the way it is done works best for everyone.   If you subtract 20 fro all the ratings, the finish order would be the same, but many more people would complain about their ratings being too harsh or not being close to the US Average.   There is a perception that PHRF LO changes a lot of ratings each year, when in reality, very few get changed.   As fleets of boats get popular, they attract better sailors and the boats start to perform better.  If you race against people who are better than you, you will normaly get better yourself, so the performance increases and the rating comes under scrutiny.  A good example is the J 24, over the years the rating has gone down and down until now it is fairly stable. 

Another misconception is that PHRF LO ratings are "out to lunch" compared to other PHRF areas. I find that PHRF LO ratings are very close to if not on the Average US PHRF rating for the class of boat.  There are exceptions, but they are getting rarer.  When PHRF LO does its mandatory review of ratings each spring, I always bring up the high, low and median rating in the US PHRF handbook. US Sailing has a list of boats with the high, low and median ratings that you can download from it website, compare PHRF LO ratings to the US median and I think you will be surprised as how close to the median that PHRF LO is.

I always thought that Youngstown Level Regatta was a Level Regatta, but it was recently brought to my attention, that that is no longer so.  Youngstown Level Regatta was had IRC and PHRF divisions for a number of years.  It is getting difficult to get enough boats in a narrow rating band to form a level division, so handicap racing is taking over at Youngstown.  The One Design fleets race level, the rest race handicap.

Changing a rating by -9 is highly unusual, I am insterested in finding out what type of boat you have.  Was the rating hit for the type of boat, for modifications or both?

Ratings are looked at in the spring of each year, race results are analyzed and some boats stand out as needing to be looked at.  PHRF LO is the only PHRF area that does an analysis of race results.  PHRF is also the largest PHRF area in North America by the number of certificates issued.

For the typical club mid week race, PHRF is just about the only option due to the very low cost and minimum measurement required  $20 - $25 per year for a certificate that allows you to enter races is a bargain.  In addition to being a PHRF handicapper, I am an IMS, ORR and IRC measurer.  These rules cost a lot more than $20 per year, but in the Toronto Area, IRC is getting very popular for the inter club racing.  An IRC certificate costs $18.70 per meter of boat length and has to be renewed each year. Measurement costs another $150-200 plus weighing if required is another $150-200.  ORR certificates cost about $5.50 per foot and will probably require measurement at around $300-400.

Sportboats are a problem, there are not enough of them entering races to have a separate sport boat division, so race organizers lump them in with the non sportboats.  There are large performance issues with sportboats, ie: being able to plane, some upwind and most downwind if their is enough wind while the average boat might surf but certainly never gets anywhere near planing.

I do the Wednesday night scoring at PCYC, I use Sailwave to score the races.  Sailwave has a feature called BCE for Back Calculated Elapsed Time, it prints a column on the results with the amount of elapsed time the boat needed to be faster, to tie the winning boat in its division.  It takes the rating into account so the BCE for the winning boat in a division is 0, all other boats have a time in seconds or minutes and seconds that shows how much slower it sailed.   Hopefully the time is less than 1 minute, but a number of boats show multiple minutes behind. 

Sailor_man, I sent you the spreadsheet I use.  Let me know if you find it of any use.  As you have noted, the formula to calculate the TOT multiplier reduces to the simple form when the constants (such as "scratch boat rating") are set and combined.   The PHRF-LO formula form is identical to what is shown on the USSailing website.  The original formula is given in the report so that guys like you and me can remember 15 or 20 years down the road where the numbers actually came from.

I totally agree that other factors cause the majority of variability in the performance data.  Personally I think rating adjustments of less than 6 sec./mile are a waste of time since I'm sure that there is an inherent inaccuracy in our predictions of at least that amount.  That being said however I still think the system works very well.

I don't disagree with what you say. Except to say that the first premise of PHRF is to create a rating for the first place boat not the middle boat in a class. Remember that part that says "well prepared boat with good crew..." That is the first place boat in your  C&C 34 fleet not the middle of the fleet. The first place boat should be sailing 141 and the middle 161 and back of the fleet should be sailing 181.

Yes PHRF has a problem when there are not a lot of boats of one class to compare. So why repeatably change a rating of that type of boat?  What appears to me to  happen, is  the rating of that boat, is changed until it appears to have a rating that puts them in the middle of the fleet they are sailing in.
 Innovative may mean bringing a new boat into the area. Not changing that boat to gain an advantage.

From your description; It would seem unfair to change a rating of any boat that is not being sailing  plus twenty better than their rating. Yet the boat I sail was -13 now and -5 before you recalculated with the new Q, and you hit me with another 9 sec penalty. I just don't get it.

I think I have figured out what to do so that I am not pulling my hair out with frustration. I have no interest in fighting with PHRF-Lo I just want to go sailing and to have fun. Fun for me includes single handing so if I want to fly chute and not use auto helm (that removes the challenge), I need to have a sprit and assy. That makes the boat list short, and more than likely, it's on your list of hard to rate boats so they get rated to be less competitive. You know evil sportboats.

 Although it still may be considered innovation- if I take an old proven design drill a hole in the bow and mount a sprit. Problem solved! Won't be solved thou. That boat will be looked at like an individual and its rating will continue to change until it is the middle of the fleet or less. Even though you are of the opinion that assy's are slower.

Truly the only answer is to sell the boat and go back to sports car racing. Unfortunately I believe that the current system we use has caused a loss of faith amongst the sailors on LO and that is why we are seeing less participation. I have heard time and again sailors tell me they are not going to Youngston because of the fleet they end up in because of their rating. That is a level regatta but the levels are still set by PHRF by assoc.

This is not a criticism as such, it is clear that you all work hard and the math is complicated and your intention, it appears as a group, that you trying to improve sailing. The average sailor can not even begin to understand the complexities. If they don't understand they don't want to play. You change ratings so frequently and without clear explanation that the perception of PHRF is= it is not fair.

Sails in front of the mast are either genoas or spinnakers.

A gennaker, does not meet the definition of a genoa, so it is a spinnaker.  It does not matter where you tack it, it is still a spinnaker.  If you take a symmetrical spinnaker and tack it to the genoa tack, does that make it a Genoa? NO, NO, NO.

It does not matter what you call the sail, gennaker, cruising spinnaker, code Zero etc, it must meet the definition of either a Genoa or a spinnaker.  To be a Genoa, the mid girth measured from the mid leech to the luff must be equal to or less than 50% of the LP.  To be a Spinnaker, the mid luff, measured mid luff to mid leech must be equal to or greater than 75% of the foot.  If it does not meet these definitions then it is neither a Genoa or a Spinnaker and is NOT LEGAL.

Staysails and Bloopers come under the definition of a Genoa.

Is a gennaker considered a flying sail if it is tacked to the deck and it is gybed through the forestay from one side to the other?

Steve,

Sailor-man,
[some text deleted]
I tried to send you a copy of my spreadsheet which I use for my clubs data but it somehow got screwed up and I didn't have time to fix it.  I'll get to it as soon as I can.
steve

Thanks. I'll look for that.

In the meantime, I think I understand what was done. Plus, looking at the relevant formula I think I know what kind of analysis was done and how to do it myself.

The standard PHRF-LO formula (from the PDF of the PowerPoint presentation off the website - cleaned up slightly) is:



This is mathematically equivalent to:



There is a standard formula for converting TOD ratings into TOD time correction factors (TCFs but also called "multipliers" on the PHRF-LO website) as follows:



If you compare the formula in my 2nd image with the final formula in my 3rd image you can see that the complicated PHRF-LO formula is just the standard TOD to TOT conversion formula with



That should make it fairly easy to do a spreadsheet in Excel that I can play around with and get a feel for the kind of analysis you are doing.

I already fooled around with Excel and the TOD results for the PHRF class that I sail in locally. When I graph the results for corrected time (using standard TOD scoring) versus TOD rating if find a slight bias in favor of the slower-rated boats (i.e., higher rating). That is the opposite of the result of the large PHRF-LO survey but of course I imagine the analysis is going to be fairly sensitive to the makeup of the class being analyzed and the class I am in is fairly narrow (42 sec/mi).

My prior studies have shown that non-rating factors can commonly be worth 60+ sec/mi - which would make them more important than ratings when the class spread is only 42 sec/mi. My class averages around 13 boats per race. But, for some races we sailed the same course as another class so for those races I should be able to combine the classes to get a bigger sample to analyze.

sailor_man

Sailor-man,
You have it correctly.   The difficulty we have found is that the conversion formula is non-linear and the optimum Q appears to be a function of the handicap.  At numerically lower Time on distance handicaps the optimum Q is numerically greater than at higher time on distance handicaps.  We have been considering solutions but for the time being have settled with the .008 value for the entire range.  This optimizes the handicaps for ratings under 100 but slightly under handicaps the slower boats (from our analysis anyway).  I tried to send you a copy of my spreadsheet which I use for my clubs data but it somehow got screwed up and I didn't have time to fix it.  I'll get to it as soon as I can.
steve

[Q]

Steve,

I sent an email to you.

I think I'm beginning to get the idea.

All of the PHRF-LO TOT work is based on a formula that came from the MIT Pratt Study. [I bought a paper copy from US Sailing years ago but have no idea where it is now. Someone mentioned here a while back that there is an electronic version floating around. If you have that and could send it or a link it would make it easier for me to understand what is going on.]

The formula that is used (presumably from the MIT Study) is posted prominently all over the PHRF-LO website (though it seems to be different in different places). The Q factor is nothing more than one variable in that formula.

To determine an "optimum" Q factor for a "race," you take the elapsed times from a number of boats that sailed a single course (if multiple classes all sailed the same course at approximately the same time you would combine the races into one for purposes of determining a Q factor). You then score and rescore those boats using TOT and "the" formula with differing Q factors until the plotted results (corrected time vs TOD rating) show a flat trendline with a linear regression analysis. [If I understand linear regression correctly, that would mean that the straight line that best fits the plotted points has a slope of zero - but in any event it would be horizontal.] In a sense, you are using the Q factor as a "fudge" factor to eliminate any perceived bias due to ratings (I don't use "fudge" in a pejorative sense here, I only mean to imply that it is continually adjusted until you get results that meet your criteria of a "flat" linear regression line; clearly, it is an empirical factor).

That gives you a Q factor for that one "race." To come up with an average Q factor for a local fleet you would take the Q factors generated from lots of races for that fleet and then come up with some "normal" value (I use "normal" instead of "average" because you might use the median or some number other than the mathematical average; at this point that detail is not important).

Am I on the right track?

Sailor-man,
Our technique to determine optimum Q is to find the Q value that produces no rating  bias over the handicap range.  This is done by calculating a least squares linear regression of the corrected time vs. handicap and varying Q until the slope of the regression is as near zero as possiblen (statistically no bias).  We do this for as many respresentative races as we can get our hands on and ultimately select an average or median value Q that best represents the group of races.  In the case of the lake wide number we use all the data we have over the last few years.

For my club I enter each race score into a spreadsheet and do the calculation for each race on a year by year basis.  I would be glad to share my spreadsheet with you if you will contact me via email  (scorona1@rochester.rr.com).  Using the spreadsheets graphing capability you will be able to see the affect of a change in Q on the actual corrected time.
steve corona