Optimizing “Q” in the PHRF-LO Time on Time ConversionNovember 2008 PHRF-LO Technical Advisory Committee “Q” is an adjustment variable available within the PHRF-LO T/D to T/T

November 2008

PHRF-LO Technical Advisory Committee

Optimizing “Q” in the PHRF-LO Time on Time Conversion

Steve Corona

Andrew Sensicle

November 2008


“Q” is an adjustment variable available within the PHRF-LO T/D to T/T

conversion formula to adjust the handicap to local racing conditions.

( )( )RsRQRs

RsRQRTOT

!!+

!!+=

( )23.378

8360000

+=TOD

R

( )23.378

8360000

+=TOD

Rs

Where:

! Changing “Q” has the effect of scaling the relative handicap over the entire handicap range. All

the ratings are “scaled” in an accordion affect. Relative positions of individual boats or ratings do

not change.

! The present “Q” value of 0.045 was selected over 20 years ago to match race results of

existing measurement systems such as LOR, MORC and IOR. It was never optimized to data.

TOT = Time on Time Multiplier - TOD = Time on Distance Number

! This study is an attempt to determine the optimum single value of “Q” for Lake Ontario.

TOT =A

B + TOD

BACKGROUND

November 2008


Why is optimizing the Q value Important?

Histogram of Handicap Spread in Analyzed Data Set

0

20

40

60

80

100

120

140

160

180

200

0 6

12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

102

108

114

120

126

132

138

144

150

156

162

168

174

180

186

192

198

Individual Division Handicap Spread

Nu

mb

er

of

Races S

co

red

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

Frequency

Cumulative %

Average rating spread within a division is approx. 60 sec/mile

Any handicap error due to Q is proportional to the rating spread

Individual Division Handicap Spread

12 sec/mile error for a 60 sec/mile spread (ratings < 100)

26 sec/mile error for ratings >100

November 2008


Analysis Method

• The analysis followed a technique described in the H.Irving Pratt Ocean

Race Handicap Study (Hazen, Newman, et.al).

• The technique involves iteratively adjusting the Q for each race until the

linear regression of the corrected time yields a slope of zero (no correlation

of handicap to corrected time). This is the “Optimum Q” for that race.

• The resulting “Optimum Q’s” of all the races and divisions are then analyzed

and plotted.

November 2008


Tuesday Race #10 7/22/08

Q= 0.025Mult E.T. Corr.Time

! B-25 126 1.0885 0:47:22 0:51:34

! C&C 27-II 189 0.9812 0:53:34 0:52:34 T

! C&C 29 177 1.0000 0:52:45 0:52:45 T

" J-80 117 1.1057 0:48:21 0:53:28

" Pearson 26 216 0.9415 0:57:12 0:53:51

! 1DR35 39 1.2819 0:42:06 0:53:58

# Wavelength 2 168 1.0145 0:53:13 0:53:59

# Sabre 28 198 0.9676 0:56:34 0:54:44

" Scampi 30 177 1.0000 0:55:55 0:55:55

$ Wavelength 2 168 1.0145 0:55:17 0:56:05

" Beneteau 10R 78 1.1873 0:47:16 0:56:07 DSQ

$ CS 30 150 1.0450 0:53:43 0:56:08 DSQ

# Soverel 33 81 1.1806 0:47:51 0:56:30

# C&C 29 177 1.0000 0:56:32 0:56:32

% J-80 117 1.1057 0:51:10 0:56:34

% X-102 132 1.0772 0:52:50 0:56:55

$ C&C 29 177 1.0000 0:58:11 0:58:11

% C&C 29 177 1.0000 0:58:22 0:58:22

$ Columbia 26 222 0.9331 1:04:12 0:59:54

% Columbia 26 225 0.9290 1:04:43 1:00:07

& J-80 117 1.1057 0:56:53 1:02:54

& Hunter 28 186 0.9859 1:03:56 1:03:02

& Columbia 26 225 0.9290 1:08:39 1:03:47

' Blazer 23 147 1.0502 1:02:23 1:05:31

& Beneteau 424 108 1.1235 1:09:46 1:18:23

()*+,-----./+01)2-3!4----------5671-891,-!4-------------------:);+,---4'<""<4=-

:+>+?);+,-@)0;+>>)7)-----------5671-:6A,-=4-------------------@B/A0+,-5CDCEC5--

-------------------------------F)716*)9,-.--------------------E+7?;G,-#H%4-----

Rating vs. Corrected Time

0:46:05

0:53:17

1:00:29

1:07:41

1:14:53

1:22:05

0 50 100 150 200 250

PHRF TOD Rating

Co

rrecte

d T

ime

Analysis Example

November 2008


Results

Optimum Q per race vs. Minimum TOD Rating

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-10 40 90 140 190 240

Time on Distance Rating

Op

tim

um

Q V

alu

e

Optimum "Q"

Scatter Plot of Optimum Q’s for 3592 Race/divisions from 526 data individual club data files.

November 2008


Results

Histogram of Optimum QData file: Q045.txt 1/15/08, All Data

0

50

100

150

200

250

300

350

400

450

-0.1

6

-0.1

1

-0.0

6

-0.0

10.

040.

090.

140.

190.

240.

290.

340.

390.

440.

490.

540.

590.

640.

690.

740.

790.

840.

890.

940.

991.

04

Optimum Q

Nu

mb

er

of

Races

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

110.00%

Frequency

Cumulative %

Optimum Q’s plotted as a Histogram

Median Optimum Q = -0.018

November 2008


Histogram of Optimum QData file: Q045.txt 1/15/08, t/d < 100

0

20

40

60

80

100

120

140

160

-0.1

75

-0.1

25

-0.0

75

-0.0

25

0.0

25

0.0

75

0.1

25

0.1

75

0.2

25

0.2

75

0.3

25

0.3

75

0.4

25

0.4

75

0.5

25

0.5

75

0.6

25

0.6

75

0.7

25

0.7

75

0.8

25

0.8

75

0.9

25

0.9

75

1.0

25

Optimum Q

Nu

mb

er

of

Races

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

110.00%

Frequency

Cumulative %

Histogram of Optimum QData file: Q045.txt 1/15/08, t/d > 100

0

50

100

150

200

250

300

350

-0.1

75

-0.1

25

-0.0

75

-0.0

25

0.0

25

0.0

75

0.1

25

0.1

75

0.2

25

0.2

75

0.3

25

0.3

75

0.4

25

0.4

75

0.5

25

0.5

75

0.6

25

0.6

75

0.7

25

0.7

75

0.8

25

0.8

75

0.9

25

0.9

75

1.0

25

Optimum Q

Nu

mb

er

of

Races

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

110.00%

Frequency

Cumulative %

Results

T/D < 100 sec/mile

Median Optimum Q = .008

T/D > 100 sec/mile

Median Optimum Q = -0.0335

Optimum Q as a Function of Rating

November 2008


What does USSailing Have to Say about PHRF Time on Time Scoring?

From the website article by John Collins:

“Over the past few years a number of PHRF fleets have started using TOT scoring. It has been

found to help some when there is a very large handicap spread in a class or if the race conditions

are “abnormal”. The following is a TOT conversion formula that is commonly used to convert the

standard PHRF TOD handicap into a TOT Time Correction Factor (TCF).

A

TCF = ------------------

B + PHRF

The denominator, B + PHRF, is the number of seconds it takes to sail a nautical mile in the

expected conditions. Another way to look at it is that the denominator divided into 3600 is the

average rhomb line boat speed in knots. Here are some commonly used B factors:

Very light air or all

windward work

650

"Average" conditions550

Heavy air or all off the

wind

480

When used

B Factor

There are no hard and fast rules for selecting the B coefficient. Basically, the lower you select it, the

more favorable it will be to the slower boats.”

Very light air or all windward work650

“Average” conditions550

Heavy air or all off the wind480

When usedB Factor

DOES NOT APPEAR TO BE BASED ON RIGOROUS ANALYSIS

Adjusting the B Factor is a “Q” adjustment.

Favors Slower boats

Favors Faster boats

Q = .037

Q = .061

Q = .096

November 2008


TOT = 685.441

TOD + 508.411Present Q = 0.045

TOT = 503.25

TOD + 326.255

Q = -0.018

Q = 0.008

TOT = 578.43

TOD + 401.43

TOT = 458.44

TOD + 281.44

Q = -0.0335

ALL DATA

Ratings < 100

Ratings > 100

RECAP OF RESULTS

November 2008


CONCLUSIONS

1. The present Q of 0.045 is not optimum for Lake Ontario

2. Optimum Q is not constant across the handicap range.

Approx. 12 sec/mile error per 60 sec/mile of rating spread for ratings < 100

Approx. 26 sec/mile error per 60 sec/mile of rating spread for ratings > 100

3. Handicap error due to the non-optimized Q of 0.045 is significant.

4. Lowering the Q value will provide more equitable racing especially

with large fleet spreads.

5. Removing the global “Q error” may provide more consistent

performance results for rating adjustment purposes.

November 2008


Two Vital Question come to mind

How will this affect the results at my club?

Checking Results

How will this affect the annual performance analysis?

EXAMPLES

November 2008


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ASP O/All

183 0 0 0 1 1 0 1 0 0 1 0 0 0 0 4

183 0 0 0 0 0 0

192 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

192 0 0 0 -1 0 -1

195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

210 0 0 0 0 0 0 0 0 0 0 0 0 0 0

210 0 0 0 0 0 0 0 0 0 0 0

213 0 0 -1 -1 -2

222 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1

range 39

114 0 0 0

132 0 0 0 0 0 1 0 0 0 0 1

138 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2

150 0 1 0 0 0 1

156 0 0 0 0 0 0 0 0 0 0 0 0

162 0 0 0 0 0 0 -1 0 -1

165 -1 0 0 0 0 0 0 0 1 0

168 -1 0 0 0 0 0 0 0 0 0 0 -1

186 0 0 0 0 0 -1 0 0 0 -1 0 0 0 -2

range 72

Positive 1 represents an increased score - second to third etc

Negative 1 represents an Improved score - second to first etc.

2007 WYC SERIES RACES

PLACE CHANGES

No Flying Sails Divisions Q = 0.008Club Example

November 2008


Flying Sails Divisions Q = 0.008

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ASP O/All

168 0 1 0 0 0 0 0 0 0 0 0 1

174 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

183 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1

183 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1

183 0 0 0 0 0 0 0 0 0 0 0

183 0 0 0 1 0 0 0 1

216 0 0 -1 0 0 0 0 0 -1 -2

231 0 0 0 0 0 0 0 0 0

range 63

57 1 0 0 1

72 0 0 0 1 0 0 0 0 0 0 1 0 0 2

78 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 2

120 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 -2

123 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1

132 -2 0 0 0 0 0 0 -2

150 0 0 0

range 93

Positive 1 represents an increased score - second to third etc

Negative 1 represents an Improved score - second to first etc.

2007 WYC SERIES RACES

PLACE CHANGES

Club Example

November 2008


Club Example

There were 18 place changes in the Non- Spinnaker and 15

place changes in the Spinnaker Divisions

No more than a 2 position change for any boat in any race.

RESULTS for a Q of .008

November 2008


Looking at the 2008 WYC

results a different way!

Club Example

November 2008


No Flying Sails

Small changes in overall score but no position changes even when

Q = -0.018

WYC 2008 Series Overall

0.045 0.008 -0.018

Rank Division Class PHRFTOT

1st 1 THUNDERBIRD 207 25 25 25

2nd 1 C&C 29 192 44.5 45 46

3rd 1 VIKING 28 IB 195 50 50 50

4th 1 ALBERG 37 186 73 72 72

5th 1 ALOHA 28/8.5 222 77 76 75

6th 1 GRAMPIAN 26 OB 210 100.5 100 100

7th 1 C&C 29-2 177 101 103 103

8th 1 TARTAN 30 198 123 123 123


1st 2 VIKING 33/34 138 23 26 29

2nd 2 TARTAN 3500 SD 150 32.5 32 30

3rd 2 CS 36 SD 156 40.5 38 37

4th 2 C&C 3/4 TON 168 58 58 58

5th 2 CS 30 165 72 72 72

6th 2 MIRAGE 30 183 87 87 87

Q =

Overall Score

Overall Score

Club Example

November 2008


Flying Sails


Results for 20 races with 4 discards 0.045 0.008 -0.018


1st 3 CATALINA 30 TM 168 22.5 23 24 ^

2nd 3 VIKING 28 IB 183 43 43 42 v

3rd 3 C&C 29-2 177 45.5 46 47 ^

4th 3 C&C 29-2 177 53.5 54 54 ^

5th 3 C&C 29-2 177 65 64 64 v

6th 3 THUNDERBIRD 183 65.5 65 65 v

7th 3 C&C 29 183 79 80 80 ^

8th 3 PEARSON 26 216 111 110 109 v

9th 3 J 24 168 135 135 135


1st 4 TRIPP 33 78 16 17 19 ^

2nd 4 C&C 38-1 120 54 52 52 v

3rd 4 X 99 105 58 57.5 54.5 v

4th 4 J 35 72 59 61 63 ^

5th 4 MARTIN 242 153 63 61 55 v

6th 4 C&C 115 57 78 78 83.5 ^

7th 4 CS 36 123 89 87.5 87 v

8th 4 OLSON 30 114 94 94 94

Q =

Overall Score

Overall Score

Larger changes in the faster fleet - Large spread in ASPs. Q = -0.018

caused a reversal in 4/5 positions


0.045 0.008 -0.018


1st 3 CATALINA 30 TM 168 22.5 23 24 ^

2nd 3 VIKING 28 IB 183 43 43 42 v

3rd 3 C&C 29-2 177 45.5 46 47 ^

4th 3 C&C 29-2 177 53.5 54 54 ^

5th 3 C&C 29-2 177 65 64 64 v

6th 3 THUNDERBIRD 183 65.5 65 65 v

7th 3 C&C 29 183 79 80 80 ^

8th 3 PEARSON 26 216 111 110 109 v


1st 4 TRIPP 33 78 16 17 19 ^

2nd 4 C&C 38-1 120 54 52 52 v

3rd 4 X 99 105 58 57.5 54.5 v

4th 4 J 35 72 59 61 63 ^

5th 4 MARTIN 242 153 63 61 55 v

6th 4 C&C 115 57 78 78 83.5 ^

7th 4 CS 36 123 89 87.5 87 v

8th 4 OLSON 30 114 94 94 94

Q =

Overall Score

Overall Score

Club Example

November 2008


Club Example

Result of Final Finish Positions

One change in final finish position for a Q of either .008 or -0.018.

November 2008


How will this affect the annual performance analysis?

• The report was recalculated with different Q values

• Original cumulative results with 4 or 5 Alert levels were extracted

• Original results set alongside the recalculated ASPs

• For brevity only the first few are presented

November 2008


Effect on the Annual Analysis Report

Represents Original calculations using Q= 0.045Bold and Italics represents classes that had handicap changes by CC in the spring

* indicate that there was a change in numbers

Calc Diff Alert Calc.Diff Alert

Boat Class/Year Orig Rev Orig Rev Orig Orig Rev Rev Change

C&C 25-1 OB 218 217 * 203 203 -15 ????? -14 ????? 1

C&C 27-4 195 195 186 187 -9 ???? -8 ???? 1

C&C 30 168 168 175 178 7 ???? 9 ???? 2

C&C 35-2 128 128 134 134 6 ???? 6 ???? 0

C&C 41 69 69 81 82 10 ???? 12 ????? 2

C&C 99 CF 99 99 108 107 9 ???? 8 ???? -1

CATALINA 30 TM BS 174 174 162 164 -12 ????? -10 ???? 2

CS 33 146 147 * 164 159 18 ????? 13 ????? -5

DRAGON 175 176 * 162 167 -13 ????? -9 ???? 4

Avg ASP Calc.ASP

Represents Revised calculations using Q= .008

November 2008



Represents Original calculations using Q= 0.045Bold and Italics represents classes that had handicap changes by CC in the spring

* indicate that there was a change in numbers

Calc Diff Alert Calc.Diff Alert

Boat Class/Year Orig Rev Orig Rev Orig Orig Rev Rev Change

EVELYN 32-2 100 100 109 108 9 ???? 8 ???? -1

GOMAN EXP 30-2 141 141 134 135 -7 ???? -6 ???? 1

J 22 170 170 147 148 -23 ????? -22 ????? 1

J 24 ODR 166 165 * 158 160 -8 ???? -5 3

J 35 72 72 65 68 -7 ???? -4 3

J 35 ODR 69 69 59 67 -10 ???? -2 8

KIRBY 25 171 171 165 165 -6 ???? -6 ???? 0

MARTIN 24-2 151 151 162 159 11 ???? 8 ???? -3

Avg ASP Calc.ASP

Represents Revised calculations using Q= .008

November 2008



What you might expect to see is…

• A general tightening of the ASP differences

November 2008





Q= -0.018Q= 0.008Q= 0.045

8910

Median absolute calculated difference

November 2008





• Fewer level 4 and 5 alerts

November 2008






578????? Alerts

192124???? Alerts

Q= -0.018Q= 0.008Q= 0.045

November 2008






• Less oscillation from year to year

November 2008


RECOMMENDATIONS

! PHRF-LO adopt a Q of .008 for 2009.

• Remove the multiplier from individual certificates and instead publish the

simplified conversion formula and resulting table of multipliers.

! TAC to continue investigation of Q related factors

• Variation (consistency) of “Optimum Q” over the handicap

range

• A method to back calculate optimum Q for each race (“floating Q”).

! Potential Future Considerations

• Readdress the Q value after a season of experience.

• Effect of course type and wind strength on Q.

• Optimized “Club Q” based on club performance and divisional spreads

Documents

Optimizing “Q” in the PHRF-LO Time on Time ConversionNovember 2008 PHRF-LO Technical Advisory Committee “Q” is an adjustment variable available within the PHRF-LO T/D to T/T