Optimizing “Q” in the PHRF-LO Time on Time ConversionNovember 2008 PHRF-LO Technical Advisory...
Transcript of Optimizing “Q” in the PHRF-LO Time on Time ConversionNovember 2008 PHRF-LO Technical Advisory...
November 2008
PHRF-LO Technical Advisory Committee
Optimizing “Q” in the PHRF-LO Time on Time Conversion
Steve Corona
Andrew Sensicle
November 2008
PHRF-LO Technical Advisory Committee
“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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
Looking at the 2008 WYC
results a different way!
Club Example
November 2008
PHRF-LO Technical Advisory Committee
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
Rank Division Class PHRFTOT
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
PHRF-LO Technical Advisory Committee
Flying Sails
WYC 2008 Series Overall
Results for 20 races with 4 discards 0.045 0.008 -0.018
Rank Division Class PHRFTOT
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
Rank Division Class PHRFTOT
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
WYC 2008 Series Overall
0.045 0.008 -0.018
Rank Division Class PHRFTOT
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
Rank Division Class PHRFTOT
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
PHRF-LO Technical Advisory Committee
Club Example
Result of Final Finish Positions
One change in final finish position for a Q of either .008 or -0.018.
November 2008
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
PHRF-LO Technical Advisory Committee
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
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
PHRF-LO Technical Advisory Committee
Effect on the Annual Analysis Report
What you might expect to see is…
• A general tightening of the ASP differences
November 2008
PHRF-LO Technical Advisory Committee
Effect on the Annual Analysis Report
What you might expect to see is…
• A general tightening of the ASP differences
Q= -0.018Q= 0.008Q= 0.045
8910
Median absolute calculated difference
November 2008
PHRF-LO Technical Advisory Committee
Effect on the Annual Analysis Report
What you might expect to see is…
• A general tightening of the ASP differences
• Fewer level 4 and 5 alerts
November 2008
PHRF-LO Technical Advisory Committee
Effect on the Annual Analysis Report
What you might expect to see is…
• A general tightening of the ASP differences
• Fewer level 4 and 5 alerts
578????? Alerts
192124???? Alerts
Q= -0.018Q= 0.008Q= 0.045
November 2008
PHRF-LO Technical Advisory Committee
Effect on the Annual Analysis Report
What you might expect to see is…
• A general tightening of the ASP differences
• Fewer level 4 and 5 alerts
• Less oscillation from year to year
November 2008
PHRF-LO Technical Advisory Committee
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