Commodore’s Cup – Personal PNs

The Commodore’s Cup is awarded on a personal handicap basis. So what Personal PN should a helm have for a class so that everyone has an equal chance of winning the Commodore’s Cup? See below.

If there are fewer than 4 races used to calculate the Personal PN for a Helm/ Class the UTLSC PN for that year is used.

Personal PNs and UTLSC PNs for a year can only be provided once the RYA provide the National PNs at the Boat Show the first weekend in March.

What is a PN?

Some classes are faster than others. E.g. A Laser is faster than a Topper.
To enable boats from different classes to compete against each other in the same race classes are given a Portsmouth Yardstick Number (PN).
These PNs are used to calculate a corrected time from the elapsed time. The person with the lowest corrected time is the winner and so on.

Corrected Time = Elapsed Time * 1000/ PN


What are Personal PNs?

Personal PNs try to make it so that everyone finishes with the same corrected time! So it should make it possible for a middle of the road (or lake?) sailor to finish first.

Personal PNs were calculated for the first time in 2019 based on the results from 2018.

Personal PNs from 2020 onwards combine the previous year’s results together with the Personal PN given to each competitor the previous year.

To compensate for those who are getting older and hence sailing fewer races and getting worse results there is an additional weighting for the previous year’s results. For 2019 races the weighting factor is 2

This also makes it more challenging for people who are getting better – sailing more races and getting better results


How have Personal PNs been calculated?

For those who want to know how Personal PNs are calculated…
(it gets complicated – so ask me if you don’t understand what I have written!

For each race in a year we calculate the PN each helm would have to have so that everyone got the same Corrected Time. The Corrected Time chosen is the average of most of the Corrected Times for the race. However, some Corrected Times have been excluded where the competitor appears to have had a bad1 race (very poor start, capsized, becalmed, sailed the wrong course). This is the helm’s Achieved PN for that race in that class.

The Average Achieved PN for a Helm/ Class is calculated using the Achieved PNs  from all races in the year.

The Average Achieved PN is more advantageous to a helm if it includes results where they had a bad race.  So the Average Good Achieved PN is calculated from races for which the helm had a good2 race and there were 4 or more competitors.

Some helms have a bad race because they make uncharacteristic mistakes, others are because that is the best they can do (so far). It is not possible to decide which without becoming personal! Some helms have no or very few good races– using only good races does not work for them

So it seems fair to take both the Average Achieved PN and the Average Good Achieved PN into consideration according to how many races count towards each Average.  So the Confidence Limit of how far we should move towards the Average Good Achieved PN is the Count of good races / Count of races.

The MyPN (yearfor a Helm/Class is a step towards the Average Good Achieved PN (AGAP) from the Average Achieved PN (AAP) for that year.
The more good races you had the closer your MyPN (year) is to your Average Good Achieved PN.

MyPN (year) = AAP + ((AGAP – AAP) * Confidence Limit)

Average Achieved PN            = 1300 for 10 races
Average Good Achieved PN  = 1250 for 6 races
MyPN (year)                           = 1300 + [(1250-1300)*(6/10)] = 1300 – 50*0.6 = 1270
Count of Races:  CoR (year)      = 10 +[ (6-10)*(6/10)] = 10 – (4*0.6)/10 = 7.6

Personal PN 2019 = MyPN 2018 as we have no Personal PNs from previous years
PPNR 2019             = Count of races used to calculate PPN 2019 (for 2019 = CoR 2018)

For subsequent years the Personal PN will be calculated as follows

PPN yn = ((MyPN yn-1  * CoR yn-1 *wn-1) + (PPN yn-1 * PPNR  yn-1))/((CoR yn-1 *wn-1) + PPNR  yn-1)
where w(year) is the weighting factor given to that races in that year

PPNR yn = CoR yn-1 + PPNR yn-1

So for 2020

PPN2020 = ((MyPN 2019 * CoR 2019 * w2019) + (PPN 2019 * PPNR  2019))/((CoR 2019 *w2019) + PPNR  2019)

MyPN 2019    = 1290
CoR 2019       = 4
W 2019          = 2

PPN 2019       = 1270
PPNR 2019     = 7.6

PPN2020        = ((1290 * 4 *2) + (1270 * 7.6)) / ((4*2)+7.6)
=       10,320     +       9,652      /        15.6
= 1280

PPNR 2020 = 4 + 7.6 = 11.6

If PPNR 2020 for a Helm Class is <4 then the UTLSC 2020 PN for that class is used.

bad1                   Corrected time is greater than Average Corrected time + Standard Deviation
good2                Not bad!