Commodore’s Cup – Personal PNs

In 2019 the Commodore’s Cup is going to be 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?

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 for that class

 

How have Personal PNs been calculated?

 For each race in 2018 we have calculated the PN each helm would have to have so that everyone got the same Corrected Time. The Corrected Time chosen was 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 was calculated using the Achieved PNs  from all races in the season.

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 was 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 bad races.

 

The Personal PN for a Helm/Class is a step towards the Average Good Achieved PN (AGAP) from the

Average Achieved PN (AAP). The more good races you had the closer your Personal PN is to your Average Good Achieved PN. If there are fewer than 4 races for a Helm/ Class the Personal PN is set to the UTLSC 2019 PN.

Personal PN = AAP + ((AGAP – AAP) * Confidence Limit)

E.g.

Average Achieved PN                = 1300 for 10 races

Average Good Achieved PN      = 1250 for 6 races

Personal PN                                = 1300 + [(1250-1300)*6/10] = 1300 – 50*0.6 = 1270

  

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