Comparing Different Methods of Sailing Scoring and the Fairness of Each Method
The findings here are applied to sailing races. I will call each race the sailors take place in an ‘event’ and each set of events a ‘series’. The winner of the series is the sailor with the most or least points, depending on the scoring methods, after all events have taken place. Each sailor in this study has a mean performance score, between 10 and 100, denoted as μ from now on. Each sailor also has a different standard deviation, a measure of consistency between 0 and 18, denoted by σ from now on. I will call the scoring methods as followed:
Method 1 - Calculating the sum of the sailors finishing positions in an event with the lowest score being best.
Method …show more content…
Ten sailors had μ of 100, ten had μ of 90, all the way down to ten with a μ of 10. Each group of sailors with the same μ were given a different σ from 0 up to 18 in multiples of two.
I firstly ran the code for 6 events in a series ten times; the results showed the sailor in first position at the end of the series was almost exclusively a sailor with a μ of 100 and with a higher than average σ (one series was won by the sailor with a μ of 90 and a σ of 18). I ran the 6 event series ten times with the average σ coming out at 6.1. The sailors with a σ of 0 finished slightly below the middle of sailors with the same μ score, the sailor with μ of 100 and σ of 0 came in with the average position of 6.6 at the end of the series. At the bottom of the table of results, as would be expected, was the sailor with the μ of 10 and σ of 0 who finished in last place more times than any other …show more content…
First place was still won by a sailor with μ of 90 in one of the series. The average σ of the winners of the series was 8.2. In last place the mean σ was just 0.1. The sailor with μ of 100 and σ of 0 finished as low as 22nd place in the series. These results further confirm that this scoring method prefers winning events to finishing consistently with sailors of high variance doing better than their similarly skilled sailors with a lower variance in results.
At 100 and 10000 events in a series the results were almost identical for each simulation. The order at the top of each series were always the sailors with a μ of 100 and standard deviations of 18, 16, 14 and 12 respectively. They were then followed by sailors with μ of 90 and standard deviations of 18, 16 and 14 respectively. This trend continued down the table with those sailors with high σ placing way above those of lower σ despite their often higher μ values. The sailor with μ of 100 and σ of 0 finished on average in 27th place with the sailor with μ of 40 and σ of 18 beating them in the series 30% of the
The findings here are applied to sailing races. I will call each race the sailors take place in an ‘event’ and each set of events a ‘series’. The winner of the series is the sailor with the most or least points, depending on the scoring methods, after all events have taken place. Each sailor in this study has a mean performance score, between 10 and 100, denoted as μ from now on. Each sailor also has a different standard deviation, a measure of consistency between 0 and 18, denoted by σ from now on. I will call the scoring methods as followed:
Method 1 - Calculating the sum of the sailors finishing positions in an event with the lowest score being best.
Method …show more content…
Ten sailors had μ of 100, ten had μ of 90, all the way down to ten with a μ of 10. Each group of sailors with the same μ were given a different σ from 0 up to 18 in multiples of two.
I firstly ran the code for 6 events in a series ten times; the results showed the sailor in first position at the end of the series was almost exclusively a sailor with a μ of 100 and with a higher than average σ (one series was won by the sailor with a μ of 90 and a σ of 18). I ran the 6 event series ten times with the average σ coming out at 6.1. The sailors with a σ of 0 finished slightly below the middle of sailors with the same μ score, the sailor with μ of 100 and σ of 0 came in with the average position of 6.6 at the end of the series. At the bottom of the table of results, as would be expected, was the sailor with the μ of 10 and σ of 0 who finished in last place more times than any other …show more content…
First place was still won by a sailor with μ of 90 in one of the series. The average σ of the winners of the series was 8.2. In last place the mean σ was just 0.1. The sailor with μ of 100 and σ of 0 finished as low as 22nd place in the series. These results further confirm that this scoring method prefers winning events to finishing consistently with sailors of high variance doing better than their similarly skilled sailors with a lower variance in results.
At 100 and 10000 events in a series the results were almost identical for each simulation. The order at the top of each series were always the sailors with a μ of 100 and standard deviations of 18, 16, 14 and 12 respectively. They were then followed by sailors with μ of 90 and standard deviations of 18, 16 and 14 respectively. This trend continued down the table with those sailors with high σ placing way above those of lower σ despite their often higher μ values. The sailor with μ of 100 and σ of 0 finished on average in 27th place with the sailor with μ of 40 and σ of 18 beating them in the series 30% of the