What is Relative Speed Performance (RSP)?
What is Relative Speed Performance (RSP)?
The Relative Speed Performance (RSP) is a statistical method to show the speed of a given boat relative to other similar boats, i.e. boats within the same category (e.g. monohull sailboats) and about same length (+/- 50 cm).
The RSP method gives a number between 0 and 100.
E.g. if a sailboat has RSP = 80 then the boat is faster than 80% of all similar sailboats.
How to calculate the Relative Speed Performance (RSP)?
The method is based on handicap data collected through the years and has the following assumptions:
As an example, the figure below shows the distribution of the LYS handicap for 9 meter (30 ft) sailboat designs.
For 9 meter sailboats the mean for LYS is 1.077. Looking at the figure, the value 1.077 is pretty much in the center of the histogram. The standard deviation σ is 0.048.
Example 1: A sailboat Impala 30 has LYS = 1.12. The σ-distance from average is then (1.12 - 1.077)/0.048 = 0.90σ.
Example 2: A motorsailer like LM Mermaid 290 has LYS = 1.04. The σ-distance from average is then (1.04 - 1.077)/0.048 = -0.77σ.
In this example we only have one handicap system, but if we had e.g. 5 systems we would just calculate the average for these 5 σ-values. In our example we have only one handicap system, so the average for Impala 30 is 0.90σ, and the average for LM Mermaid 290 is -0.77σ
For the Impala 30 the x = 0.90, and the integral from -∞ to 0.90 = 82%. Having an RPR of 82 means that the Impala 30 is faster than 82% of all other 9m sailboat designs.
Likewise, for the LM Mermaid 290 the x = -0.15, and the integral from -∞ to -0.15 = 21%. Having an RPR of 46 means that the LM Mermaid 290 is faster than 21% of all other 9m sailboat designs.
Note: For people unfamiliar with integrals the values can also be looked up in tables in most statistical handbooks[3].
- All handicap systems are equally good.
- The handicap for the boats are distribution as a normal distribution[1].
- For each handicap system: calculate the mean and standard deviation[2] for the boat length in scope.
- For each handicap system: calculate the difference (in units of σ) from mean to the boat length in scope.
- Calculate the average σ (Aσ) of the σs from step 2.
- Calculate the area under the standard normal curve from minus ∞ to average Aσ.
Step 1: Calculate the mean and standard deviation for the boat length in scope.
| Abrev. | Description |
|---|---|
| σ | Standard Deviation |
| n | The number of data points in the data set |
| xi | Value of the ith point in the data set |
| ñ | The mean value of the data set |
As an example, the figure below shows the distribution of the LYS handicap for 9 meter (30 ft) sailboat designs.
For 9 meter sailboats the mean for LYS is 1.077. Looking at the figure, the value 1.077 is pretty much in the center of the histogram. The standard deviation σ is 0.048.
Step 2: calculate the difference (in units of σ) from mean to the boat length in scope.
Example 1: A sailboat Impala 30 has LYS = 1.12. The σ-distance from average is then (1.12 - 1.077)/0.048 = 0.90σ.
Example 2: A motorsailer like LM Mermaid 290 has LYS = 1.04. The σ-distance from average is then (1.04 - 1.077)/0.048 = -0.77σ.
Step 3: Calculate the average σ.
In this example we only have one handicap system, but if we had e.g. 5 systems we would just calculate the average for these 5 σ-values. In our example we have only one handicap system, so the average for Impala 30 is 0.90σ, and the average for LM Mermaid 290 is -0.77σ
Step 4: Calculate the area under the standard normal curve from -∞ to the average σ.
For the Impala 30 the x = 0.90, and the integral from -∞ to 0.90 = 82%. Having an RPR of 82 means that the Impala 30 is faster than 82% of all other 9m sailboat designs.
Likewise, for the LM Mermaid 290 the x = -0.15, and the integral from -∞ to -0.15 = 21%. Having an RPR of 46 means that the LM Mermaid 290 is faster than 21% of all other 9m sailboat designs.
Note: For people unfamiliar with integrals the values can also be looked up in tables in most statistical handbooks[3].
References
[Ref 1]: Normal distribution in Wikipedia.
[Ref 2]: Standard deviation in Wikipedia.
[Ref 3]: Mathematical Handbook of formula and tables, Schaum's outline series, table 47, page 257
[Ref 2]: Standard deviation in Wikipedia.
[Ref 3]: Mathematical Handbook of formula and tables, Schaum's outline series, table 47, page 257