# 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. 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:
• All handicap systems are equally good.
• The handicap for the boats are distribution as a normal distribution.
The method has four steps:
1. For each handicap system: calculate the mean and standard deviation for the boat length in scope.
2. For each handicap system: calculate the difference (in units of σ) from mean to the boat length in scope.
3. Calculate the average σ (Aσ) of the σs from step 2.
4. 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.  Nomenclature
Abrev.Description
σStandard Deviation
nThe number of data points in the data set
xiValue of the ith point in the data set
ñThe 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.

References

[Ref 2]: Standard Deviation in Wikipedia.
[Ref 3]: Mathematical Handbook of formula and tables, Schaum's outline series, table 47, page 257