# πLocation Scale

The location scale is one of the multipliers used to calculate a stations reward. Its goal is to distribute rewards in areas with a high number of base stations.

It is a number between 1 and 0, obtained after multiplying all the reduction factors ($RF$) of its neighbor stations within a 70km radius. The neighboring stations $i=1\ldots n$ are sorted by distance to our own station.

A location scale of 1 will mean you get full rewards regarding the location, a location scale of 0 means you will get no rewards regarding our location.

Each Reduction Factor $RF$ is a function of the distance and the quality of the stream so that:

The two nearest stations will not affect your location scale ($RF_1 = 1$and $RF_2 = 1$), which is to promote redundancy

The further away a neighbor is, the lower the distance penalty ($DP$)

The higher your signal quality and availability compared to that of your neighbors, the higher your share of the rewards. A Share Factor ($SF$) is calculated for each of the neighbors. This means that a low quality stream does not heavily affect the rewards of high quality streams. It is still profitable to install a high quality base station in an area already covered by low quality base stations

### Distance Penalty ($DP$)

For each neighboring station, a Distance Penalty will be calculated.** **The distance penalty of each neighboring base station is defined using the following rules:

The two closest base stations are ignored, because we want to incentivize network redundancy

Stations within 20 kilometers from your own base station will have a distance penalty of 1

The distance penalty for stations located between 20 and 70 kilometers varies linearly between 1 and 0, where at 20 km it is 1 and at 70 km is 0

$DP= 1-\frac{DistanceToStation-20~\text{km}}{70~\text{km}-20~\text{km}}$

Stations further away than 70 kilometers are ignored

### Share Factor ($SF$)

Similarly, for each neighboring station, a Share Factor is calculated. It is taking into account the signal quality and the availability (Qual factor) of each station:

### An example

Letβs look at a practical example of how the location scale is calculated for each station.

This is the widget displayed in your *Reference Stations* tab. On the right side of the map, we can see your exemplary base station, in green color, surrounded by 4 third party base stations scattered through the surrounding land, in purple color.

Next to your exemplary base station, we can click on each of the four neighboring stations to get the details.

#### Calculating Reduction Factors ($RF$)

If we sort the neighboring stations simply by the distance to your own station, we can create a plot showing the relation between the distance and the distance penalty $DP$:

The dashed gray line represents the continuous function so that you can see the behavior of the penalty as a function of the distance.

In this example, the distance penalties have been scaled up from 0% to 100% but for the calculation purposes the punctuations range from 0 to 1.

Let's take station ESPBARSAB4 as an example and calculate $DP$, $SF$ and $RF$.

ESPBARSAB4 has $Qual_{\text ESPBARSAB4} = 0.934$ and a distance to your exemplary station of 25.522 km. In comparison, $Qual_{\text Your Station} = 0.99$.

This process is repeated for all stations between 20 and 70 km radius:

Now we can calculate your station's final Location ccale by multiplying all the Reduction Factors:

This Location Scale factor will then be used to be multiplied with the other reward factors, resulting in your total Reward Scale.

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