# Formulæ

### General Formula to calculate Participation Score

$\displaystyle PS_{n} = PS_{n-1} \cdot \overrightarrow P_n$

where $\overrightarrow P$ is the Performance of a Member (*j*) in a given period, represented as the ratio between **given and expected contribution points** $(\frac {GCp}{ECp})$, using *ECp'* to include a time factor $\Delta T$

We calculate $\overrightarrow P_{\tiny j}$ as:

$\overrightarrow P_{\tiny j} = \frac {GC_{\tiny j}} {EC'_{\tiny j}}$

**Deep-dive:** *Performance Stability*

In some use-cases, may be relevant to calculate the “stability” in someone’s performance.

To simplify this process, you may want to use the parameter $\Delta \overrightarrow P$ - representing the change in Performance of a member between a period and the other, and calculated as:

$\displaystyle \Delta \overrightarrow P = (\frac {\overrightarrow P_{\tiny(n)} - \overrightarrow P_{\tiny(n-1)}} {\overrightarrow P_{\tiny(n-1)}})$

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