# 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:

> $$\overrightarrow P\_{\tiny j} = \frac {GC\_{\tiny j}} {EC'\_{\tiny j}}$$

{% hint style="info" %}
**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:

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

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<figure><img src="https://2854338415-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Ftx5aZfM9w94ooSZf3y3O%2Fuploads%2FfxYdTcnlWwVIbkh0JRmJ%2FScreenshot%202025-03-07%20at%2017.12.25.png?alt=media&#x26;token=5818c2f2-6128-4f46-b247-ddf3b331bc34" alt=""><figcaption><p>The complete contracts flow - from joining a Hub to updating Participation Score.</p></figcaption></figure>

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