Hi there,
I think there might be a mistake in the documentation. The Understanding Scaled F-Score section says
The F-Score of these two values is defined as:
$$ \mathcal{F}_\beta(\mbox{prec}, \mbox{freq}) = (1 + \beta^2) \frac{\mbox{prec} \cdot \mbox{freq}}{\beta^2 \cdot \mbox{prec} + \mbox{freq}}. $$
$\beta \in \mathcal{R}^+$ is a scaling factor where frequency is favored if $\beta < 1$, precision if $\beta > 1$
I believe it should say
$\beta \in \mathcal{R}^+$ is a scaling factor where frequency is favored if $\beta > 1$, precision if $\beta < 1$
For beta >> 1
$$ (1 + \beta^2) \frac{\mbox{prec} \cdot \mbox{freq}}{\beta^2 \cdot \mbox{prec} + \mbox{freq}}
\approx (\beta^2) \frac{\mbox{prec} \cdot \mbox{freq}}{\beta^2 \cdot \mbox{prec}}
= \mbox{freq}
$$
and for beta --> 0
$$ (1 + \beta^2) \frac{\mbox{prec} \cdot \mbox{freq}}{\beta^2 \cdot \mbox{prec} + \mbox{freq}}
\approx (1) \frac{\mbox{prec} \cdot \mbox{freq}}{0 + \mbox{freq}}
= \mbox{prec}
$$
