  Extrapolations of sensitivity to new interactions and standard model
parameters critically inform the programme at the Large Hadron Collider (LHC)
and potential future collider cases. To this end, statistical considerations
based on inclusive quantities and established analysis strategies typically
give rise to a sensitivity scaling with the square root of the luminosity,
$\sqrt{L}$. This suggests only a mild sensitivity improvement for LHC's
high-luminosity phase, compared to the collected data up to the year 2025. We
discuss representative analyses in top quark, Higgs boson and electroweak gauge
boson phenomenology and provide clear evidence that the assumption that the
sensitivity in searches and measurement scales only with $\sqrt{L}$ at the
High-Luminosity LHC is overly conservative at best, and unrealistic in
practice. As kinematic coverage enables more targeted search strategies with
sufficient statistical sensitivity, employing a multitude of features in data
dispels the scaling based on more inclusive selections.
