  We are in an era of precision measurements at the Large Hadron Collider. The
precision that can be achieved on some of those is limited however due to large
systematic uncertainties. This paper introduces a new technique to reduce the
total systematic uncertainty by quantifying the systematic impact of single
events and correlating it with event observables to identify classes of events
that are more sensitive to systematic effects. A proof of concept is presented
by means of a simplified top quark mass estimator applied on simulated events.
Even without a thorough optimization, it is shown that the total systematic
uncertainty can be reduced by at least 30%.
