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Some quantum measurements can not be performed simultaneously, i.e. they areincompatible. Here we show that every set of incompatible measurements providesan advantage over compatible ones in a suitably chosen quantum statediscrimination task. This is proven by showing that the Robustness ofIncompatibility, a quantifier of how much noise a set of measurements toleratesbefore becoming compatible, has an operational interpretation as the advantagein an optimally chosen discrimination task. We also show that if we take aresource-theory perspective of measurement incompatibility, then the guessingprobability in discrimination tasks of this type forms a complete set ofmonotones that completely characterize the partial order in the resourcetheory. Finally, we make use of previously known relations between measurementincompatibility and Einstein-Podolsky-Rosen steering to also relate the laterwith quantum state discrimination.

All sets of incompatible measurements give an advantage in quantum state discrimination