Centrality definition in A$+$A collisions at colliders such as RHIC and LHC suffers from a correlated systematic uncertainty caused by the efficiency of detecting a p$+$p collision ($50pm 5%$ for PHENIX at RHIC). In A$+$A collisions where centrality is measured by the number of nucleon collisions, $N_{rm coll}$, or the number of nucleon participants, $N_{rm part}$, or the number of constituent quark participants, $N_{rm qp}$, the error in the efficiency of the primary interaction trigger (Beam-Beam Counters) for a p$+$p collision leads to a correlated systematic uncertainty in $N_{rm part}$, $N_{rm coll}$ or $N_{rm qp}$ which reduces binomially as the A$+$A collisions become more central. If this is not correctly accounted for in projections of A$+$A to p$+$p collisions, then mistaken conclusions can result. A recent example is presented in whether the mid-rapidity charged multiplicity per constituent quark participant $({dN_{rm ch}/deta})/{N_{rm qp}}$ in Au$+$Au at RHIC was the same as the value in p$+$p collisions.
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