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We derive, within the replica formalism, a generalisation of theCrisanti-Sommers formula to describe the large deviation function (LDF) ${\calL}(e)$ for the speed-$N$ atypical fluctuations of the intensive ground-stateenergy $e$ of a generic spherical spin-glass in the presence of a randomexternal magnetic field of variance $\Gamma$. We then analyse our exact formulafor the LDF in much detail for the Replica symmetric, single step ReplicaSymmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations.Our main qualitative conclusion is that the level of RSB governing the LDF maybe different from that for the typical ground state. We find that while thedeepest ground-states are always controlled by a LDF of replica symmetric form,beyond a finite threshold $e\geq e_{t}$ a replica-symmetry breaking starts tobe operative. These findings resolve the puzzling discrepancy between ourearlier replica calculations for the $p=2$ spherical spin-glass and therigorous results by Dembo and Zeitouni which we are able to reproduce invokingan 1-RSB pattern. Finally at an even larger critical energy $e_{c}\geq e_{t}$,acting as a "wall", the LDF diverges logarithmically, which we interpret as achange in the large deviation speed from $N$ to a faster growth. In addition,we show that in the limit $\Gamma \to 0$ the LDF takes non-trivial scalingforms (i) ${\cal L}(e) \sim G((e-e_c)/\Gamma)$ in the vicinity of the wall (ii)${\cal L}(e) \sim \Gamma^{\eta \nu} F((e-e_{\rm typ})/\Gamma^{\nu})$ in thevicinity of the typical energy, characterised by two new exponents $\eta\geq 1$and $\nu$ characterising universality classes. Via matching the latter allowsus to formulate several conjectures concerning the regime of {\it typicalfluctuations}, identified as $e-e_{\rm typ} \sim N^{-1/\eta}$ and $\Gamma \simN^{-1/(\eta \nu)}$.

Replica-symmetry breaking transitions in the large deviations of the ground-state of a spherical spin-glass