  Quantum teleportation is one of the most pioneering features of the quantum
world. Typically, the quality of a teleportation protocol is solely judged by
its average fidelity. In this work, we analyze the performance of teleportation
in terms of both fidelity and the deviation in fidelity. Specifically, we
define a quantity called teleportability score, which incorporates
contributions from both the fidelity and its deviation. It also takes into
account the sensitivity one requires for a protocol in which the teleportation
of a quantum state is required in one or many intermediate steps. We compute
the teleportability score in the noiseless scenario and find that it increases
monotonically with the entanglement content of the resource state. The result
remains same even if we consider an n-chain repeater-like configuration.
However, in the presence of noise, the teleportability score, can sometime
display a nonmonotonic behaviour with respect to the entanglement content of
the initially shared resource state. Specifically, under local bit-flip and
bit-phase-flip noise, lesser entangled states can have higher teleportability
score for certain choice of system parameters. In the presence of global
depolarizing noise, for low entangled resource states and high sensitivity
requirements, the noisy states can have better a teleportability score in
comparison to the noiseless scenario.
