  Performance of quantum teleportation is typically measured by the average
fidelity, an overlap between the input and output states. Along with the first
moment, we introduce the second moment of fidelity in CV teleportation, i.e.,
the fidelity deviation as the figures of merit to assess the protocol's
efficiency. We show that CV states, both Gaussian and non Gaussian, can be
better characterized by considering both average fidelity and fidelity
deviation, which is not possible with only average fidelity. Moreover, we shed
light on the performance of the teleportation protocol in two different input
scenarios - one is when input states are sampled from constrained uniform
distribution while the other one is Gaussian suppression of the input states
which again lead to a different classification of CV states according to their
performance. The entire analysis is carried out in noiseless and noisy
scenarios with noise being incorporated in the measurement and the shared
channels. We also report that one type of noise can make the protocol robust
against the other one which leads to a `constructive effect' and identify the
noise models which are responsible for decreasing average fidelity and
increment in fidelity deviation.
