Implementations of quantum key distribution as available nowadays suffer from
inefficiencies due to post processing of the raw key that severely cuts down
the final secure key rate. We present a simple model for the error scattering
across the raw key and derive "closed form" expressions for the probability of
a parity check failure, or experiencing more than some fixed number of errors.
Our results can serve for improvement for key establishment, as information
reconciliation via interactive error correction and privacy amplification rests
on mostly unproven assumptions. We support those hypotheses on statistical
grounds.