  It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the
maximum of a variable-speed branching Brownian motion (BBM) in the weak
correlation regime converges to a randomly shifted Gumbel distribution. The
random shift is given by the almost sure limit of McKean's martingale, and
captures the early evolution of the system. In the Bovier-Hartung extremal
process, McKean's martingale thus plays a role which parallels that of the
derivative martingale in the classical BBM. In this note, we provide an
alternative interpretation of McKean's martingale in terms of a law of large
numbers for high-points of BBM, i.e. particles which lie at a macroscopic
distance from the edge. At such scales, 'McKean-like martingales' are naturally
expected to arise in all models belonging to the BBM-universality class.
