  Evaluation measures have a crucial impact on the direction of research.
Therefore, it is of utmost importance to develop appropriate and reliable
evaluation measures for new applications where conventional measures are not
well suited. Video Moment Retrieval (VMR) is one such application, and the
current practice is to use R@$K,\theta$ for evaluating VMR systems. However,
this measure has two disadvantages. First, it is rank-insensitive: It ignores
the rank positions of successfully localised moments in the top-$K$ ranked list
by treating the list as a set. Second, it binarizes the Intersection over Union
(IoU) of each retrieved video moment using the threshold $\theta$ and thereby
ignoring fine-grained localisation quality of ranked moments.
  We propose an alternative measure for evaluating VMR, called Average Max IoU
(AxIoU), which is free from the above two problems. We show that AxIoU
satisfies two important axioms for VMR evaluation, namely, \textbf{Invariance
against Redundant Moments} and \textbf{Monotonicity with respect to the Best
Moment}, and also that R@$K,\theta$ satisfies the first axiom only. We also
empirically examine how AxIoU agrees with R@$K,\theta$, as well as its
stability with respect to change in the test data and human-annotated temporal
boundaries.
