  The canonical Bartnik-McKinnon solitons are regular solutions of the coupled
Einstein-Yang-Mills system in which gravity may balance the repulsive nature of
the Yang-Mills field. We examine the role played by gravity in balancing the
system and determine its strength. In particular, we obtain an analytic lower
bound on the fundamental mass-to-radius ratio, max{2m(r)/r}>2/3, which is a
necessary condition for the existence of globally regular Einstein-Yang-Mills
solitons. Our analytical results are in accord with numerical calculations.
