  An extension (K(X)|K, v) of valued fields is said to be valuation
transcendental if we have equality in the Abhyankar inequality. Minimal pairs
of definition are fundamental objects in the investigation of valuation
transcendental extensions. In this article, we associate a uniquely determined
positive integer with a valuation transcendental extension. This integer is
defined via a chosen minimal pair of definition, but it is later shown to be
independent of the choice. Further, we show that this integer encodes important
information regarding the implicit constant field of the extension (K(X)|K, v).
