Thanks for all the comments. It seems to me that we have two kinds of edge: the methodical edge and the executioner edge.
The former is based on the relationship between entries, exits, stops, position size, etc where over an infinite number of trades, the net result is that the trader returns a little bit extra over break even on average for each trade . The edge is, essentially, a statistical one where if you were to look at the past trading history of the traders method the calculation:
[(W x AW) - C] / |[(L x AL) - C]| > 1
Where:
W - number of winners
AW - average winner amount
C - trade cost
L - number of losers
AL - average loser amount
In short, the method has a positive expectaion in the long run.
The latter, executioner edge, is based on the trader's ability to execute their method flawlessly and under emotional discipline, such that each trade is entered and exited at the optimal point based on the methodical edge.
Personally, I would be inclined to say that an 'Edge' literally means a 'positive expectation in the long run'.