The Arctic has a very bad annual memory - min one year has no correlation with next year, max has no correlation with min etc. Decadal memory is presumably better, a minimum like 2012 would not have happened in 1992. And repeated sub-4m minimums are a result of the general, decadal, state of the ice.
In trying to understand (and predict) what happens in a particular melt year, we are up against a multitude of factors, big and small, and more or less random. The state of the ice at maximum is one such factor, and as oren explains above, a rather insignificant one in the longer run (so far). The points made by jdallen above are also very appropriate. It is very difficult to deny any causality, from a logical point of view, but it is swamped by other factors and thus has near-nil predictive value.
But things are changing and I agree with oren that the state of the Barents at max is likely quite significant, probably more significant than the actual maximum extent reached.
Just to remind us all of how fast things are changing - atmospheric rivers may have ben the direct cause of as much as one third of ice decline Barents, Kara and Central Arctic Seas of the last 50 years. This is a major and growing factor and mostly invisible to us. And the weaker the Barents, the stronger the effects.
See
Glen Koehler's post in the What's new in the Arctic" thread.