Why does decreasing the distance between the electrodes in an electrolytic cell increase the rate of electroplating?

I did an experiment on the effect of the distance between the electrodes on the rate of electroplating in an electrolytic cell (copper electrodes with copper sulfate electrolyte).

As I expected, when the electrodes were closer, the current was greater and the rate of copper plating was also faster. But why does less distance increase the current? My initial thought was that less distance to travel=ions arriving at cathode quicker=greater current. That doesn't seem right though, because different ions are depositing and liberating electrons and hence not really flowing through (right?). I'm probably overthinking this, but any help is appreciated.