This disclosure is directed to a catheter having an asymmetric basket-shaped electrode assembly at the distal end of the catheter body formed from a plurality of spines with electrodes. The plurality of spines are radially distributed across a first circumferential portion. One or more counter spines are radially distributed across a remaining second circumferential portion. Diagnostic electrodes are arrayed across the spines, while the counter spines may have one or more reference electrodes.