We study dynamic matching in a spatial setting . Riders arrive in some (possibly adversarial) order at random points . Unmatched riders incur a waiting cost $c$ per period . The cost of matching a driver to a rider is equal to the distance between them . We quantify the value of slightlyincreasing supply . Our results shedlight on the important role of (small) excess supply in spatial matching markets . We prove that when there are $(1+\epsilon)$ drivers per rider (for any $\epsilons > 0$), the cost of . matching returned by a simplegreedy algorithm which pairs each arriving rider to the closest availabledriver is $O(\log^3(n)$, where $n$ is the number of riders. On the other hand, even the