The frequency and distribution of wet events on Mars is a key constraint on its climate and hydrology evolution. Mars’ surface records surface liquid water availability since the intense fluvial activity of the valley network forming period is recorded by features such as low-latitude alluvial fans and small, mid-latitude craters with outlet valleys, or “pollywogs”. Pollywogs are craters between 0.5 and 15 km in diameter with a single outlet channel cutting an otherwise fresh crater rim, indicating that these craters were previously filled with water. The two possible sources for this water are precipitation/snowmelt and groundwater discharge. We constructed Digital Elevation Models (DEMs) of 18 pollywog craters (21 outlet valleys) and used these to measure crater and outlet valley geometry. These measurements were used as inputs into a 0-D model that couples lake drainage and breach erosion by combining conservation of mass, Manning’s Law for water discharge in a channel, and the Meyer-Peter Mueller relation for transport-limited erosion. Using this approach, we constrain the expected erosion for a single pollywog overspilling event. We compare this to the observed erosion to give constraints on the number, duration, and intensity of wet events in the Martian mid-latitudes in the Hesperian/Amazonian. The results of our 0-D model of breach erosion indicate that the majority of pollywog crater outlet valleys are consistent with formation in a single crater overspill event. However, no existing climate models for Hesperian Mars or impact induced climates are able to provide sufficiently high precipitation or snowmelt rates to fill and overspill a pollywog crater in a single event. Our model also predicts that at least 2 of 21 outlet valleys studied should have undergone runaway erosion (i.e. erosion to the base of the crater rim). This is not observed in our DEM data, which suggests that erosion may either have been halted by a change in crater rim properties, or that the crater may have been predominantly ice-filled at the time of draining, limiting the liquid water available for erosion. Our results favor either pollywog overspill during a single groundwater discharge event, or repeated climate-driven meltwater overspill from ice-filled craters.