The effectiveness of exploration robots is contingent upon their capability and efficiency to locomote on contorted and multifaceted terrains. Traditional wheeled robots do not suffice at overcoming such terrains and complications they introduce. The proposed work explores the performance of WhegRunner, a whegged (i.e., wheel-legged) robotic platform used to examine the mechanics of running on granular media at different saturation levels. In particular, the effect of bipedal/quadrupedal gait, saturation level, stride length, and stride frequency on robot's forward body velocity and cost of transport (COT) was studied. To increment nominal stride length, the robot was fitted with different number of spoked whegs from 3 to 7. In addition, eight evenly spaced motor speeds ranging from 2.33 to 7.43 Hz were used to observe the effect of stride frequency. Similar trends were observed between the two gaits, with the quadrupedal gait showing better overall performance. On dry sand, wider strides were attained at reduced motor speeds with lower spoked whegs. However, on wet sand (15% and 30% saturation), wider strides were achieved with higher motor speeds and lower spoked whegs. As a result, lower spoked whegs accomplished higher body forward velocity and lower COT as saturation increased. The acquired knowledge elucidates underexplored mechanics of locomotion on granular media at different saturation levels. The WhegRunner can be used as a platform to obtain a greater insight on how to develop more proficient exploration robots, ones which can face complex and deformable terrains and mediums.