An impact damping mat comprises a plurality of layers arranged in a stacked formation. The stacked formation has a total thickness of no greater than 4 and 7/16 inches. The plurality of layers cooperate to provide the impact damping mat with at least one of a coefficient of restitution no greater than 30% and a selected sound reduction characteristic. The selected sound reduction characteristic can be a reduction of a maximum sound level of at least 5 dB from 40 to 63 Hz 1/3 octave bands and at least 13 dB at and above 80 Hz 1/3 octave bands normalized to a conventional ⅜ inch rollout rubber flooring product.