A paving system (10) includes a machine (11) having a frame (12) with a plurality of ground-engaging elements (16) coupled with the frame (12), and a height adjustable screed (22) coupled with the frame (12). The paving system (10) may also include a paving control system (40) having a receiver (42) configured to receive screed control data indicative of a position of the height adjustable screed (22) relative to a reference position. The paving control system (40) may further include a computer readable memory (48) storing a control algorithm, which may include a smoothness estimating algorithm and a screed adjusting algorithm. An electronic control unit (42) is coupled with the computer readable memory (48) and is configured via the control algorithm to determine a smoothness value for a region of a mat of material which corresponds with an irregular pattern of screed position, in response to screed control data received via the receiver (42).