A splitter should not degrade the quality of the signal, but it will, as Ratman pointed out, decrease the power level of the signal by 3-4 dB, a bit more than half (-3 dB).
Digital reception requires a balancing act between acceptable signal quality within a range of minimum and maximum power levels. As long as the power level is adequate and enough fade margin is maintained, installing splitters or extra cabling will not affect reception right up to the point where the reception falls off a "cliff".
Ratman's simple suggestion is a great one.
Tech support for Antennas Direct