I think people in this thread are underestimating the degree to which Senate races are independent of Presidential ones. They're correlated, sure, but not excessively. Remember the coattails in 1972 and 1984? Thought not.
Those were in the days where ticket splitting was far more prominent.
Ok, how about 1996? And is there really much of a decline in ticket-splitting outside the South? Looking at say, the 2008 Senate races, even when a state's Senate vote was for the same party as the President there was often a gap of over 5 points. And ticket splitters don't unanimously break one way - even when Biden was simultaneously running for President and Senator, a decent number of voters split their tickets both ways.