Every politician, even a legislator, can explain his votes especially on a party line.The contents of a bill is where the influence game is played. Heck if they are certain the bill will pass they can vote against it anyway.
How legislation is constructed matters far more. I haven't seen the type of focus on the influence that committee members have on bills and senators have on homestate appointments. A chairman can personally rewrite a bill and only send it to the floor when he is satisfied that it will be supported by the leadership. It is a tremendous position of power that isn't recognized.