Sportsbooks don't set the line to split the action. There is a great book called "The Odds" by Thad Millman who spent a football season with the lines makers at the Stardust in Vegas and describes how lines are set and why they move.
As detailed in the book, its common for an inordinate amount of public money to be on one side of the game, without a line move or a move in the opposite direction. If the theory was true that Vegas just wants 50/50 split of the money on a game then the line would move to attract money on the side opposite where the bets are being made, but that often doesn't happen. There are number of examples of that this week. (BTW, a successful handicapping technique is to simply look at the lines moves against where the money is, and to bet the opposite side of those games).
Taking one example for this Saturday: Duke hosts UVA this week, the opening line is Duke -4 (which is a key number because so many games fall in the 3 to 4 point range). 65% of the action on the game is on Duke; yet the line has dropped to Duke -3.5. Why? Because even though a majority of the money is on Duke, the sharps (professional bettors like Billy Walters) like UVA. So, the Sportsbooks are willing to take a position on the game and attract even more money on Duke because experience tells them that the sharps side covers more often than the public side, and the Sports books can make even more money if 65% of the action is on the losing side as opposed to 50%. Another example of that was the WF at Duke game a couple of weeks ago. The public was all over Duke (as was many on this board) yet the line dropped because the smart money was on WF. WF covered and the books made killing.
Those that run the Sportsbooks are gamblers too; they will take positions on games; it further helps them that the vig is on their side. The concept that Sportsbooks look to split the action is wrong. Sportsbooks are in the business to maximize the money that they make, and to do that they will gladly take more than 50% of the action on what the bookie considers the wrong side.
Laughable... Millman's work has been quoted as everything from lightly studied to outright laughable.
Guys like Millman don't want you to know that houses goal is to make money by getting no more than 52.6% of money on one side.