Originally <a href='http://www.sportsbookreview.com/forum/showthread.php?p=22956051'>posted</a> on 11/09/2014:

Proof why hedging is -EV, and not middling is -EV

You can do any of the following options. For the sake of easy math, we are going to say Philly wins the game 75% of the time (3 out of 4). Of those Philly wins, we are saying Philly will win by 7 or less 50% of the time (1 out of 2). (3/4) * (1/2) = (3/8) or 37.5% of the time Philly wins by 7 or less points (so we win both our bets and MIDDLE IT!!).

Philly wins the game 75% of the time (3/4)
Carolina wins the game 25% of the time (1/4)
Philly wins the game by 7 or less 37.5% of the time (3/8)
Philly wins the game by 8 or more 37.5% of the time (3/8)

1. Do nothing. 3/4 of the time Philly wins and we are ahead (+$1100). 1/4 of the time Carolina wins and we are down (-$100).

If Philly wins (75% of the time): (3/4) * $1100 = ($825.00)
If Carolina wins (25% of the time): (1/4) * (-$100) = (-$25.00)

Add the two totals, and our expected value here is (+$800.00)

2. Hedge "x" amount on Carolina ML (+250). We will hedge for equal profit no matter which team wins. That amount would be $350 ($350 to win $875). We will profit $775 if Carolina wins ($875 of the hedge bet minus the $100 parlay). We will profit $750 if Philly wins. Our expected value is calculated as following based on us capping the game as 3/4 Philly wins and 1/4 Carolina wins:

If Carolina wins (25% of the time) : (1/4) * $775 = ($193.75)
If Philly wins (75% of the time) : (3/4) * $750 = ($562.50).

Add the two totals, and our expected value here is (+$756.25)

3. Attempt a middle by betting Carolina +7.5 (-135). We will attempt to middle for equal profit if we only win one of the bets. That amount would be $675 ($675 to win $500). We profit $400 if Carolina wins the game outright ($500 minus $100 parlay). We profit $425 if Philly wins the game by 8 or more ($1100 minus $675). We profit $1600 if Philly wins the game by 7 pts or less.

EV calculation:
If Carolina wins (25% of the time): ($400) * (1/4) = (+$100.00)
If Philly wins by 8 or more (37.5% of the time) = ($425) * (3/8) = (+$159.38)
If Philly wins by 7 or less (37.5% of the time) = ($1600) * (3/8) = (+$600.00)

Add the 3 totals, and our expected value is (+$859.38)

Obviously adjusting your handicap of the percantages of the time each teams wins and by how much will effect your expected values. So that plays into deciding whether or not to middle as well.

If you truly handicap the game the way I do, then middling is more +EV than leaving it alone. And obviously hedging is always -EV.