Sportsbooks refer to their profit as hold, and the anticipated profit margin on any given bet is known as theoretical hold. 

If the book is offering spread bets at -110 and anticipates getting even action on both sides of that line, then their theoretical hold can be calculated as follows:

• 50% of action wins (book wins) for $110 each
• 50% of action loses (bettor wins) for $100 each

Mathematically

• (.50)($110) + (.50)(-$100) =
• $55 + (-$50)
• $5

For every $110 in wagers accepted, the sportsbook can expect to earn $5. 4.55%  The theoretical hold for the sports book is just another name for their positive expectation, which, unremarkably, is the same as the house advantage.

Calculating Theoretical Hold for Moneyline Bets

How would you calculate theoretical hold for a moneyline?  It's a multi-step process that first required calculating the overround.  Overround is simply the sum of all of the zero-vig odds available for an event.  Zero-vig odds are the odds that the line would be offering if there was no Juice built in.  An example will probably help.  Take the following moneyline:

• -170 / +150

The sum of the two probabilities is the overround, in this case 62.96% + 40% = 102.96%

Calculating Theoretical Hold

A quick check shows that the sum of the implied odds = 100%.

calculating theoretical hold at this point is quite straight forward.

• theoretical hold = 1-(1/O)
• where O = Overround
• theoretical hold = 1-(1/102.96%)
• theoretical hold = 2.87%

The book can expect to make 2.87% of every bet made on this line.

Sportsbook Handle

Sportsbooks use the term handle to describe the total amount bet on an event.  If the handle for the betting line -170/+150 described above was $600,000, then the books theoretical hold on that event would be

• ($600,000)(2.87%) =
• $17,220

Not a bad way to make a living!