Theoretical Hold vs Reported Hold: Reading a State Sportsbook Revenue Report

Sportsbook hold percentage means two different things. Theoretical hold is the margin built into a price, about 4.5 percent on a -110/-110 line. Reported hold is what a state revenue report shows: the book's revenue for the month divided by the amount wagered. The second number moves with results, parlays, promotions and timing, so it can sit far above or below the first in any given month.

Theoretical hold: the margin inside a price

Start with the price, not the report. Each American price converts to an implied probability:

• Negative price -X: X / (X + 100).
• Positive price +Y: 100 / (Y + 100).

On a fair two-way market the two implied probabilities would add to exactly 1. On a real market they add to more than 1, and that excess is the overround. The theoretical hold, meaning the share of total money wagered that the book keeps if it takes bets on each side in proportion to the prices, is:

Theoretical hold = 1 − 1 / (implied probability A + implied probability B)

The -110/-110 case shows it in dollars. A book takes $110 on each side, $220 in total. Whichever side wins collects $210 (its $110 back plus $100). The book keeps $10. Ten divided by 220 is 4.545 percent, and the formula gives the same number: each side implies 110 / 210 = 0.5238, the sum is 1.0476, and 1 − 1 / 1.0476 = 0.04545.

The worked table runs the same steps for several common price pairs.

Three things to take from the table:

1. The hold depends on both sides of the market together. A single price, on its own, does not have a hold.
2. Shading one side (-115 / -105) barely changes the hold compared with -110 / -110. The book is moving the line, not raising its cut.
3. Theoretical hold is a property of the price, before any game is played. It says what the book earns per dollar of handle if action is balanced and the book is priced correctly. It says nothing about any particular month.

Parlays have their own theoretical hold, and it is higher than a single bet's because the margin compounds across legs. A two-leg parlay at -110 per leg pays about 2.64 to 1 (1.9091 × 1.9091 = 3.645 in decimal odds), while the fair payout on two independent 50 percent legs is 3 to 1 (decimal 4.0). The book's expected take on that ticket is 1 − 3.645 / 4.0 = 8.9 percent of the stake, roughly double the single-bet figure.

Reported hold: what the state report actually measures

A state monthly report does not show prices. It shows money. The Pennsylvania Gaming Control Board's FY 2025/2026 Monthly Sports Wagering Report Summary is a useful example because it puts each step on its own line, for each operator and as a statewide grand total:

• Handle: the total amount wagered.
• Revenue: what the operators kept from wagers after paying winners.
• Promotional Credits: the value of promotional play the operators deducted.
• Gross Revenue (Taxable): revenue minus promotional credits, the figure the state taxes.
• State Tax Due (34%) and Local Share Assessment (2%): the taxes calculated on the taxable figure.

Reported hold is a division done by the reader: revenue ÷ handle. The report's statewide grand total gives three examples worth working through.

The same report gives two different "hold" figures depending on which revenue line is used. In September 2025, Pennsylvania operators deducted $42,043,916 in promotional credits, which cut the taxable figure to well under half of revenue. A headline built on the taxable line would report a 3.5 percent hold for that month; one built on the revenue line would report 8.4 percent. Both are correct arithmetic. They answer different questions.

New Jersey publishes the comparable figure differently. The New Jersey Division of Gaming Enforcement's September 2025 gaming revenue release reports Sports Wagering Gross Revenue of $89.8 million for the month, split into Online Sports Wagering of $89,830,908 and Retail Sports Wagering of negative $13,173. Handle is not in the release; it sits in the monthly sports wagering tax returns the release points to. To compute a New Jersey hold, the handle has to come from those returns, and the reader has to check how New Jersey treats promotional play before comparing it with a Pennsylvania figure.

Why reported hold drifts away from the theoretical figure

Every month's reported hold is the theoretical margin plus or minus several effects that the price formula ignores.

Results. Theoretical hold assumes balanced action or correct prices. Books rarely have perfectly balanced liability on every game. When popular sides win, books pay out more and reported hold falls; when they lose, it rises. The New Jersey September 2025 retail line shows the extreme case: for the month as a whole, the state's retail sportsbooks combined reported negative gross revenue.

Product mix. Handle in a report is all bet types together. Straight bets near -110 carry a theoretical margin around 4.5 percent; parlays carry more, as the parlay arithmetic above shows. A month in which more of the handle goes into parlays will show a higher reported hold even if every individual line was priced the same as the month before.

Timing. A futures bet or a long-dated wager is placed in one month and settled in another. Depending on how the state's reporting rules book handle and revenue, a month's figures can mix money from wagers taken earlier with handle from wagers that have not settled yet. That shifts reported hold up or down in a way that has nothing to do with the prices offered that month.

Promotions. States differ in whether and how far promotional credits may be deducted before the taxable figure. Pennsylvania's report shows the deduction on its own line, which is why the gap between its two hold calculations can be large in a month with heavy promotion. A hold figure taken from a taxable revenue line in one state is not directly comparable with a hold figure taken from a gross line in another.

Channel and operator mix. Online and retail books, and different operators within a state, report separately. A statewide figure is a weighted average of all of them, so a shift in where the money goes changes the statewide hold.

Over a long period, the effects that depend on luck tend to wash out and the remaining gap reflects mix and promotions. That is why Pennsylvania's fiscal-year revenue-over-handle figure of 10.92 percent is a more stable number than any single month, It is still more than twice the 4.55 percent on a single -110 line. The report does not break handle down by bet type, so it cannot say how much of that gap comes from parlays and other higher-margin products, but the arithmetic above shows why such products push the figure up.

A routine for reading the next hold headline

1. Find the report. Identify the regulator, the month and the report name. A hold figure without those three is not checkable.
2. Write down handle and the revenue line used. Note whether the revenue figure is before or after promotional deductions, and whether it covers online, retail or both.
3. Do the division. Revenue ÷ handle. If the headline's number does not match, it was built on a different line.
4. Compare like with like. Compare a state's hold with the same state's earlier months on the same line, not with another state that defines revenue differently.
5. Keep theoretical hold separate. The 4.55 percent on a -110/-110 line describes one price. A monthly report describes a mix of prices, products, promotions and results, and it should be read as that.

The Pennsylvania figures quoted here come from the Pennsylvania Gaming Control Board FY 2025/2026 Monthly Sports Wagering Report Summary, and the New Jersey figures from the New Jersey Division of Gaming Enforcement September 2025 revenue release.