Vig, Overround and Hold: Three Ways to Measure One Sportsbook Margin, and Why State Reports Differ
A standard −110/−110 line has an overround of 4.76%, but a sportsbook that takes equal money on both sides keeps 4.55% of what was bet, not 4.76%. Both numbers describe the same margin measured against different bases. State revenue reports then publish a third figure, actual hold, which can land far from either in any given month. This piece separates the three.
Concept: one margin, three bases
Overround is the amount by which a market's implied probabilities exceed 100%. It is measured against probability.
Theoretical hold is the share of total money wagered that the book expects to keep if the line is priced as posted. It is measured against handle, the total amount bet.
Actual hold, the figure in state revenue reports, is what the book kept after results were settled, divided by handle. It is measured against what actually happened.
The first two are fixed by the price. The third depends on outcomes and on which bets customers chose.
Formula
For each side, implied probability from American odds:
- Negative odds −X: X ÷ (X + 100)
- Positive odds +Y: 100 ÷ (Y + 100)
Overround = (sum of implied probabilities) minus 1
Theoretical hold on a two way market = 1 minus 1 ÷ (sum of implied probabilities)
Actual hold = (handle minus payouts to winners, stakes included) ÷ handle
Worked example 1: a balanced book at −110/−110
Each side: 110 ÷ 210 = 52.38%. Sum: 104.76%. Overround: 4.76%.
Theoretical hold: 1 minus 1 ÷ 1.0476 = 4.55%.
Check it with money. The book takes $110,000 on each side, $220,000 of handle. Whichever side wins, it returns $110,000 in stakes plus $100,000 in winnings, $210,000 in total. It keeps $10,000. That is 10,000 ÷ 220,000 = 4.55% of handle. The 4.76% figure is the same margin expressed per unit of probability rather than per dollar bet.
Worked example 2: the same line, lopsided money
Same price, same $220,000 handle, but 70% of the money, $154,000, is on side A and $66,000 is on side B.
| Result | Paid out (stakes plus winnings) | Book result | Actual hold |
|---|---|---|---|
| Side A wins | $154,000 + $140,000 = $294,000 | Loses $74,000 | −33.6% |
| Side B wins | $66,000 + $60,000 = $126,000 | Keeps $94,000 | 42.7% |
If each side is truly a 50% proposition, the expected book result is the average of +$94,000 and −$74,000, which is +$10,000. That is 4.55% of handle again. The expected hold is unchanged by lopsided money; only the variance changes. On any single event, the book's actual hold can swing from heavily negative to far above the theoretical figure.
Conversion table: price, overround and theoretical hold
| Two way price | Decimal | Fractional | Overround | Theoretical hold |
|---|---|---|---|---|
| −105 / −105 | 1.952 / 1.952 | 20/21 / 20/21 | 2.44% | 2.38% |
| −110 / −110 | 1.909 / 1.909 | 10/11 / 10/11 | 4.76% | 4.55% |
| −115 / −115 | 1.870 / 1.870 | 20/23 / 20/23 | 6.98% | 6.52% |
| −120 / +100 | 1.833 / 2.000 | 5/6 / 1/1 | 4.55% | 4.35% |
Decimal odds from American: 1 + 100 ÷ X for −X, and 1 + Y ÷ 100 for +Y.
Worked example 3: why parlays raise the reported number
A three leg parlay, each leg at −110, pays at decimal 1.9091 × 1.9091 × 1.9091 = 6.958. If each leg is a true 50% proposition, the fair decimal price is 2 × 2 × 2 = 8.000.
Theoretical hold: 1 minus 6.958 ÷ 8.000 = 13.03%.
The single leg holds 4.55%; the parlay holds 13.03%. A month in which customers place more parlays will tend to show a higher actual hold in a state report even if no individual price changed. Product mix moves the reported number as much as pricing does.
Common error: comparing a state's monthly hold with a line's vig
A reader sees a state report showing a double digit hold for a month and concludes the books' lines carry double digit margins. That comparison mixes bases. The monthly figure blends straight bets and parlays, reflects which side the money was on, and captures how events actually finished. A single month can also run below the theoretical figure, or negative on a heavily backed result. Treat the monthly number as an outcome, and the priced margin as the structure.
A second error is subtracting overround from 100% and calling the result the payout rate. On −110/−110, the book returns 95.45% of handle in expectation, not 95.24%.
State availability and reporting note
Legal sports betting is set state by state, and some states permit none. Where it is legal, the state gaming or lottery regulator licenses operators and, in many states, publishes monthly handle and revenue. How "revenue" is defined, including whether promotional credits are deducted, varies between states, so read the notes on a report before comparing one state with another. The minimum age for legal sports betting is 21 in most states, with a few setting it at 18; check your state regulator.
What the math does not tell you
Overround and theoretical hold describe the price. Actual hold describes what happened last month. None of the three predicts an outcome, identifies a mispriced line, or says anything about which side of any market to take. Over enough bets at these prices, the bettor's side of the ledger is the negative of the hold.
Responsible Gambling
Bet only with licensed operators in a state where sports betting is legal, and only if you meet your state's minimum age. The specific trap in this topic is the parlay: its bigger quoted payout comes with roughly three times the margin of a single leg at −110. If betting stops being affordable or enjoyable, 1-800-GAMBLER offers free, confidential support around the clock.