Hedge or Middle? The Math Behind Locking In a Sports Bet
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A hedge converts an open ticket into a fixed result by betting the other side, and it always costs you the sportsbook's margin on the second bet. A middle goes the other way: you accept a small, certain cost for a chance at winning both bets. Both are simple arithmetic once you set the equations up.
Key points
- A full hedge solves for a second stake that makes both outcomes pay the same; it equals (profit + original stake) divided by (1 + hedge payout per dollar).
- In the example below, a $100 ticket at +2000 hedged at -180 locks in $650 against an expected value of about $705, so the "insurance" costs about $55.
- A partial hedge keeps part of the upside and costs proportionally less.
- A middle at +3.5 and -2.5 at -110 each risks $10 on a miss and wins $200 if the final margin is exactly 3.
- Whether a hedge is "worth it" depends on the price you get, not on the feeling of relief.
Full hedge: the equation
Suppose you hold a preseason futures ticket: $100 on a team at +2000, which pays $2,000 profit. The team has now reached the final against an opponent. The market says the opponent is -180 and your team is +150. You bet H dollars on the opponent at -180, which wins H x 100/180 = 0.5556 H.
| Outcome | Futures ticket | Hedge bet | Net |
|---|---|---|---|
| Your team wins | +$2,000 | -H | 2,000 - H |
| Opponent wins | -$100 | +0.5556 H | -100 + 0.5556 H |
Set the two nets equal: 2,000 - H = -100 + 0.5556 H. That gives 2,100 = 1.5556 H, so H = $1,350. Check both sides: 2,000 - 1,350 = $650, and -100 + 1,350 x 0.5556 = -100 + 750 = $650. The result is the same in either case, a locked-in $650 profit.
What the lock-in costs
The posted prices include margin: 40.00% implied for +150 and 64.29% for -180, a total of 104.29%. Scale them to 100% and the fair chances are 38.36% and 61.64%. Then:
- Expected value of keeping the ticket: 0.3836 x $2,000 - 0.6164 x $100 = $767.12 - $61.64 = about $705.
- Locked-in value: $650.
- Cost of the insurance: about $55, which is 4.1% of the $1,350 hedge stake. That is the sportsbook's margin on the second bet.
So a hedge is not free. What you buy with that $55 is a removal of variance: instead of a 38% chance at $2,000 and a 62% chance of losing $100, you get $650 either way. That can be a good trade if $2,000 would change your month and $55 will not. It is a poor one if you do it on every ticket. Sizing decisions like this belong in a bankroll plan made before the bet.
Partial hedges
You do not have to hedge fully. Using the same ticket and the same -180 price:
| Hedge stake | If team wins | If opponent wins | Expected value | Cost vs. no hedge |
|---|---|---|---|---|
| $0 | +$2,000 | -$100 | $705.48 | $0 |
| $500 | +$1,500 | +$177.78 | $684.93 | $20.55 |
| $1,000 | +$1,000 | +$455.56 | $664.38 | $41.10 |
| $1,350 | +$650 | +$650 | $650.00 | $55.48 |
Verify the $500 row: if the opponent wins, $500 x 100/180 = $277.78, minus the $100 ticket = $177.78. If your team wins, $2,000 - $500 = $1,500. Each dollar hedged costs about 4.1 cents of expected value, so the cost scales in a straight line. The choice among rows is a choice about how much risk you want, not about which row has more value.
When a hedge means handing money to the book
- Your original ticket was a good price. Every dollar of hedge removes some of the edge you paid to get. Lock in only as much as the risk requires.
- The hedge market is expensive. Props and alternate lines can carry more margin than a main moneyline, so the same locked profit costs more.
- You hedge by feel. If you would not make the opposite bet fresh at that price, the hedge is a bet you are making because of an old ticket.
- You are hedging a small ticket. On a $10 ticket the locked dollars are tiny, and the time is not worth it.
Middle: the setup
A middle requires the line to move after you bet. You take Team B -2.5 at -110 early. Later the line moves to B -3.5, and you take Team A +3.5 at -110. Each ticket risks $110 to win $100.
| Final margin | B -2.5 | A +3.5 | Net |
|---|---|---|---|
| A wins, or B wins by 1 or 2 | -$110 | +$100 | -$10 |
| B wins by exactly 3 | +$100 | +$100 | +$200 |
| B wins by 4 or more | +$100 | -$110 | -$10 |
The window is the single number between 2.5 and 3.5. You pay $10 on every miss, which is the vig on the pair, and you win $200 on a hit. The break-even chance is 10 / 210 = 4.76%.
| Chance margin lands exactly on 3 | Expected value of the pair |
|---|---|
| 4.76% | $0.00 |
| 8% | +$6.80 |
| 10% | +$11.00 |
| 14.8% | +$21.08 |
The formula is 210 x p - 10. Three is the most common margin of victory in the NFL, and the figure often quoted from ESPN and Action Network data is about 14.8% of games, though sources date it differently. That share is for all games, so treat it only as a rough guide for a single matchup. A window sitting on a number that rarely occurs in basketball or hockey is worth much less than one on 3 or 7 in football.
Hedge or middle: how to choose
- If you want a fixed result on a ticket with a big payout, hedge, and price-shop the hedge.
- If the line has moved a full point or more through a key number, a middle can turn a losing position into a small cost with a large upside.
- If the line moved against you without opening a window, the opposite bet can lose both. Do not buy a second ticket only to feel active.
Hedging a parlay leg is the same equation with a larger payout; for how those tickets are built, see parlays and teasers.
FAQ
How do I calculate a hedge bet?
Set your two outcomes equal. For a ticket paying W profit with stake S, and a hedge at odds that pay r per dollar, solve W - H = -S + rH, so H = (W + S) / (1 + r).
Is hedging always a good idea?
No. It reduces risk and costs expected value equal to the margin on the hedge bet. It is a choice about risk, not a way to make extra money.
What is a middle in sports betting?
It is a pair of bets on opposite sides at different numbers, such as B -2.5 and A +3.5, so that one result can win both. If the margin falls outside the window you lose the vig on one side.
Does a middle need a line move?
Yes, or two books with different lines on the same game. Without a gap between the numbers, there is no window.
Can I hedge with a different sportsbook?
You can bet the opposite side anywhere you have an account, and doing so is often how you find a better price. Check the account rules and limits of each operator first.