Expected Value With Pushes: Spreads and Whole-Number Totals

The quick answer

Formula: EV per dollar staked = p(win) x (d - 1) - p(loss), where d is the decimal price. A push returns the stake, so it adds nothing to EV and takes nothing away.
Break-even: across all bets you need to win (1 - push chance) / d of the time. At -110 with a 10% push chance, that's 47.14%, against 52.38% when nothing can push.
Worked example: a -3 favorite at -110 that covers 48% of the time, pushes 10% and fails 42% is worth +1.64% per dollar. Count the push as a loss and the same bet looks like -8.36%.
Data: of 433 NFL games listed at a 3-point spread from 2015 to 2025, 44 finished exactly on 3 (10.2%). Games listed at a whole-number total finished on the number 1.9% of the time.
Half points: Novig files its NFL spread and total contracts at half points only, so they settle yes or no and EV goes back to two outcomes.

A whole-number spread or total can finish three ways: the bet wins, it loses, or the game lands on the number and the stake comes back. The usual EV formula has two terms, and on an NFL spread of 3 the missing third one covers about one game in 10.

The three-outcome formula

Call the chances of a win, a push and a loss p(win), p(push) and p(loss). They add to 100%. At decimal price d:

EV per dollar staked = p(win) x (d - 1) - p(loss)

A pushed bet gets back exactly what it put in, so its term is zero. The same EV can be written as:

EV = (1 - p(push)) x (c x d - 1)

Here c is the chance of winning once a push is ruled out, p(win) / (p(win) + p(loss)). This form shows that the break-even on decided bets stays at 1 / d, and that EV per dollar staked shrinks by the push share, since those bets earn nothing. The two-outcome version, with break-even rates for common prices, is in our explainer on positive EV betting.

How we checked

Push frequencies come from the nflverse games file (spread line, total line and final score for 3,028 games over the 2015 through 2025 seasons, playoffs included). EV figures come from the formula above, with each example's probabilities stated as assumptions. DraftKings' push rule comes from its published house rules and the half-point line formats from the NFL terms filed by Ludlow Exchange and from Kalshi's open NFL markets, all checked 12 October 2026.

How push chance changes the break-even rate

At -110 (decimal 1.9091), the win rate you need across all bets is (1 - p(push)) / 1.9091:

Push chance	Break-even, all bets	Break-even, decided bets only
0%	52.38%	52.38%
2%	51.33%	52.38%
5%	49.76%	52.38%
10%	47.14%	52.38%

Match the column to the way your probability was measured. Compare a 48% cover rate on a -3 favorite with 52.38% and you'll pass on a bet that can be +EV. A 53% measured on decided games only, held against 47.14%, makes a thin edge look wide.

Worked example: an NFL favorite at -3

Three is the most common NFL margin. In the nflverse file, 449 of 3,028 games (14.8%) were decided by exactly 3 and 263 (8.7%) by 7, the next most common. Of the 433 games listed with a 3-point spread, 44 landed on it, a push rate of 10.2%. At 7 it was 11 of 172, or 6.4%.

Say your read on a -3 favorite is 48% to win by 4 or more, 10% to win by exactly 3 and 42% for everything else. At -110:

EV = 0.48 x 0.9091 - 0.42 = +0.0164, or +1.64% per dollar staked

On decided games that's a 53.33% cover rate, above the 52.38% break-even. Treating the push as a loss gives 0.48 x 1.9091 - 1 = -8.36%, and the bet gets thrown out.

The same read priced on three lines (the prices are assumptions for the example; no book quoted them):

Line	Price	Win	Push	Loss	EV per dollar staked
-2.5	-135	58%	0%	42%	+0.96%
-3	-110	48%	10%	42%	+1.64%
-3.5	+105	48%	0%	52%	-1.60%

With these probabilities the fair prices are -138 for -2.5, -114 for -3 and +108 for -3.5. Buying the half point from -3 to -2.5 is worth about 24 cents of American price here, so -135 still pays more than the fair price, and it returns +0.96% against +1.64% for -3 at -110. Moving to -3.5 throws away the 10% push slot and needs +108 just to break even.

Worked example: a whole-number total

Totals land on the number far less often than spreads, because no single total works like 3. Across the 1,456 games listed at a whole-number total, 28 finished exactly on it (1.9%). At 44, the most common whole-number total in the file, it was four of 145 games (2.8%).

Say you put the Over 44 at 51.5% to go over, 3% to land on 44 and 45.5% to stay under. At -110:

EV = 0.515 x 0.9091 - 0.455 = +0.0132, or +1.32% per dollar staked

The break-even across all bets is 0.97 / 1.9091 = 50.81%.

A half-point line hands the push slot to one side. Over 44.5 wins only on 45 or more (51.5% here), while Over 43.5 also wins on exactly 44 (54.5%). On a prediction market, say Over 44.5 is quoted at 50 cents and Over 43.5 at 53 cents, with no fee. EV is the win chance divided by the price, minus 1: 0.515 / 0.50 - 1 = +3.00% and 0.545 / 0.53 - 1 = +2.83%. Those prices aren't quotes either. With a 3% push slot, the 44 line at -110 and both half-point lines at those prices finish within two percentage points of each other.

Half-point vs whole-number pricing

What a half point is worth depends on how often games finish on the number it moves you off. Moving from -3 to -2.5 turns a slot near 10% into wins, while moving a total from 44 to 43.5 converts one near 3%. By that arithmetic a half point off 3 or 7 should cost more than a half point off 44, and a book that charges the same for both has one of them wrong.

How prediction markets handle the push

DraftKings' house rules settle a whole-number spread that lands exactly as a push, with the stake returned, and use a 3-point spread ending 13 to 10 as the example.

Prediction markets usually list NFL lines at half points, so a push can't happen. Novig's spread and total terms, filed by Ludlow Exchange, set every line at a half point, and the filing notes that the margin can never equal it, so every contract resolves yes or no. On 12 October all 357 of Kalshi's open NFL spread markets and all 266 of its open NFL total markets were listed at half points. The rules on how each platform settles ties, voids and postponements are compared in our settlement guide.

With two outcomes, EV on a contract is your win chance divided by the price, minus 1, after fees. On Novig a pre-game straight trade carries no fee for either side. Other trades charge takers coefficient x price x (1 - price) per contract: 0.03 on most live straights, 0.06 on live NCAAF, NHL and MLB and on futures (golf and tennis futures excepted), and 0.10 on parlays, built into the quoted price. Makers pay nothing. At 50 cents the 0.03 fee is $0.0075 per contract, which takes the Over 44.5 example from +3.00% to +1.48%.

What to look for

Line: whole number or half point, and how often games finish on that number.
Probability: know whether your win rate counts pushes or leaves them out.
Break-even: use (1 - push chance) / d across all bets, or 1 / d on decided bets.
Hook price: set what a half point costs against the push share it removes.
Costs: subtract the vig or the fee for the exact trade type before calling anything +EV.

Expected value with pushes FAQ

How do you calculate EV when a bet can push?

Multiply the win chance by the profit per dollar, d - 1, and subtract the loss chance. The push adds zero. A -3 favorite at -110 with a 48% / 10% / 42% split is worth +1.64%.

Does a push count as a loss in EV?

No. A push returns the stake. Counting it as a loss turns that same +1.64% bet into -8.36%.

What win rate do you need at -110 on -3?

52.38% of decided bets. If 10% of bets push, that's 47.14% of all bets.

Can a bet push on a prediction market?

Not on a half-point line. Novig sets its NFL spreads and totals at half points in its filed terms, so each contract settles yes or no, and Kalshi's open NFL spreads and totals were all at half points on 12 October.