The Half-Point Math: When Buying Off Key NFL Numbers Is Worth the Price
Every sportsbook will sell you a half-point. The question is whether the price they charge clears the mathematical bar.
In the NFL, buying a half-point off the key number 3 costs roughly 20 extra cents of juice. That turns a standard -110 bet into -130. To understand if that trade is worth making, you need two numbers: the break-even rate at each price, and the actual frequency of games landing on the number you're buying through. This article shows you both.
Why Key Numbers Exist
Football scoring is built around a rigid structure. A field goal scores exactly 3 points. A touchdown with an extra point scores exactly 7. Two-point conversions, safeties, and missed kicks create other scores, but the 3 and 7 dominate. The result is that NFL final margins cluster hard around a small set of numbers.
Hal Stern's foundational 1991 paper in The American Statistician (Vol. 45, No. 3) modeled the NFL margin of victory over the point spread as a normal distribution with mean zero and standard deviation of roughly 13.86 points. That model holds up, but it does not capture the spikes at the key numbers. The underlying score distribution is lumpy in ways the bell curve cannot describe.
A 2,560-game study of NFL betting lines (arXiv:1211.4000) confirmed the spread is an efficient probability estimate, yet the researchers also found that the raw frequency of specific margins means the practical value of a half-point is not uniform across the number line.
The data from Covers.com spanning 2000 through the 2025 season shows:
| Margin | Frequency | What drives it |
|---|---|---|
| 3 | ~15% | One field goal difference |
| 7 | ~9.1% | One TD + PAT difference |
| 6 | ~5.5% | Two field goals |
| 10 | ~5.3% | TD + PAT + field goal |
| 4 | ~5.2% | Field goal + safety or PAT |
| 14 | ~3.8% | Two TDs + two PATs |
Three and 7 alone account for roughly one in four NFL games. That concentration is what makes the pricing question real. BetMGM's NFL margins analysis found that these top six numbers together account for 42.5% of all results since 1922, and the pattern has held even after the 2015 extra-point rule change (which moved the PAT to the 15-yard line and slightly reduced the frequency of the number 7).
The Break-Even Formula
Before you buy any half-point, run this calculation.
Break-even rate at American odds
break-even % = (juice / (juice + 100)) × 100
Example at -110: 110 / (110 + 100) = 110 / 210 = 52.38%
At -120: 120 / 220 = 54.55%
At -125: 125 / 225 = 55.56%
At -130: 130 / 230 = 56.52%
At -135: 135 / 235 = 57.45%
Every 10 cents of juice you pay to buy a half-point raises your break-even rate by roughly 1-2 percentage points. The question is whether the value of the key number covers that gap.
Buying Off 3 in the NFL: The Only Case Worth Running
You have a line at -3.5 (-110). The book offers you -3 for -130. Should you pay the 20-cent premium?
The math works like this. At -3.5, any game that ends with your team winning by exactly 3 is a loss. You covered -3 but not -3.5. At -3, the same outcome is a push: you get your stake back. The gross value of buying that half-point is the probability of landing on exactly 3, which is roughly 15%.
But you only recapture that 15% as pushes, not wins. A push returns your stake but earns nothing. The precise comparison:
Buying -3.5 to -3: scenario math
Assume: 55% win rate at -3.5 (-110)
Games landing on exactly 3: ~15% → all losses at -3.5 → pushes at -3
At -3.5 (-110): EV per $110 bet
Win 55% → collect $100 = +$55.00
Lose 45% → lose $110 = -$49.50
Net EV: +$5.50 per $110 bet
At -3 (-130), converting ~7.5% of losses to pushes:
Win 55% → collect $100 × (100/130) = +$42.31 per $100 risked
Push 7.5% → break even
Lose 37.5% → lose $1 per unit
Break-even at -130: need 56.52%
Bottom line: at -130 the math is roughly neutral. At -135+, the book wins.
The standard charge at most major sportsbooks to move through the key number 3 is 20-25 cents. At 20 cents (-130), the bet is approximately break-even compared to taking -3.5 at -110. At 25 cents (-135), you're paying for a marginal improvement that doesn't cover the juice.
Buying Off 7: Slightly Better Math, Lower Price
Moving from -7.5 to -7 captures a smaller prize: the 9.1% of games that land on exactly 7. Sportsbooks typically charge 15 cents (not 20) for this move, because the underlying frequency is lower and the market knows it.
Buying -7.5 to -7: quick check
Extra break-even cost at -125 vs -110:
55.56% - 52.38% = 3.18 percentage points
Games landing on exactly 7: ~9.1%
Push recovery from -7.5 losses: ~4.5% of bets
(9.1% games × ~50% are -7.5 losses)
4.5% push value vs 3.18pp break-even cost: marginally positive
The 7 offers slightly better mathematical support for buying than the 3, because books typically price it more cheaply. Still marginal. If the price goes to -130 for buying off 7, skip it.
The Full NFL Key Number Buying Guide
| Move | Frequency | Max price to buy | Typical price | Verdict |
|---|---|---|---|---|
| -3.5 to -3 (or +3 to +3.5) | ~15% | -130 | -130 to -135 | Marginal |
| -7.5 to -7 (or +7 to +7.5) | ~9.1% | -125 | -120 to -125 | Sometimes yes |
| -10.5 to -10 | ~5.3% | -120 | -110 to -115 | Worth it at standard price |
| -14.5 to -14 | ~3.8% | -115 | -110 | Worth it at standard price |
| Any non-key number | <2% | Never pay extra | -120 (standard) | Decline |
The pattern is consistent: the more frequent the key number, the more the book charges, and the more the math compresses to near break-even. Lower-frequency key numbers (10, 14) are where buying works, because the book charges standard juice but you still get meaningful push value.
Why the NFL Is the Only Sport Where This Matters
Every sport with a spread has key numbers in theory. The NFL is the only one where the math makes buying worth a real conversation. Here is why the other sports are different.
NBA: No Dominant Key Number
NBA games end across a wide spread of margins. The 2023-24 season data shows one-possession games (1-3 points) at 13.9% of outcomes, but no single margin reaches the NFL's 15% concentration at 3. The 7-9 point band accounts for 17.9% as a group, spread across three numbers. No individual margin in the NBA reaches even 8%.
Because the distribution is flatter, there is no strong argument for paying extra juice to buy any specific half-point. Line shop instead.
NHL: Puck Line Is Fixed
The NHL puck line is always -1.5 at every major sportsbook, with the odds varying rather than the spread. About 24% of NHL games are decided by exactly 1 goal, and roughly 25-30% go to overtime or a shootout. A team winning in overtime by definition wins by 1, making the -1.5 a loss regardless.
That 24% frequency at the 1-goal margin is enormous, far larger than even the NFL's 3-point concentration. Buying from -1.5 to -1 would be very valuable. Most books do not offer it at movable prices. Where alternate puck lines exist (typically -0.5 at -200 or similar), the price already reflects the structural value and then some.
MLB: Run Line Is Fixed
The baseball run line sits at -1.5 with varying moneyline-style odds. Alternate run lines exist at most books, but moving from -1.5 to -1 requires taking a significantly worse moneyline price, and the math rarely works out. The run line is a separate bet structure, not a half-point buy.
The Real Alternative: Line Shopping
Before you pay any sportsbook to buy a half-point, check whether another book already offers the line you want at standard juice.
If DraftKings has -3.5 at -110 and FanDuel has -3 at -115, you do not need to buy anything. You open the FanDuel account and take the better number at five cents extra instead of twenty. The half-point is still there, and you saved 15 cents of juice.
Line shopping is free. Buying juice has a cost that starts at break-even and gets worse. The Sportsbookreview half-point calculator and odds comparison tools exist precisely for this reason. Before you buy, verify the number isn't already available elsewhere.
The general consensus from researchers who have studied decades of point-spread data is that buying points is not profitable on average. The exception is buying through key numbers at reasonable prices, and even then the margin is thin. The profitable play is having accounts at multiple books so you rarely need to buy at all.
When Buying Is Worth It: A Decision Framework
Use this three-question filter before you pay for any half-point.
- Is the target a key number? For the NFL: 3, 7, 10, 14. For all other sports: there is no equivalent. If the answer is no, decline.
- What is the price? Check the table above. If the book charges more than the max price listed, decline.
- Have you checked other books? If a competitor offers the better number at standard juice, take it there instead.
All three conditions have to point toward buying before the math supports paying the premium. In practice, most bettors will find that line shopping resolves the question before they reach step 3.
The 10 and 14: The Hidden Value
The NFL's 10 and 14 deserve more attention than they typically get. Because they are less famous than 3 and 7, books often price the half-point move at standard juice (-110 to -120). But 10 accounts for roughly 5.3% of game outcomes and 14 accounts for roughly 3.8%. Those frequencies easily clear the break-even bar at standard pricing.
If you see a line at -10.5 or -14.5 and your book offers a move to -10 or -14 at standard juice, that is close to a free improvement. The same math that makes buying off 3 risky at -135 makes buying off 10 or 14 at -120 sensible.
The reason most bettors miss this: they focus on the famous numbers. The forgotten middle of the key-number table is where the value actually sits.
Summary
Buy a half-point in the NFL only when three conditions hold: the number is a known key number, the price is within the threshold listed in the table above, and no other book offers the better number at standard juice. The NFL's 3 is the hardest case to justify given how aggressively books price it. The 7 is marginally better. The 10 and 14 are genuinely worth the standard move price. For every other sport, line shopping dominates buying in every realistic scenario.
Sources
- Stern, H.S. (1991). "On the Probability of Winning a Football Game." The American Statistician, 45(3), 179-183. https://www.tandfonline.com/doi/abs/10.1080/00031305.1991.10475798
- Wever, M. and Aadland, D. (2012). "The Performance of Betting Lines for Predicting the Outcome of NFL Games." arXiv:1211.4000. https://arxiv.org/abs/1211.4000
- Covers.com. "NFL Key Numbers for Point Spreads and Over/Unders." https://www.covers.com/nfl/key-numbers
- BetMGM. "Most Common NFL Margins of Victory." https://sports.betmgm.com/en/blog/nfl/most-common-margins-of-victory-nfl-betting-bm16/
- Action Network. "NFL Key Betting Numbers: How Margins Changed with Longer Extra Point." https://www.actionnetwork.com/nfl/nfl-key-betting-numbers-spread-margins-of-victory-line-value
- BettorEdge. "NFL Teaser Strategy: Why Crossing 3 and 7 Is the Whole Bet." https://www.bettoredge.com/post/nfl-teaser-strategy
- SBO.net. "NFL Wong Teasers — How Basic Strategy Teasers Work." https://www.sbo.net/strategy/wong-teasers/
- SportsBookReview. "Half Point Calculator." https://www.sportsbookreview.com/betting-calculators/half-point-calculator/
- Bleacher Nation. "Are NHL Puck Lines Always 1.5 on Online Sportsbooks?" https://www.bleachernation.com/betting/2026/05/31/are-nhl-puck-lines-always-1-5/
- NBAAnalytic.com. "How Often Is an NBA Game Actually Close? The 2023-24 Margin Distribution." https://nbaanalytic.com/articles/how-often-is-an-nba-game-actually-close.html