Half-Point Calculator

The "Hook" Mechanism: Converting Losses into Pushes

The hook is the half-point (0.5) attached to NFL spreads. When you see Patriots -3.5 or Cowboys +7.5, that decimal prevents ties. The bet must have a winner and a loser. No refunds.

Buying the hook means paying the sportsbook to shift the line by half a point in your favor. The transaction converts a potential loss into a push. If you bet Patriots -3.5 and they win by exactly 3, you lose $110. If you buy the hook to move the line to Patriots -3 at worse odds (-130 instead of -110), that same 3-point Patriots win becomes a push—you get your $130 back instead of losing it.

The mechanic is simple: you're buying insurance against one specific outcome (the game landing on the exact number). The sportsbook charges this insurance through worse odds. Your question: is the insurance premium worth the coverage?

Rarely do sportsbooks allow you to buy a push into a win. The standard transaction is loss-to-push conversion. You're eliminating one losing outcome from your probability distribution, but paying vigorish tax to do it.

The Math of "The Tax" (Vigorish Efficiency Analysis)

American odds convert to implied probabilities that represent your break-even win rate. At -110, you risk $110 to win $100. The calculation: 110 / (110 + 100) = 52.38%. Win 52.38% of your bets at -110 and you break even over the long run. Win less and you lose money. Win more and you profit.

Moving from -110 to -130 changes the equation. At -130, you risk $130 to win $100. The calculation: 130 / (130 + 100) = 56.52%. Your required win rate jumped from 52.38% to 56.52%—a 4.14 percentage point increase. That gap is the vigorish tax you're paying to buy the hook.

The raw cost difference is $20 per $100 won. At -110, you risk $110. At -130, you risk $130. But the percentage cost is non-linear. Moving from -110 to -120 increases your break-even rate by 1.93 points (from 52.38% to 54.31%). Moving from -120 to -130 increases it by 2.21 points (from 54.31% to 56.52%). Same 10-point juice shift, different percentage impact.

This is vigorish efficiency: each additional point of juice extracts a larger percentage of your edge. The cost accelerates as the juice increases. At -140, you need 58.33% to break even. At -150, you need 60.00%. At -160, you need 61.54%. The required win rate climbs faster than the odds number suggests.

The Golden Rule of Point Buying

If the number you are buying doesn't land at least as often as the percentage cost you're paying, you are burning money. At -110 to -130 (4.14% cost), the number must land more than 4.14% of the time to justify the purchase. Actually, you need the number to land at a rate higher than (New Prob - Old Prob) / New Prob to account for the full probability shift. For -110 to -130, that's (56.52 - 52.38) / 56.52 = 7.33%.

The 3 lands 15.1% of the time in NFL games. The required rate is 7.33%. The 3 passes the test with a 106% surplus. The 5 lands 4.0% of the time. The required rate is 7.33%. The 5 fails the test with a 45% deficit. Every time you buy the 5 at -130, you're systematically losing 3.33 percentage points of expected value.

Vigorish at Different Price Points

The same logic applies across all price shifts. Moving from -105 to -115 costs you 1.89 percentage points (from 51.22% to 53.49%). The required push rate is 3.56%. Moving from -125 to -135 costs you 2.14 points (from 55.56% to 57.45%). The required push rate is 3.29%.

Books rarely offer uniform pricing. The 3 might cost -135 while the 5 costs -130. This is price discrimination based on statistical value. The book extracts maximum value from informed bettors who know the 3 matters while still profiting from uninformed bettors willing to buy any number.

The Hierarchy of Key Numbers: NFL Margin Data

Football scoring is discrete, not continuous. Points come in specific increments: 1 (missed PAT or made 2PT differential), 2 (safety), 3 (field goal), 6 (touchdown without PAT), 7 (touchdown with PAT), 8 (touchdown with 2PT conversion). This structure creates clustering around certain final margins.

The 3: Field Goal Dominance

The 3-point margin appears in 15.1% of NFL games—more than any other margin by a factor of 1.7x. The reason: field goals are the most common scoring play that doesn't require crossing the goal line. Teams settle for field goals in the red zone. Teams kick field goals to take or extend leads late in games. Teams win by field goals in overtime. All of these scenarios create 3-point final margins.

Specific game scripts that produce the 3: Team A leads by 10, Team B scores a touchdown to cut it to 3 with no time left. Team A leads by 6, Team B kicks a field goal to make it 3 late. Team A and Team B trade scores all game, Team A kicks a game-winning field goal with seconds remaining. The field goal (3 points) is the bridge between touchdown-based scoring and zero—it's the most accessible way to change the scoreline without needing to traverse 70+ yards or execute red zone offense.

Buying from -3.5 to -3 converts 15.1% of your losses into pushes. At -130 pricing, you need 7.33% to break even. You're getting more than double the required frequency. The surplus is 7.77 percentage points—a massive edge that persists even as the price climbs to -140 or -145.

The 7: Touchdown Dependency

The 7-point margin occurs in 9.1% of games. This is the touchdown plus PAT differential—one team scores exactly one more touchdown with successful PAT than the other. The 7 appears frequently because touchdowns are the primary method of scoring, and the vast majority of teams kick the PAT (99%+ success rate) rather than attempting 2PT conversions.

Game scripts: Team A leads 28-21, Team B fails to score again. Team A and Team B both score multiple touchdowns, but Team A has one extra. Team A shuts out Team B after Team B's opening touchdown drive. The 7 is common enough to justify buying at -125 or -130, but the edge is thinner than the 3. At -135, you need 7.95% and you're getting 9.1%—only a 1.15 point surplus. At -140, you need 10.2%, and now the 7 (9.1%) doesn't clear the threshold.

The 10: Combination Margin

The 10-point margin (5.5%) represents a touchdown plus field goal differential. It's the third-most common key number, but far behind the 3 and 7. Buying the 10 at standard -130 pricing requires a 7.33% push rate. You're getting 5.5%. The deficit is 1.83 points—you're paying for protection that doesn't arrive often enough. Avoid buying the 10 unless you find pricing at -120 or better, which almost never appears.

The "Sucker Bet" Scenarios: Why Dead Numbers Destroy Bankrolls

Dead numbers are margins that occur less than 5% of the time. The most dangerous dead numbers for bettors: 5, 8, and 9. These numbers "feel" close to key numbers (5 is near 3 and 7, 8 is one point from 7, 9 is two points from 7), but the math reveals they're traps.

The pattern across all dead numbers: the required push rate (7.33% at -130) exceeds the actual frequency by 30-70%. You're paying for insurance that doesn't protect you often enough to justify the premium. Over 100 bets, you're losing 3-4 units of expected value compared to taking the original line. Over 1,000 bets, that's 30-40 units gone.

Spread Betting vs. Totals Betting: Why Hooks Matter Less on Totals

Buying a half-point on a total (over/under) is rarely justified. The math shows why: in a total bet, one point represents a much smaller percentage of the outcome than in a spread bet.

Consider a game with a total of 45 points. Buying from Over 44.5 to Over 44 costs the same vigorish as buying a spread from -3.5 to -3 (typically -110 to -130). But the value proposition differs. In a 45-point game, 1 point equals 2.2% of the total score. In a 3-point spread, 1 point equals 33% of the margin.

The dilution effect: totals have wider variance and less clustering around specific numbers. NFL game totals from 2010-2023 show a nearly uniform distribution from 35 to 55 points. No single total appears more than 4% of the time. Compare that to spreads, where the 3 appears in 15.1% of games. The clustering is what creates buying value—without clustering, you're just paying extra juice for no statistical advantage.

Over/Under 47 and Over/Under 47.5 behave differently than -3 and -3.5. The total can land on 47 by countless scoring combinations. The margin can land on 3 through far fewer combinations (field goal differential being the dominant one). Less clustering means less value in buying.

The exception: buying totals off key numbers like 41, 44, 47, or 51 (which represent 6 touchdowns with PATs ± a field goal) can show marginal value, but the edge is razor-thin compared to buying the 3 on spreads. Most professional bettors avoid buying totals entirely and allocate that vigorish cost to line shopping across multiple sportsbooks instead.

Is It Worth It? Detailed Scenario Analysis

You're evaluating a Week 10 NFL matchup: Bills -3.5 at -110 against the Chiefs. Your handicapping suggests the Bills should win by 4-6 points. You're considering buying the hook to Bills -3 at -135 to protect against a Bills win by exactly 3.

Buying the hook adds cost to your bet. Use the Vig Calculator to see if the extra juice destroys your edge.

The verdict for this specific scenario: buying Bills -3.5 to -3 at -135 is slightly +EV because the 3 appears 15.1% of the time versus the 8.83% required. The edge is thin at -135—around 1-2% of expected value improvement. At -140, the math flips neutral or negative. Always shop for the best price. One book might offer -130 while another charges -140, and that 10-point difference equals 1.8% in break-even rate.

Line Shopping: The Alternative to Buying

Before you buy a half-point, check if another sportsbook offers the line you want at better odds. If Book A has Bills -3.5 at -110 while Book B has Bills -3 at -115, you can "buy" the hook by switching books and only paying 5 points of juice instead of 25.

Professional bettors maintain accounts at 5-8 sportsbooks specifically to line shop. The difference between -110 and -115 is 1.05% in break-even rate (52.38% vs 53.49%). The difference between -110 and -135 is 5.07% (52.38% vs 57.45%). Over 1,000 bets at $100 per bet, that 4% gap equals $4,000 in expected value.

Line shopping also reveals market inefficiencies. If Book A prices Bills -3 at -135 while Book B prices it at -125, Book B is offering better value. The market hasn't aligned, and you can exploit the discrepancy. This is arbitrage at the margin—not pure arbitrage (which requires betting both sides for guaranteed profit), but value arbitrage where you're consistently getting the best available number.

When Buying Makes Sense

• You're crossing the 3 and the price is -135 or better
• You're crossing the 7 and the price is -125 or better
• You have a strong read that this specific game will be close and the key number will matter more than the historical average suggests
• You've already line-shopped and this is the best available number across all your outs

When to Avoid Buying

• You're crossing any number except 3 or 7
• The price exceeds -140 for the 3 or -130 for the 7
• You haven't line-shopped yet and are making the decision at a single book
• You're buying a total instead of a spread (almost always -EV)
• You're buying in basketball, baseball, or hockey (no key numbers exist in these sports)

The Long-Term Impact

The difference between good and bad buying decisions compounds over thousands of bets. A bettor who buys the 3 at -135 when appropriate but avoids all other buys will outperform a bettor who buys every half-point by 2-3% ROI. On a $100,000 annual betting volume, that's $2,000-3,000 in profit differential.

The sportsbook's edge on point buying comes from aggregate behavior. For every sharp bettor making mathematically sound buys on the 3, there are twenty recreational bettors buying the 5, 8, 9, 11, and 13. The house collects from the majority while tolerating small losses to informed players. Your goal: be in the minority making +EV buys, not the majority making -EV donations.