Sports Betting Math: Every Formula You Actually Need

Sports betting is a math problem

Sports betting math is the entire game. Every profitable bettor in history is running some version of the same calculations, whether they formalize it or not. The sportsbook certainly does. Their models are doing the math on every line they post, and they're calibrated to extract a fee on every dollar you wager.

The good news: the math isn't complicated. There are a handful of core concepts, and once you understand them, you can evaluate any bet on any platform in about 30 seconds. The bad news: most bettors skip the math entirely and wonder why they lose.

This is the complete framework. Every formula below connects to the next. Expected value tells you if a bet is worth taking. Vig tells you what you're really paying. Kelly tells you how much to bet. Closing line value tells you if your edge is real. Master these, and you have everything you need.

Expected value: the only number that matters

Expected value (EV) is the average profit or loss per bet over infinite repetitions. Positive EV means the bet makes money long-term. Negative EV means it loses. There is no third option.

The formula:

EV = (Win Probability x Profit) - (Loss Probability x Stake)

Example: You find +150 on an NBA underdog. After de-vigging a sharp line, you estimate the true win probability at 45%.

• Win probability: 45%
• Loss probability: 55%
• Profit if win: $150 (on a $100 stake)
• Loss if lose: $100

EV = (0.45 x $150) - (0.55 x $100) = $67.50 - $55.00 = +$12.50

That's a 12.5% edge on every $100 wagered. Take that bet every time it appears.

The critical question is where the "true probability" comes from. Three common sources: de-vigging sharp closing lines (Pinnacle is the standard), building your own model, or using high-liquidity prediction market prices as benchmarks. Run any bet through the EV calculator to quantify the edge before you place it.

For the full breakdown, read expected value explained.

Vig: the tax you're always paying

Every sportsbook charges vig (also called juice). It's the built-in margin that guarantees the house profits regardless of outcome.

A fair coin flip should be priced at +100 on both sides. Sportsbooks price it at -110/-110. You're paying $110 to win $100 on a 50/50 proposition. That gap is the vig.

To quantify it, add up the implied probabilities of all outcomes. On a -110/-110 line:

• Each side implies 52.4% probability
• Total: 104.8%
• That 4.8% above 100% is the overround

The hold percentage tells you how many cents the book keeps per dollar wagered:

Hold = 1 - (1 / book sum) = 1 - (1 / 1.048) = 4.6%

Vig varies dramatically by market type. NFL spreads carry roughly 4.6% hold. Player props can hit 13%. Parlays compound the vig across legs and regularly exceed 15%. This is why parlay math works against you so aggressively.

The de-vig calculator strips the vig from any line using seven different methods and shows you the true implied probability underneath. The hold calculator tells you exactly what the book is charging on any market. These two tools are the foundation of everything else. For the full breakdown, read what is vig.

True probability and de-vigging

You cannot calculate expected value without a probability estimate, and you cannot get a good probability estimate without removing the vig from the odds.

The simplest approach: take a sharp book's closing line (Pinnacle is the gold standard), de-vig it, and treat the result as your true probability benchmark. If you bet on a recreational sportsbook at better odds than the de-vigged sharp line, you have an edge.

If you need to convert between American, decimal, or fractional odds before de-vigging, use the odds converter. For a two-outcome market at American odds a and b, the multiplicative de-vig method works like this:

1. Convert both sides to implied probability: P_a and P_b
2. Book sum = P_a + P_b (should be > 1.00)
3. True probability of side A = P_a / book sum

Example: A market is priced at -130 / +118.

• -130 implies 56.5%, +118 implies 45.9%
• Book sum: 102.4%
• True probability of the favorite: 56.5% / 1.024 = 55.2%

That 55.2% is your benchmark. If another book is offering the favorite at odds that imply less than 55.2%, you're getting a better price than the market's best estimate. That's an edge.

The de-vig calculator handles all of this across seven methods, including Shin and power models that account for favorite-longshot bias.

Bet sizing with the Kelly Criterion

Finding a +EV bet is step one. Sizing it correctly is step two. Bet too much on a +EV proposition and a losing streak wipes you out before the math converges in your favor.

The Kelly Criterion gives the mathematically optimal bet size:

Kelly % = (p x d - 1) / (d - 1)

Where p is your estimated win probability and d is the decimal odds.

Example: 55% estimated probability on a +120 line (decimal 2.20).

Kelly % = (0.55 x 2.20 - 1) / (2.20 - 1) = 0.21 / 1.20 = 17.5%

Full Kelly says bet 17.5% of your bankroll. In practice, this is dangerously aggressive. The formula is extremely sensitive to probability inputs. If your edge estimate is even slightly wrong, full Kelly oversizes dramatically, and the expected drawdowns are brutal.

Almost every serious bettor uses half Kelly (8.75% in this example). It captures roughly 75% of the growth rate with dramatically less variance. Quarter Kelly is appropriate when you're uncertain about your edge.

If Kelly returns zero or negative, the bet is -EV. Don't take it. Run your sizing through the Kelly Criterion calculator alongside the EV calculator to confirm both the edge and the correct wager amount. For the full breakdown, read the Kelly Criterion guide.

Closing line value: proving your edge is real

You'll lose plenty of +EV bets. A 55% edge still loses 45% of the time. Over 50 or even 200 bets, your win rate tells you almost nothing about your skill. Variance dominates small samples.

Closing line value (CLV) is the metric that cuts through the noise. It measures whether the odds moved in your favor after you bet. If you bet +150 and the line closes at +130, you captured value. The market confirmed you were right to bet when you did.

CLV = Closing Implied Probability - Your Implied Probability

Professional bettors typically achieve 2-5% CLV on average. Even 2% CLV, compounded over thousands of bets, produces significant profit. Sportsbooks use CLV as their primary metric for identifying sharp bettors. If your CLV is consistently positive, your edge is real. If it's consistently negative, the market is sharper than you.

Three ways to capture CLV: bet early (lines are softest at open), find soft books that are slow to adjust, and have a genuine information or modeling edge. The edge calculator helps you determine whether your record reflects skill or variance. For the full breakdown, read closing line value explained.

Bankroll turnover: the overlooked multiplier

Most bettors fixate on edge percentage. A 5% edge sounds better than a 2% edge. But edge is only half the equation. How frequently you reinvest your bankroll matters just as much.

A 2% edge bet 500 times will outperform a 5% edge bet 50 times. The math:

• 2% edge x 500 bets x $100 average = $1,000 expected profit
• 5% edge x 50 bets x $100 average = $250 expected profit

This is why bankroll turnover is one of the most underappreciated concepts in betting math. Higher turnover means your edge compounds faster, variance normalizes sooner, and your bankroll growth accelerates. The turnover calculator shows exactly how turnover rate affects long-term growth.

Putting it all together

Sports betting math is a pipeline. Each concept feeds the next:

Step 1De-Vig

→

Step 2Calculate EV

→

Step 3Size with Kelly

→

Step 4Track CLV

→

Step 5Maximize Turnover

1. De-vig the line to find the true probability (de-vig calculator)
2. Calculate EV to determine if the bet has an edge (EV calculator)
3. Size the bet with half Kelly based on your edge (Kelly calculator)
4. Track CLV to verify your edge is real over time (edge calculator)
5. Maximize turnover to compound your edge faster

Skip any step and the system breaks down. Find edge without proper sizing and a drawdown wipes you out. Size correctly without verifying your edge and you're compounding a losing strategy. The math works as a complete system or not at all.

Every tool on this site exists to make one of these steps faster. Run the numbers, trust the math, and repeat thousands of times. That's the entire strategy.

Frequently asked questions

Is sports betting math hard?

No. The core formulas are basic algebra. Expected value is multiplication and subtraction. The Kelly Criterion is one equation. The hard part isn't the math, it's finding accurate probability estimates and having the discipline to follow the numbers consistently.

What is expected value in betting?

Expected value (EV) is the average amount you win or lose per bet over many repetitions. A +EV bet makes money long-term. A -EV bet loses money long-term. The formula is: EV = (Win Probability x Profit) - (Loss Probability x Stake).

How much should I bet on a +EV bet?

Use the Kelly Criterion to determine optimal bet size. The formula accounts for both your edge and the odds. Most professional bettors use half Kelly, which captures about 75% of the growth rate with much lower risk of ruin.

What is closing line value and why does it matter?

Closing line value (CLV) measures whether odds moved in your favor after you placed your bet. It's the most reliable indicator of betting skill because it directly measures your edge against the market's final, most efficient price. Sportsbooks use CLV to identify sharp bettors.

Do I need a math background to be a profitable bettor?

No. The five formulas covered in this guide are all you need. What matters more is consistently applying them, maintaining accurate records, and having the patience to let the math play out over hundreds of bets.