FinanceCalcs
Sports Betting Expected Value Calculator
Not all sports bets are created equal. The key question isn’t whether your team wins — it’s whether the odds offer value. A bet can be +EV (positive expected value) even if you lose it, and −EV even if you win. Calculate the true expected value of any bet and what the Kelly Criterion says to stake.
Professional bettors don’t bet on who they think will win. They bet when the true probability exceeds the implied probability embedded in the odds.
Sports Betting Expected Value
Odds: 0 • True prob: 0%
EV per $100 bet: $0
Bet Analysis
Line Comparison
| Sportsbook | Odds | Implied Prob. | EV at 0% | Best? |
|---|
EV at Different True Probabilities
| True Prob. | EV / $100 | Bet Type | Kelly Bet ($) | Break-Even? |
|---|
"The sportsbook doesn’t win because they know who will win the game. They win because they set lines that make both sides attractive — and collect the vig regardless of outcome."
— Sports Betting Mathematics
How sports betting expected value works
Every sports bet has two probabilities: the implied probability embedded in the odds (what the sportsbook thinks), and the true probability (what you think). When your true probability exceeds the implied probability, the bet has positive expected value. When it’s lower, negative.
At -110 (standard American odds), the implied probability is 52.38%. If you believe the team actually has a 55% chance of winning, the edge is 2.62 percentage points. EV = (0.55 × $90.91) − (0.45 × $100) = $49.99 − $45 = +$4.99 per $100 bet. Over hundreds of bets, positive EV is how professional bettors build an edge.
The vig (vigorish or juice) is what makes beating sports betting hard. A standard −110/−110 line means the sportsbook takes about 4.55% regardless of outcome. To profit long-term, a bettor must win more than 52.4% of −110 bets — consistently. Most recreational bettors hit 45–48%, meaning they are negative EV players even when they feel like they’re “good at picking games.”
lightbulb Odds Conversion Reference
| American | Decimal | Fractional | Implied Prob. |
|---|---|---|---|
| -200 | 1.50 | 1/2 | 66.7% |
| -150 | 1.67 | 2/3 | 60.0% |
| -110 | 1.91 | 10/11 | 52.4% |
| +100 (even) | 2.00 | 1/1 | 50.0% |
| +110 | 2.10 | 11/10 | 47.6% |
| +150 | 2.50 | 3/2 | 40.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +500 | 6.00 | 5/1 | 16.7% |
Sports Betting EV FAQs
What is the vig and how does it affect EV?
The vig (vigorish, juice, or overround) is the sportsbook’s built-in profit margin. On a standard -110/-110 line, both sides have an implied probability of 52.38%, which sums to 104.76% — the 4.76% excess is the vig. For a bet to have positive EV, your true probability must exceed the implied probability by more than enough to overcome the vig. At -110, break-even requires winning exactly 52.38% of the time.
What is the Kelly Criterion?
The Kelly Criterion is a formula that determines the optimal fraction of your bankroll to bet to maximize long-run growth: f = (bp − q) / b, where b = decimal odds minus 1, p = your win probability, q = 1 − p. Full Kelly is mathematically optimal but produces large swings; most professional bettors use half Kelly or quarter Kelly to reduce variance while still growing the bankroll.
How accurate do I need to be to profit from sports betting?
At -110 standard lines, you need to win 52.38% of bets to break even. Most profitable bettors win 53–57% of bets — a seemingly small edge that compounds dramatically over thousands of bets. The hardest part is accurately estimating true probabilities better than the market consistently. Sportsbooks employ entire teams of analysts; their lines are usually efficient except for niche markets and early lines.
Terminology
Expected Value (EV)
The probability-weighted average outcome of a bet. Positive EV (+EV) means the bet is mathematically profitable long-term; negative EV (−EV) means it loses money over time. EV = (Win Probability × Profit) − (Loss Probability × Stake).
Implied Probability
The win probability implied by the betting odds. Accounts for the sportsbook’s vig. For American odds: negative odds: |odds| / (|odds| + 100); positive odds: 100 / (odds + 100). The sum of implied probabilities for both sides always exceeds 100%, with the excess representing the vig.
Kelly Criterion
An optimal bankroll management formula that sizes bets to maximize the long-run growth rate of a bankroll. Inputs: your edge (true probability minus implied probability) and the decimal odds. Output: the fraction of bankroll to bet. Full Kelly maximizes growth but produces high variance; fractional Kelly reduces variance at a modest cost to growth rate.
Vig / Juice / Overround
The sportsbook’s built-in profit margin embedded in the odds. Standard American lines of −110/−110 imply a 4.55% vig. The vig is the primary reason most recreational bettors lose money — they must win substantially more than 50% of bets just to break even.
Sharp vs. Recreational Bettor
Sharp bettors (professionals) focus on finding +EV bets and have documented win rates above break-even. Recreational bettors bet based on preference, gut, or fun without EV analysis. Sportsbooks can identify sharp action by line movement and will limit or ban sharp bettors — the opposite of casinos, which always accept action.
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