Implied probability is the single most useful number in sports betting and the one most casual bettors never compute. Once you can read a price and immediately know what chance the sportsbook is pricing in, the rest of betting strategy follows. You stop chasing big numbers because they look big and start hunting prices that disagree with your own probability estimate.
Implied probability is the single most useful number in sports betting and the one most casual bettors never compute. Once you can read a price and immediately know what chance the sportsbook is pricing in, the rest of betting strategy follows. You stop chasing big numbers because they look big and start hunting prices that disagree with your own probability estimate.
This post covers the math, the vig (the sportsbook's margin baked into every price), the difference between implied and true probability, and how to use this combination to find +EV bets — bets where the math says you have an edge.
When a sportsbook prices a market, they're communicating two things: their estimate of the true probability of each outcome, plus their margin. Implied probability is the percentage chance the price implies, ignoring (for now) the margin component.
Examples:
| Price (decimal) | Price (American) | Implied probability |
|---|---|---|
| 2.00 | +100 | 50.0% |
| 1.50 | −200 | 66.7% |
| 1.91 | −110 | 52.4% |
| 3.00 | +200 | 33.3% |
| 5.00 | +400 | 20.0% |
| 10.00 | +900 | 10.0% |
The math is one division: implied probability = 1 ÷ decimal odds. For American odds, the formula bifurcates:
implied prob = 100 ÷ (N + 100). So +200 → 100/300 = 33.3%.implied prob = N ÷ (N + 100). So −150 → 150/250 = 60%.Or save yourself the mental math and use the Odds Converter — it shows implied probability beside any price you type.
Take any two-sided market. Sum both sides' implied probabilities and you'll get more than 100%. Take a soccer 1X2 market with three outcomes. Sum all three. Same result — over 100%.
That excess is the vig (also called overround or juice or margin). It's the sportsbook's expected profit margin on the market.
A typical NFL spread offers both sides at −110: - Side A: decimal 1.909 → implied 52.4% - Side B: decimal 1.909 → implied 52.4% - Sum: 104.7% - Vig: 4.7%
What that 4.7% means: if a thousand bettors split evenly across both sides, the sportsbook's expected profit is 4.7% of the total handle, regardless of who covers.
A favorite at −180 vs. an underdog at +150: - Favorite: decimal 1.556 → implied 64.3% - Underdog: decimal 2.50 → implied 40.0% - Sum: 104.3% - Vig: 4.3%
Home / Draw / Away market on a Premier League game: - Home: decimal 2.50 → 40.0% - Draw: decimal 3.40 → 29.4% - Away: decimal 3.20 → 31.3% - Sum: 100.7% - Vig: 0.7%
Wait — that's much lower than the NFL spread? Yes, on the sharpest soccer markets at top books, vig can be under 1%. NFL spreads run 4–5%. Same-game parlays run 10–20%. Long-tail futures markets run 20–40%. Always sum the market's overround before betting. A 25%-vig market is a sucker bet regardless of what side you take.
Implied probability is what the price says. True probability is what the actual chance is — the real-world frequency that this outcome would happen if the same game were played a thousand times.
These two are usually close but not identical. The market is wise but not infallible. The bettor's job is to spot situations where the true probability differs meaningfully from the implied — that's where the edge lives.
Three approaches, in increasing rigor:
Most retail bettors won't outmodel a sportsbook on a high-liquidity market like NFL spreads. But on lower-liquidity markets — minor sports, props, futures, niche events — sportsbooks build less infrastructure and book less attention, so the gap between implied and true can be wider.
To compare your true-probability estimate against the price fairly, first strip the vig out of the price. The result is the "no-vig" or "fair" probability — what the price would say if the sportsbook took zero margin.
For a 2-way market (e.g., NFL spread with Side A at decimal a and Side B at decimal b):
implied_A = 1/a
implied_B = 1/b
sum = implied_A + implied_B
no-vig_A = implied_A / sum
no-vig_B = implied_B / sum
The two no-vig probabilities will sum to exactly 100%.
NFL spread at −115 / −105 (asymmetric vig): - Side A: decimal 1.870 → implied 53.5% - Side B: decimal 1.952 → implied 51.2% - Sum: 104.7% - No-vig A: 53.5 / 104.7 = 51.1% - No-vig B: 51.2 / 104.7 = 48.9%
So even though Side A is "priced at 53.5%," the sportsbook's actual probability estimate (after stripping the margin) is 51.1%. That's the number to compare your own estimate against.
A bet is +EV when your true probability of winning, multiplied by your potential profit, exceeds the cost of being wrong, multiplied by the chance of losing.
EV = (true_prob × profit_if_win) − ((1 − true_prob) × stake)
For decimal odds, this simplifies:
EV = (true_prob × decimal × stake) − stake
= stake × (true_prob × decimal − 1)
The bet is +EV if true_prob × decimal > 1. Equivalently, if true_prob > 1/decimal — that is, if your estimated true probability exceeds the implied probability.
A market lists Team A at decimal 2.50 (implied 40%, no-vig 38%). You estimate Team A's true probability at 45%.
That's a strong edge. Most edges in real-world betting are 1–4%, not 12.5%. But the math is the same — you're betting whenever your estimated true probability exceeds the implied, sized appropriately.
Market: Team A at decimal 2.00 (implied 50%, even-money). You estimate true probability at 50%. EV per $100 = $100 × (0.50 × 2.00 − 1) = $0. The bet has zero EV. Don't bet — variance gives you the same expectation as flipping a coin, with the added cost of the time it takes to place and track.
Standard NFL −110 spread. Implied probability 52.4%. You think Team A is exactly 50% to cover. EV per $100 = $100 × (0.50 × 1.909 − 1) = −$4.55. You'd lose $4.55 per $100, on average, betting a coin-flip outcome at standard juice. The vig is what makes the bet −EV even though the underlying outcome is genuinely 50/50.
The closing line is the final price a market settles to before kickoff. Markets get sharper as kickoff approaches because money moves the line toward the true probability.
If you consistently take prices that are better than the closing line, you're systematically betting at +EV and your long-term results should reflect that. If you consistently get worse prices than the close, you're betting −EV regardless of whether your individual bets win or lose.
After every bet, record: - Your bet's price (in decimal). - The closing line price (in decimal). - The implied probability difference.
Aggregate over hundreds of bets. If your average price beats the close by 1–2%, you have a real edge. If you're consistently below, you're paying the book a tax.
CLV is a leading indicator of skill — it shows up before bankroll growth, because variance can mask edge for hundreds of bets. If your CLV is positive, your bankroll will catch up.
Where do retail bettors actually find +EV?
Sportsbooks regularly boost odds as a marketing hook — a market priced at +180 becomes +220. The implied probability shift is large, easily large enough to overcome vig. A boosted 3.20 line becoming a 3.30 line is roughly +3% EV.
The catch: max stakes are small (often $10–$50). The dollar profit per boost is modest, but if you stack multiple boosts a week, it compounds.
Long-tail futures, minor leagues, women's sports, esports, prop bets — markets where the sportsbook has set generic prices without putting their best modelers on it. Bettors with domain knowledge can find +EV consistently.
A team announces a star player out 30 minutes before kickoff. Sharp money has moved the line. Slow-to-move books still have stale numbers. Quick bettors hit the stale number before it moves. Edge can be 5–15% on the right side, evaporating in minutes.
These are different beasts that exploit pricing differences directly rather than betting against true probability.
Both are +EV by structure, not by probability estimation. Both also have account-longevity risks since sportsbooks notice and limit accounts that exclusively place +EV bets.
You've found a +EV bet. How much should you stake?
Too little: you're not capturing the edge. Too much: variance can wipe you out before the edge plays out. The Kelly criterion gives the math.
fraction = edge / odds
Where edge is the no-vig EV (true_prob − implied_prob) and odds is the decimal payout minus 1.
Most professionals use half-Kelly to reduce variance — divide the Kelly fraction in half before sizing. Kelly is mathematically optimal for long-term geometric growth, but it's brutal in the short term. Half-Kelly cuts variance by 75% while only giving up 25% of growth.
A bet at decimal 2.50 (implied 40%) where you estimate true probability at 45%. - Edge: 5% - Odds (decimal − 1): 1.50 - Kelly fraction: 5% / 1.50 = 3.33% of bankroll - Half-Kelly: 1.67% of bankroll
On a $1,000 bankroll, you'd bet roughly $17 (half-Kelly) or $33 (full Kelly).
The price reflects the sportsbook's opinion plus margin, not a guaranteed truth. On sharp markets the difference is small. On soft markets the gap can be exploitable. Don't mistake a market price for a verified probability.
Two markets at the same implied probability can have very different vig structures. A market priced at −110 / −110 has 4.7% vig; a market priced at −105 / −115 has the same average but asymmetric exposure. Always check overround before deciding the market is "fair."
If your gut says a +200 underdog is "definitely going to win" but your model says they're 30% to win — math wins. Variance can confirm your gut on individual results; only long-run frequency tells the truth. Trust the math.
Two sportsbooks offer the same underdog at +180 and +200. Picking +180 is a meaningfully worse bet — over hundreds of bets, that 20-cent difference (on +180 vs +200) is what separates winning bettors from losing ones. Always line shop.