Sports
Match Outcome Odds Calculator
Remove a three-way bookmaker margin, compare independent model probabilities with market-implied probabilities, and calculate commission-adjusted expected return and fractional Kelly stake.
PRICE AND EDGE AUDIT
Do not confuse quoted odds, fair market probability, and your own forecast
This page starts with all three 1X2 prices, removes proportional overround, and then compares the resulting market baseline with probabilities entered from an independent model. It calculates commission-adjusted expected return and a deliberately fractional Kelly stake.
CURRENT DECISION RECORD
Three-way odds decision ledger
Every row is generated from the current inputs and reused by Copy, TXT, and the page-specific PDF.
| Outcome | Decimal odds | Raw implied (%) | Margin-free market (%) | Model (%) | Model edge (pp) | Expected return (%) | Full Kelly (%) | Fractional stake ($) |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
raw implied p_i = 1/odds_i; fair market p_i = raw p_i / sum(raw p); EV_i = model p_i x net win multiple - (1-model p_i)
Waiting for valid inputs.
USE STEPS
Five steps for a disciplined price comparison
- Record all three prices from the same bookmaker and timestamp.
- Enter model probabilities produced without tuning them to these quotes.
- Confirm the probabilities sum to 100% and add the applicable winnings commission.
- Review overround, margin-free market probability, edge, and expected return separately.
- If stake sizing is permitted, use a conservative Kelly fraction and aggregate exposure across related bets.
FOUNDATIONS
Five price concepts that are not interchangeable
Decimal odds
Total return including stake per unit wagered if the selected outcome settles as a win.
Raw implied probability
One divided by decimal odds; three raw probabilities usually total more than 100%.
Overround
The excess implied total, used here as a simple measure of embedded three-way margin.
Model edge
Model probability minus proportionally normalized market probability in percentage points.
Expected return
Probability-weighted net profit per unit staked after commission, not a guaranteed yield.
DEEP ANALYSIS
Three reasons a positive row may still be rejected
Margin removal method
Proportional normalization is transparent but assumes margin is distributed proportionally. Favorite-longshot bias and bookmaker risk management can make more advanced methods preferable.
Probability uncertainty
Kelly reacts strongly to small probability differences. Stress model probability downward and price downward before treating a point estimate as stakeable.
Portfolio of wagers
Several bets on the same match, league, or team are correlated. Single-bet Kelly can over-allocate when shared downside is ignored.
DECISION CASES
Two very different market comparisons
Small edge in a liquid league
A model places home win at 51% while proportional market probability is 47%. The analyst tests 48% and a shorter executable price; if expected return disappears, the apparent edge is too fragile for action.
Large edge in a thin cup market
A lower-league cup match shows a large away edge, but limits are small and lineup information is stale. The analyst records the quote yet rejects the stake because information and execution risk overwhelm the numerical edge.
TERMS
Odds glossary
- Decimal odds
- The gross return multiple, including returned stake, for a winning selection.
- Overround
- The amount by which raw implied probabilities across outcomes exceed 100%.
- Margin-free probability
- A normalized market probability after removing overround by a stated method.
- Expected return
- The probability-weighted average net profit divided by stake.
- Kelly fraction
- The growth-optimal bankroll fraction under exact probabilities and repeated independent opportunities.
- Commission
- A deduction from winnings that reduces the effective net win multiple.
EVIDENCE
Keep price and forecast provenance separate
Preserve bookmaker, timestamp, market rules, available limit, commission, model version, probability generation cutoff, stake decision, and any later price movement. Never overwrite the original forecast with the closing market.
LIMITS
Price-audit boundaries
- Overround is removed proportionally and may not match the bookmaker's margin allocation.
- Kelly assumes correct probabilities, repeatability, and bankroll utility conditions that rarely hold exactly.
- Correlated wagers, price movement, stake limits, void rules, tax, and execution are outside the formula.
- A positive expected return can still produce a complete stake loss.
Disclaimer: Gambling can cause financial harm. Use legal, age-appropriate, responsible-gambling controls and never stake funds needed for living costs.
SOURCES
Probability, football, and responsible-use references
FAQ
Questions about 1X2 odds auditing
Why use all three odds?
Overround belongs to the complete mutually exclusive market; one quote alone cannot identify it.
Are normalized market odds truly fair?
They are margin-free under proportional normalization, not proof of correct outcome probabilities.
Why can model edge be positive but expected return negative?
Commission and the quoted payout can erase a small probability advantage.
Why cap negative Kelly at zero?
The unconstrained formula would imply betting against the outcome, which is not offered by this one-sided stake output.
Should I use full Kelly?
Full Kelly is highly sensitive to estimation error and assumes a repeated, correctly specified environment. The default is quarter Kelly.
Does the calculator account for void or dead-heat rules?
No. Enter prices only after confirming settlement rules and adapt expected payoff separately when rules differ.