Sports
Match Outcome Expected Value Calculator
Calculate expected profit for a three-outcome stake portfolio, including commission, break-even probabilities, and profit under each mutually exclusive match result.
STAKE PORTFOLIO PAYOFF
Reconcile expected profit with the money won or lost in each outcome
This page accepts separate stakes on home, draw, and away. It computes each selection's expected profit, then calculates full portfolio profit if each mutually exclusive result settles as the winner. The two views must reconcile.
CURRENT DECISION RECORD
Selection EV and settlement ledger
Every row is generated from the current inputs and reused by Copy, TXT, and the page-specific PDF.
| Outcome | Model probability (%) | Decimal odds | Stake ($) | Break-even probability (%) | Selection EV ($) | Portfolio profit if outcome wins ($) |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
selection EV_i = stake_i x [p_i x (odds_i-1) x (1-commission) - (1-p_i)]; total EV = sum(selection EV_i)
Waiting for valid inputs.
USE STEPS
Five steps from forecast to payoff record
- Enter one coherent set of home, draw, and away probabilities totaling 100%.
- Record executable decimal odds and commission under the same settlement rules.
- Enter the actual stake on each outcome, including zero where no bet is placed.
- Review selection EV and full portfolio payoff for every possible match result.
- Compare expected ROI with worst-case affordability and retain the pre-match record.
FOUNDATIONS
Five payoff concepts
Mutually exclusive settlement
Only one 90-minute 1X2 outcome wins, so the other two stakes are lost in that state.
Selection EV
Each stake's expected profit combines its win payoff and loss of stake using model probability.
Portfolio state profit
The realized profit for one result includes the winning selection's net payout minus losing stakes.
Break-even probability
The probability required for zero selection EV after commission reduces the net win multiple.
Expected ROI
Expected profit divided by total stake is an average over repeated comparable decisions, not one-match return.
DEEP ANALYSIS
Three portfolio-level questions
EV-payoff reconciliation
Summing selection EV must equal weighting the three full settlement profits by their outcome probabilities. A mismatch signals inconsistent payoff or commission treatment.
Hedging versus value
Adding a stake to cover an unprofitable state can improve worst-case payoff while lowering EV. Treat risk-shaping and value-seeking as separate objectives.
Probability error
Expected profit may be small relative to payoff spread. Stress every probability within a defensible error band before treating a positive point estimate as robust.
DECISION CASES
Two stake portfolios with different priorities
Single value selection
An analyst stakes only on home because draw and away are below break-even probability. Total EV equals home selection EV, while the outcome table makes the full stake loss in two states explicit.
Three-way promotional cover
A promotion changes effective payoffs across all three outcomes. The user enters each actual stake and adjusted quote, then checks whether smoother settlement profits were purchased at the cost of negative total EV.
TERMS
Expected-value glossary
- Selection expected value
- The probability-weighted average net profit for one outcome stake.
- Total expected profit
- The sum of selection EV across the complete stake portfolio.
- Settlement state
- One mutually exclusive match result and the resulting profit across all stakes.
- Break-even probability
- The win probability at which commission-adjusted selection EV equals zero.
- Expected ROI
- Total expected profit divided by total money staked.
- Payoff spread
- The difference between best and worst portfolio profit across settlement states.
EVIDENCE
Retain the entire settlement basis
Save forecast timestamp and model version, all three probabilities, bookmaker and quote time, rules, commission, stake acceptance, promotions, and the unedited pre-match decision. Keep realized result separate from model validation.
LIMITS
Expected-value boundaries
- Probabilities are point estimates and the calculator does not model their uncertainty.
- Only one 90-minute home/draw/away settlement is represented.
- Limits, voids, partial acceptance, taxes, bonuses, and correlated external wagers are omitted.
- Expected profit describes a long-run average and can coexist with a 100% loss of stake in one match.
Disclaimer: Gambling can cause financial harm. Follow applicable law and responsible-gambling controls; never use essential funds.
SOURCES
Football, probability, and rules references
FAQ
Questions about match expected value
Why can total EV be positive while two states lose money?
A sufficiently profitable and probable winning state can outweigh losses in the other mutually exclusive states on average.
Why does probability of positive payoff differ from EV?
It counts how often profit is positive but ignores how large each gain or loss is.
Can I enter zero stake for an outcome?
Yes, as long as total stake across all outcomes is positive.
Why does commission raise break-even probability?
Commission reduces net winnings, so a selection must win more often to offset losing stakes.
Does spreading stakes guarantee a profit?
No. A three-way cover can still lose in every state if prices and stake ratios are unfavorable.
Is positive expected ROI enough to bet?
No. Probability uncertainty, stake affordability, rules, limits, correlation, and responsible-gambling constraints still apply.