Inputs: write one joint event
Translate every selection into one sentence. For example: "The home team wins in regulation and total regulation goals exceed 2.5." Using DraftKings' current market rules as one operator example, record event, market, line, period, player participation, provider definition and accepted price.
The accepted product quote controls payout; it does not disclose or validate a probability model.
Map compatible score states
| Score | Home win | Over 2.5 | BTTS | Joint home win + over 2.5 |
|---|---|---|---|---|
| 1-0 | Yes | No | No | No |
| 2-0 | Yes | No | No | No |
| 2-1 | Yes | Yes | Yes | Yes |
| 3-0 | Yes | Yes | No | Yes |
| 1-1 | No | No | Yes | No |
| 1-2 | No | Yes | Yes | No |
The table exposes logical relationships before modelling. Player and event props require additional dimensions for participation, minutes, cards, corners or shots.
Worked conditional probability
Suppose a hypothetical model estimates:
- P(home win) = 0.52
- P(over 2.5 | home win) = 0.62
Then:
P(home win and over 2.5) = 0.52 * 0.62 = 0.3224, or 32.24%
If the standalone over probability is 0.55, multiplying marginals would give:
Independent approximation = 0.52 * 0.55 = 0.286, or 28.60%
The difference is the consequence of the illustrative conditional assumption. OpenStax's independence rule explains why related events cannot automatically use marginal multiplication.
At an illustrative accepted same-game price of 3.20:
Raw break-even probability = 1 / 3.20 = 0.3125, or 31.25%
This illustrative difference does not establish a recommendation. Model uncertainty, margin, omitted states, participation and settlement can reverse it.
Dependence map
| Shared cause | Legs commonly affected |
|---|---|
| Score state | Result, totals, team totals, BTTS |
| Player minutes | Shots, goals, assists, cards |
| Red card | Result, totals, corners, player props |
| Tactical role | Player props, team attack, possession events |
| Set-piece duty | Goals, assists, shots, corners |
| Match period | Regulation, extra time, shoot-out markets |
Use Correlated Parlay for a deeper conditional-probability treatment.
Validation
Validate the joint product, not only each marginal leg. Group forecasts into probability bands and compare the complete same-game event with later outcomes. scikit-learn's calibration guidance explains reliability assessment for probability forecasts.
Record rejected combinations and unavailable prices as part of the evidence. Do not evaluate only tickets that an operator accepted after seeing the outcome.
Settlement and voids
DraftKings' soccer rules illustrate product-specific regulation-time and player-event definitions. For each same-game ticket, test a push, non-participant, abandonment, market correction and resettlement. Repricing after a void can differ from simply assigning decimal 1.00 to one leg.
Expected-value boundary
Use every joint settlement state and net payoff under OpenStax's expected-value framework. A higher combined price or accepted correlated combination is not proof of value.
Continue learning
- Next guide: Soccer Parlay Apps in 2026
- Related guide: World Cup 2026 Parlays
Assumptions and limitations
The score matrix and probabilities are illustrative and omit many scores and player states. Same-game pricing methods, eligible markets, limits, promotions and void treatment vary by sportsbook, state, account and date.
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