The question
"Home win is 1.95 and over 2.5 is 2.08. Multiply them and you get 4.04. So why is the Match Odds and Over/Under 2.5 market offering only about 3.4 for both?"
Why you can't multiply same-game bets is one of the most useful things a football bettor can learn. The shorter price isn't the market robbing you. It's the market doing the sum properly, and the naive 4.04 is the wrong answer.
The idea in one sentence
You can only multiply chances when one result tells you nothing about the other, and outcomes from the same match nearly always tell you something about each other because they're built from the same goals.
The picture
Take one match and one scoreline model: home expected goals 1.6, away 1.0, each side's goals following a Poisson pattern. (Illustrative.) Now ask how often the home side wins, and how often there are three or more goals, and how often both happen.
| Combination | Chance each | Multiplied | Real chance (from the grid) | Link |
|---|---|---|---|---|
| Home win and over 2.5 | 51.3% and 48.2% | 24.7% (4.04) | 30.0% (3.34) | Positive |
| Draw and over 2.5 | 25.0% and 48.2% | 12.0% (8.31) | 5.7% (17.58) | Strongly negative |
| Home win and both teams score | 51.3% and 50.5% | 25.9% | 22.0% | Negative |
Chances with fair odds in brackets.
The pattern makes sense once you picture the scorelines. Home wins include 2-0, 3-0, 3-1 and 4-1, which pile up goals, so "home win" and "over 2.5" tend to arrive together. Draws are mostly 0-0 and 1-1, so a draw with three or more goals needs at least 2-2, which is rare.
Home win and both teams to score pull the other way. Clean-sheet wins like 1-0 and 2-0 are a big share of home wins, and both teams scoring rules them out.
Seeing it with "given"
Another way to see the link is the conditional probability from Lesson 3.2. In this match:
- P(over 2.5 given a home win) = 58.3%
- P(over 2.5 given no home win) = 37.4%
- P(over 2.5 given a draw) = 22.8%
If the events were independent, all three would equal the plain 48.2%. They don't, so the events are linked, and multiplying is off the table.
Worked Betfair example
The Match Odds and Over/Under 2.5 market is live on Betfair, and it offers 3.50 on "Home and Over 2.5". Your model is the one above: home 1.6, away 1.0. (Illustrative.)
- Price each leg on its own. Home win 51.3% (fair 1.95). Over 2.5 48.2% (fair 2.08).
- The wrong sum. 0.513 × 0.482 = 24.7%, a "fair" price of 4.04. By this sum, 3.50 looks poor value and you'd pass.
- The right sum. Add up every scoreline in the grid where the home side wins and there are three or more goals: 2-1, 3-0, 3-1, 4-0 and so on. That totals 30.0%, a fair price of 3.34.
- Expected value at 3.50 on £20, after 2% commission. Win: 0.300 × £50 × 0.98 = £14.68. Lose: 0.700 × £20 = £14.01. EV = +£0.67.
- Break-even price. At a 30.0% chance with 2% commission, the break-even is about 3.39.
- The other side of the coin. "Draw and Over 2.5" multiplies out to 8.31, but the grid says 17.58. Back it at 12.0 believing you've got value, and your real EV is −33p per £1.
Verdict: multiplying made a good price look bad and a terrible price look good. Same-game combinations must be priced from a full scoreline grid (Lesson 4.2).
Independent teams, dependent outcomes
Notice what this model assumes: the home side's goals and the away side's goals are completely separate. The teams are independent. The market outcomes still aren't, because each one is a different way of slicing the same scoreline. Real matches add even more linking, which is what the bivariate Poisson and Dixon-Coles models try to capture.
The formula
The test for independence
- A and B are two outcomes, such as "home win" and "over 2.5".
In plain English: multiplying is correct only if the two events are independent. If the real joint chance differs from the product, they're linked.
The general "and"
- P(B | A) is the chance of B given that A happens.
In plain English: always true, linked or not. For home win and over 2.5: 51.3% × 58.3% = 30.0%.
How strong is the link?
- φ (phi) is the correlation between two yes/no outcomes. It runs from −1 to +1, with 0 meaning no link.
In plain English: the top line is how far the real joint chance sits from the multiplied one. For home win and over 2.5, φ is about 0.21: a real, moderate link.
Pricing any same-game combination
In plain English: list every scoreline, keep the ones where both parts of your bet win, and add them up. The square brackets are 1 for scorelines you keep and 0 otherwise.
Try it
Pen and paper: using the table above, a friend says "home win at 1.95 and BTTS at 1.98, so the double is 3.86". Is the true price shorter or longer?
Answer
Longer. Home win and both teams to score are negatively linked here: 22.0% together, not 25.9%. The fair price is 1 ÷ 0.220 ≈ 4.55, not 3.86.Common mistakes
- Multiplying legs from the same match. Home win, over 2.5, BTTS and a Correct Score band are all slices of one scoreline. Price them together from a grid.
- Assuming the link is always positive. Some combinations go together and some push apart. Draw with over 2.5 and home win with BTTS are both negative.
- Counting linked bets as separate evidence. Backing City and City-over-2.5 is closer to one big bet than two. That matters for sample size (Lesson 1.1) and for staking (Lesson 6.1).
- Staking linked bets as if they were independent. They win and lose together, so the swings are bigger. Size them as a group, as in simultaneous Kelly.
- Thinking a same-game price is a rip-off because it's shorter than the product. Often it's just correct. Check with a grid before you call it poor value.
Hidden links between bets are one of the quiet reasons good models still lose money: the model looks diversified when it isn't.