Betting mathematics
What is closing line value and how is it calculated
Closing line value (CLV) compares the odds you took with the closing odds, the last odds before kick-off. Odds of 2.20 taken against a close of 2.00 give 2.20 / 2.00 − 1 = 10.0%. The same bet gives 7.2% or 4.55 percentage points under other definitions, so a CLV figure always needs to say how it was calculated.
Contents
Key terms
- Odds taken
- The odds at which the bet was actually placed.
- Closing odds
- The last odds before kick-off. By then the market has the most information: line-ups, injuries and other bettors' money.
- Closing line value (CLV)
- How much better or worse the odds taken are than the closing odds.
- Fair closing odds
- The closing odds without the margin, calculated as in the guide to implied probability.
The simplest formula
CLV = odds taken / closing odds − 1A bet on over 2.5 goals was placed at odds of 2.20. By kick-off the odds had dropped to 2.00, with under 2.5 goals at 1.90.
2.20 / 2.00 − 1 = 0.10 → 10.0%
The odds taken are 10% higher than the closing odds.
CLV without the margin
The closing odds of 2.00 still include the margin. The probabilities in that market add up to 1 / 2.00 + 1 / 1.90 = 50.00% + 52.63% = 102.63%. Once the margin is removed, the closing odds for over 2.5 goals go up.
| Outcome | Closing odds | 1 / odds | No margin | Fair odds |
|---|---|---|---|---|
| Over 2.5 | 2.00 | 50.00% | 48.72% | 2.053 |
| Under 2.5 | 1.90 | 52.63% | 51.28% | 1.950 |
2.20 / 2.053 − 1 = 0.072 → 7.2%
Against the fair closing odds the edge is smaller: 7.2% instead of 10.0%.
CLV as a probability difference
A third approach compares probabilities instead of odds. The result is in percentage points, not percent.
CLV (pp) = 1 / closing odds − 1 / odds taken1 / 2.00 − 1 / 2.20 = 50.00% − 45.45% = 4.55 pp
Using the fair closing probability (48.72%), the difference is 3.26 percentage points.
Three numbers for the same bet
| Definition | Calculation | CLV |
|---|---|---|
| Odds ratio | 2.20 / 2.00 − 1 | 10.0% |
| Ratio to fair closing odds | 2.20 / 2.053 − 1 | 7.2% |
| Probability difference | 50.00% − 45.45% | 4.55 pp |
None of the definitions is wrong, but the numbers cannot be compared with each other. When someone quotes a CLV, ask which definition they use and whether the margin was removed.
Negative CLV
Taken at 1.90, closed at 2.00:
1.90 / 2.00 − 1 = −0.05 → −5.0%
The odds rose after the bet was placed, so it was taken at a worse price than the close.
Why CLV is tracked
The result of a single bet depends on chance, while CLV is known as soon as the match starts. If the closing odds are a good estimate of the probability, bets taken above them have a better expected value on average than bets taken below them. That is why CLV is used as a faster signal than profit, especially while there are still few bets.
Limitations
- CLV is an indirect sign. A bet with positive CLV can still lose, and a run of positive-CLV bets can still be behind.
- Closing odds are not the same at every bookmaker, so the result depends on whose closing odds are used as the yardstick.
- Fair closing odds depend on the method used to remove the margin. The proportional method in the example is only one of them.
- In thinly traded markets the closing odds are a weaker estimate, so CLV is less reliable there too.