Polaroid
I need a tittle
- Since
- Jan 21, 2010
- Messages
- 2,890
- Score
- 3
- Tokens
- 0
In order to profit long term from gambling, it is good to understand the underlying statistical concept behind the odds offered by sportsbooks. Using a line offered at Pinnacle Sports for a mythical MLB game between the Boston Red Sox and the Philadelphia Phillies, the Red Sox are offered at -200 and the Phillies at +180 and, by converting those sportsbook lines, we can then ascertain what statistical chance each team has winning the game by calculating the implied/actual probability.
When dealing with a favorite (where the quoted odds are negative) calculating the implied probability is done by taking the absolute value of the odds (where the absolute value of -200 is 200) and then dividing that by the absolute value of the odds plus 100. In terms of the Red Sox, the moneyline offered by the sportsbook implies the probability of winning as:
200 / (200 + 100) = 200 / 300 = 0.6667 = 66.67%
For the calculation of implied probability for the underdog (where the odds are positive), the process is slightly different. In this case we divide 100 by the sum of the offered line (in this case, +180 for the Phillies) plus 100. So, for the Philadelphia, the implied probability of them winning the game is:
100 / (180 + 100) = 100 / 280 = 0.3571 = 35.71%
When adding together the percentages, the sum of the two is greater than 100 which is generally a bad sign; the sum of them in this case is 102.38%. This additional 2.38% is the sportsbooks theoretical hold which is more often referred to as the vigorish (and usually shortened to vig) which represents the percentage taken by the sportsbook for its services, much like a house edge on casino games. Under the assumption that the sportsbook attracts equal action on both sides of an offered line (in this example, either a Boston or Phillies win results in an identical payout to the respective winners) then the sportsbook will make 2.38% profit on each bet placed, and hence 2.38% on the total of all bets placed. This hold is still only a theoretical hold since it is unlikely that a sportsbook will attract equal action on an individual betting line.
Since we know that the earlier calculated winning percentages contain a degree of vigorish, we need to remove that element and so we calculate the no vig line which will give us the actual winning percentages rather than the implied winning percentages through the sportbooks lines. To calculate the no vig line, we divide each implied winning percentage by the total of each of the implied winning percentages.
For the Red Sox, the implied probability of winning is calculated as:
0.6667 / 102.38 = 0.6512 = 65.12%
Similarly the implied probability of winning for the Phillies, derived from the sportsbook line, is:
0.3571 / 102.38 = 0.3488 = 34.88%
Since the sum of the two percentages equals 100, we can convert the two implied win percentages into a no-vig line. This represents a line based on the two quoted odds but with zero vigorish.
In a situation where the implied win probability is greater than or equal to 0.50 (50% in percentage terms) then the formula to calculate the no vig line, for the Red Sox in this scenario, (where FV is equal to favored teams decimal win probability) is:
-100 / [(1 / FV) 1] = -100 / [(1 / 0.6512) 1] = -186.7
Where the implied win probability is less than 0.50, as is the case with the Phillies, a different formula is used where UD represents the underdogs decimal win probability.
[(1 / UD) 1] * 100 = ((1 / 0.3488) - 1) * 100 = +186.7
Since the sportsbook vig has been removed from the lines, the lines are identical in absolute terms.
The example used here is where there is a clear favorite (with negative moneyline odds) and a clear underdog (with positive moneyline odds). In a scenario where both teams have negative odds which can be a situation where both teams are near to equally favored, or more likely the betting lines are using a point spread than a moneyline, the calculation is slightly different. In this case, the implied probability can be calculated by using the Red Sox (i.e. the favored team) example of calculating the implied and actual probability of winning for both teams.
As a footnote, it should be understood that while implied probability can be derived from a set of lines of any sportsbook, actual probability cant be done, or at least not be done with 100% accuracy, from any random sportsbook. Using the theory of arbitrage, the probability derived from a no-vig line at an efficient sportsbook should be very close to the actual probability. However, with a non-efficient sportsbook that may not be the case where off market lines are offered to profit from square bettors who tend to bet on certain sides whatever the offered price.
When dealing with a favorite (where the quoted odds are negative) calculating the implied probability is done by taking the absolute value of the odds (where the absolute value of -200 is 200) and then dividing that by the absolute value of the odds plus 100. In terms of the Red Sox, the moneyline offered by the sportsbook implies the probability of winning as:
200 / (200 + 100) = 200 / 300 = 0.6667 = 66.67%
For the calculation of implied probability for the underdog (where the odds are positive), the process is slightly different. In this case we divide 100 by the sum of the offered line (in this case, +180 for the Phillies) plus 100. So, for the Philadelphia, the implied probability of them winning the game is:
100 / (180 + 100) = 100 / 280 = 0.3571 = 35.71%
When adding together the percentages, the sum of the two is greater than 100 which is generally a bad sign; the sum of them in this case is 102.38%. This additional 2.38% is the sportsbooks theoretical hold which is more often referred to as the vigorish (and usually shortened to vig) which represents the percentage taken by the sportsbook for its services, much like a house edge on casino games. Under the assumption that the sportsbook attracts equal action on both sides of an offered line (in this example, either a Boston or Phillies win results in an identical payout to the respective winners) then the sportsbook will make 2.38% profit on each bet placed, and hence 2.38% on the total of all bets placed. This hold is still only a theoretical hold since it is unlikely that a sportsbook will attract equal action on an individual betting line.
Since we know that the earlier calculated winning percentages contain a degree of vigorish, we need to remove that element and so we calculate the no vig line which will give us the actual winning percentages rather than the implied winning percentages through the sportbooks lines. To calculate the no vig line, we divide each implied winning percentage by the total of each of the implied winning percentages.
For the Red Sox, the implied probability of winning is calculated as:
0.6667 / 102.38 = 0.6512 = 65.12%
Similarly the implied probability of winning for the Phillies, derived from the sportsbook line, is:
0.3571 / 102.38 = 0.3488 = 34.88%
Since the sum of the two percentages equals 100, we can convert the two implied win percentages into a no-vig line. This represents a line based on the two quoted odds but with zero vigorish.
In a situation where the implied win probability is greater than or equal to 0.50 (50% in percentage terms) then the formula to calculate the no vig line, for the Red Sox in this scenario, (where FV is equal to favored teams decimal win probability) is:
-100 / [(1 / FV) 1] = -100 / [(1 / 0.6512) 1] = -186.7
Where the implied win probability is less than 0.50, as is the case with the Phillies, a different formula is used where UD represents the underdogs decimal win probability.
[(1 / UD) 1] * 100 = ((1 / 0.3488) - 1) * 100 = +186.7
Since the sportsbook vig has been removed from the lines, the lines are identical in absolute terms.
The example used here is where there is a clear favorite (with negative moneyline odds) and a clear underdog (with positive moneyline odds). In a scenario where both teams have negative odds which can be a situation where both teams are near to equally favored, or more likely the betting lines are using a point spread than a moneyline, the calculation is slightly different. In this case, the implied probability can be calculated by using the Red Sox (i.e. the favored team) example of calculating the implied and actual probability of winning for both teams.
As a footnote, it should be understood that while implied probability can be derived from a set of lines of any sportsbook, actual probability cant be done, or at least not be done with 100% accuracy, from any random sportsbook. Using the theory of arbitrage, the probability derived from a no-vig line at an efficient sportsbook should be very close to the actual probability. However, with a non-efficient sportsbook that may not be the case where off market lines are offered to profit from square bettors who tend to bet on certain sides whatever the offered price.
