Odds, Implied Probability and Closing Line Bets
Using a random line at a Las Vegas casino bookmaker for a mythical Yankees / Royals game, we see that New York is offered at -220 and Kansas City at +206 and from those betting lines we can calculate the implicit probability each team has of winning that. particular game.
To calculate the implied probability of winning for a favorite (where the probabilities are negative), take the absolute value of the probabilities and divide it by the absolute value of the probabilities plus 100. For the New York Yankees, the implied probability of winning is :
220 / (220 + 100) = 220/320 = 0.6875 = 68.75%
To calculate the implied probability of winning for a loser (where the probabilities are positive), divide 100 by the sum of the line plus 100. For the New York Yankees, the implied probability of winning is:
100 / (206 + 100) = 100/306 = 0.3268 = 32.68%
As for percentages, the sum of them is greater than 100, which is never a good sign for percentages; in fact, the sum of them is 101.43%. The additional 1.43% represents the bookmaker’s theoretical retention or more commonly called vigorish (and generally abbreviated to vig), which is the percentage amount charged by the bookmaker for its services. Assuming the bookmaker attracts the same action on both sides, then you will make a profit of 1.43% on the total amount of bets placed, but since they are unlikely to hit the same action on most betting lines , it is only a theoretical retention.
Since the winning percentages contain an element of vigor, we have to remove that to end up with the actual winning percentages, rather than the implicit ones, and this will give us the no vig line; This is done by dividing each implied profit percentage by the sum of both profit percentages.
For the New York Yankees, the actual probability of winning is:
0.6875 / 101.43 = 0.6778 = 67.78%
For the New York Yankees, the actual probability of winning is:
0.3268 / 101.43 = 0.3222 = 32.22%
Now we can convert the two actual winning odds into a no-wake line.
For an actual victory probability equal to or greater than 0.50 – or 50% in percentage terms – the formula (where FV is equal to the decimal probability of victory of the favorite team) for the Yankees line is:
-100 / ((1 / FV) – 1) = -100 / ((1 / 0.6778) – 1) = -210.4
For an actual win probability less than 0.50 – or 50% in percentage terms – the formula (where UD equals the loser’s decimal win probability) for the Royals line is:
((1 / UD) – 1) * 100 = ((1 / 0.3222) – 1) * 100 = +210.4
Since the sports betting vig has been removed from the lines, the lines are identical in absolute terms.
This example above is where there is a clear favorite (with negative odds) and a clear loser (with positive odds). However, in cases where there are two teams that are equally favored by the market or, more commonly, bet lines that use a point spread, the calculation is slightly different. In this case, the implied probability and the actual probability can be calculated using the example of the New York Yankees to calculate the implied and actual probability of winning.
Simply knowing how to calculate no-vig odds won’t make you a winning bettor, but you can use those odds to help you win; One way to do this is to create a model that is more accurate than a bookmaker’s starting lines.
Suppose tomorrow you model the game between the Yankees and the Royals and the lines are -160 / + 150 respectively and you model the game with a fair line of -170 / + 170. Obviously, the loser is not a good bet, since only you get a price of +150 in a game where you predict they should get +170. On the contrary, the -160 price is more attractive as the line is better than it has modeled. The -170 line you forecast turns into a 62.96% gain percentage compared to the actual -160 line which gives 61.54%; this means that taking the Yankees at a price of -160 gives you a 1.42% advantage.
When you bet with a positive edge (based on the line you bet versus the closing line of no vig, assuming you are betting on efficient markets), you will win in long-term sports betting. If you bet with a negative edge, just like in a roulette game at your local casino, you will be a loser for life.
