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Odds, Probability and Overround
03-27-2009, 04:02 AM (This post was last modified: 03-29-2009 05:34 AM by KillJoy.)
Post: #1
Odds, Probability and Overround
Odds that are offered by the bookmaker represent the bookmakers prediction about the probability of an outcome for a certain event. We know that probability is calculated in percentages, but it's much easier for the bookmakers to represent the odds of a certain event using a number like 1.40 (European or Decimal) or 2/5 (British or Fractional) or -250 (American or Whole) than with a percentage number like 71.43% and of course, it's easier for the bettors to calculate their possible winnings and bet amount.

Odds Format

Bookmakers operate with three different types of odds. Depending on which markets the bookmaker operates (targets), they offer odds in Decimal, American or British format.

American odds (Moneyline or Whole)
Positive odds indicated the winnings earned with a stake of 100 units ($100)
Example: Wager = $100 on Team A winning
Odds = 240
Payout = stake x (1 + odds / 100) = $100 x (1 + 240 / 100) = $340
Winning = stake x (odds / 100) = $100 x 240 / 100 = $240

Negative odds indicate the required stake to win 100 units (ie. $100)
Example: Wager = $100 on Team B winning
Odds = -120
Payout = stake x (1 + 100 / odds) = $100 x (1 + 100 / 120) = $183.33
Winning = stake x (100 / odds) = $100 x 100 / 120 = $83.33

Fractional odds (British or UK)
Fraction odds show how many units are won per unit stake – winnings equals stake multiplied by odds. When converting odds into Fraction formats, rounding errors may occur.
Example: Wager = $100 on Team A winning
Odds = 12/5
Payout = stake x (odds + 1) = $100 x (12/5 + 1) = $340
Winning = stake x odds = $100 x 12/5 = $240

Decimal odds (European or Continental)
Decimal odds show how many units are paid out per unit staked – payout equals odds multiplied by stake.
Example: Wager = $100 on Team A winning
Odds = 3.4
Payout = stake x odds = $100 x 3.4 = $340
Winning = stake x (odds - 1) = $100 x (3.4 – 1) = $240


Converting Odds to Probability

So, how do we calculate the probability from the odds given by the bookmaker?

American Odds (Moneyline or Whole)

Positive Odds: Probability (%) = 100 – (100/(100/Odds+1))

Example: Odds = 240
Probability for this outcome to occur = 100 – (100/(100/240+1)) = 29.41%
This means that the bookmaker predicts the probability of this outcome to occur is 29.41%.

Negative Odds: Probability (%) = 100/(-100/Odds + 1)

Example: -120
Probability for this outcome to occur = 100/(-100/-120 + 1) = 54.55%
This means that the bookmaker predicts the probability of this outcome to occur is 54.55%.


Fractional Odds (British or UK)


When converting fractional odds to probability we need to divide the right hand side of the fraction by the sum of the left and right hand sides and multiply the answer by 100. When written like that it looks complicated, but it really isn't.

Probability (%) = Denominator/(Numerator + Denominator) x 100

(Note: Numerator (upper or left number) represents a number of equal parts and the denominator (bottom or right number) tells how many of those parts make up a whole.)

Example: Odds = 7/4
7/4 becomes 4/(7+4) which is 4/11 = .3636
Multiply by 100 and the answer is 36.36 so probability is 36.36%
This means that the bookmaker predicts the probability of this outcome to occur is 36.36%.


Decimal Odds (European or Continental)

We simply divide 100 with the odds and the number we get is the probability in percents.

Probability(%) = 100/Odds

Example: Odds = 1.60

Probability for this outcome to occur (%) = 100/1.60 = 55.56%

This means that the bookmaker predicts the probability of this outcome to occur is 62.5%.


Overround – Bookmakers Profit

Taking match odds on a soccer (football) match as an example, there are three possible results home win, away win or draw. Assuming the game is priced as follows:
Home win = 1.75 (57.14%)
Away win = 3.9 (25.64%)
Draw = 3.5 (28.57%)

Logically the sum of all outcome possibilities can only be 100%, but we can see here that by adding up the probabilities (in brackets) we actually arrive at a total of 111.35% this extra 11.35% is called the overround, it is the profit that the bookmaker is expecting to make on this event and is generated by offering worse odds on the event than the actual true odds.
In this example, if total wagered money on the event is $100 he will earn $11.35 no matter which of the possible outcomes occur.


If math isn't your stronger side you can use the following table in which you can see probability for all three standard odds format:

[Image: Odds_Format_Conversion_Table.JPG]

"Depend on the rabbit's foot if you will, but remember it didn't work for the rabbit." - R. E. Shay
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