The Bookmaker’s Math: Calculating Sports Betting Odds and Pay-Outs – The Sports Mirror – Sports News, Transfers, Scores














To the uninitiated, the world of online gambling, in all its formats, can be overwhelming. The industry is growing exponentially with statistics showing that the current size of the industry is worth about $66.6 billion (USD).

Soccermatics: Mathematical Adventures in the Beautiful Game

And, there are a large number of sportsbooks all offering substantial sign-up bonuses and a large number of betting options such as traditional win, draw, or lose bets, and accumulator bets.

Additionally, David Sumpter, author of “Soccermatics: Mathematical Adventures in the Beautiful Game,” developed a set of betting models that tried to predict the outcome of football games more accurately then the bookmakers offering odds on a particular football match. He summarised his work as follows:

Gambling is not about picking winners. The trick is to know your probabilities better than the bookies.”

Therefore, the question that begs is how do you calculate both implied and real probabilities to mitigate the risk of losing the bet and placing yourself in the best possible position to win all of the bets you place?

By way of answering this question, let’s consider the following points:

Bookmaker’s odds

It is essential to note that a sportsbook or casino, like William Hill, is in business to make money. And like all successful businesses, they aim to keep their expenses as low as possible by reducing the number of winning pay-outs. The statement, “the house always wins,” is relevant here. And bookmakers generally add a 5% mark-up on all betting odds. But they can add less, especially when offering bonuses and promos.

Reading and understanding the format of betting odds

American or Moneyline odds, decimal odds, and fractional odds are the three ways betting odds are indicated. Let’s take a brief look at each within the context of this scenario: 

You are interested in betting on an English football match between Manchester City and Manchester United. The odds are indicated as follows:

Fractional odds:

Fractional odds are mainly used in the UK, but they are also the most popular odds in the world. They indicate the stake versus the total winnings. Therefore, if City wins, for every £6 you bet, you receive £4 back. And if United wins, for every £13 you bet, you will be paid £8. These figures do not include your original stake.

Manchester City: 4/6

Manchester United: 8/13

Decimal odds

These odds are popular on Continental Europe, Australia, New Zealand, and Canada. They are easier to read than fractional and Moneyline odds. As described below, you can instantly see who the favourite to win is, and well as the underdog.

Manchester City: 1.67

Manchester United: 1.62

The decimal odds also indicate your total payout, including your stake. Therefore, if City wins, for every £1 you bet, you will get £1.67 back. And, if United wins, for every £1 you bet, you will get £1.62 back

Moneyline odds

Moneyline or American odds are used in the USA. They are indicated as follows:

Manchester City: -250

Manchester United: +405

The minus sign indicates the favourite and the plus sign indicates the underdog. And the total payout is calculated in the following way:

To bet on City to win, you need to wager £250 to win £100. Therefore, your total payout will be £350. To bet on United to win, you need to wager £100 to win £405. Therefore, your total payout will be £505.

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