Probability Theory: Do Subjective Probabilities Influence Betting Odds?

Are you interested in learning how the art and science of probability theory influences the betting odds that a bookmaker offers on a specific match. As an aside, betting odds have very little to do with random guesswork.

An oddsmaker, or a specialist mathematician considers different elements such as the history of rivalry between the two teams or individuals, the history of all the matches played at the venue where the match in question will be played, the type of wagers offered, and additional aspects such as the home ground advantage, and the weather conditions forecast for the day of the match. In summary, all of these elements play a part in the eventual outcome of the event.

The role implied probabilities play in calculating betting odds

Implied probabilities and true chances play a fundamental role in the calculation of sports betting odds.

What is the concept of a true chance?

Succinctly stated, the phrase "true chance" translates into the probability or likelihood of an outcome or event occurring.

The simplest example of a true chance is the traditional coin flip. There are only two sides to a coin – heads and tails. Therefore, the probability or likelihood of the coin landing on heads is 50% and vice versa. And, if two people bet £100 each, one for heads and one for tails, the total value risked for every coin toss is £200. And, each person has the ability to win 50% of the £200 every time the coin is tossed. Therefore, the fractional representation of the odds of the coin landing on heads or tails is £100/£200 or 1/2.

Even though the implied probability theorem is a critical concept in sports betting circles, it is not only used in sports betting circles. It is also a crucial notion in the financial market trading industry where it is used to analyse stocks, options, currencies, and futures. However, the focus of this discussion is on implied probabilities within the sports betting context.

As described below, sportsbooks use implied probabilities as part of the betting odds calculation. Sportsbooks that offer bonuses, such as bonuses linked to the Bet365 bonus code, use implied probabilities to calculate their odds as well as the value of the bonuses they offer.

What are implied probabilities?

Simply stated, the implied probability is merely a representation of the traditional odds of one or more outcomes of a sporting event.

Let’s use our example of a coin toss again and change the payment regimen. This will change the implied probability ratios. As an aside, the percentages noted in the example represent the probability of an outcome occurring.

Let’s assume that the person who bets on heads to win gets paid £200 to the £100 for the person who bets on tails to win. The implied probability of heads winning is now 2/3 (£200/£300) or 66.66%. And the implied probability of tails winning is now 1/3 (£100/£300) or 33.34%.

Another example of how implied probabilities are used to calculate betting odds is to look at the odds of the three outcomes of an English Premier League football match. The three outcomes and the likelihood of each occurring are as follows:

Home win: 50%

Draw: 33 1/3%

Away win: 16 2/3%

In summary, there is a 50% chance of either team winning the match if they are playing at home. In other words, if the match between Liverpool and Manchester United is played at Liverpool’s home ground, Anfield, then the chance of Liverpool winning is 50%. Juxtapositionally, if the match is played at United’s home ground, Old Trafford, then Manchester United has a 50% chance of winning the match.

Additionally, if the match is played at Anfield, Manchester United has a 16 2/3% chance of winning the match. The same rule applies to Liverpool winning at United’s home ground.

Finally, there is a 33.34% chance of the match ending in a draw.

Another interesting point to note is that these three percentages add up to 100%. As described below, the house edge changes the total percentage from 100% to more than 100%.

Adding the house edge to the probability calculation

The house edge or bookmaker’s margin is the percentage that is added to the implied probabilities. If we look at the example of the coin toss cited above, the total probabilities will always add up to 100%, with 100% being the perfect outcome. When we add the overround, the total probability figure will always add up to more than 100%.

For example, let’s consider an American NFL match between Dallas and New York. The odds are listed as follows:

New York -3.5

Dallas +3.5

If we wager £110 on New York, our payout is either £210 for a win or £0 for a loss. Equally so, for Dallas. Therefore, our total payout is £210 and there are only two options (win or lose). Therefore, the implied probability of either Dallas or New York winning is 52.4% (£110/£220). And if we add these two outcomes together, we get a total of 104.8%.

To determine the house edge, we must subtract 104.8% from 100%. Therefore, in this scenario, the overround is 4.8% on each GBP wagered.

Subjective probabilities

It is important to briefly discuss the impact of what is known as a subjective probability on determination of betting odds by a sportsbook. It is human nature to have a personal preference when it comes to a favourite team or individual player. There are no calculations that can quantify what role subjective probability plays in our betting choices.

Finally, the question that begs is, what role does subjective probability play in the calculation of betting odds by the bookmaker and the oddsmaker? No one will ever know the answer to this question because a subjective probability percentage is abstract in its nature.

Final thoughts

This article is far from being the final word on probabilities and their impact on the betting odds calculation. If nothing else, it provides the starting point for the imperative to understand how betting odds are calculated. Without this knowledge, it’s virtually impossible to place successful bets.