Arbitrage Training

How to calculate probability, odds & payouts

Odds are only a representation of something more important

Odds are only a representation of something more important probability. Getting a handle on how to derive decimal odds from probability is the first step in developing your own assessments of sports betting value.

What do odds represent?

There is a conversation that all seasoned bettors will have had numerous times with friends and relatives who want a casual punt on a major sporting event. “What are the odds on x; what do they mean? what will I win if I bet x amount?”

Understanding probability

Understanding odds is the biggest challenge that anyone new to betting faces. What do odds actually represent and how can you simply understand what return you might get for a given stake? Once you get past that hurdle, it is liberating to start comparing odds between bookmakers, but to consider sports betting to be just about odds is to miss the bigger picture. To really expand your understanding of odds and betting you need to understand probability.

Sports Betting is about assessing the chance or probability of an event happening and bookmakers like Pinnacle use odds to translate probability into a more usable form in order to offer betting. The fact that there are many different odds formats – decimal, fractional, money line – illustrates the point that odds are simply a means to an end i.e. offering betting. Bookmakers really deal in risk measured by probability.

Considering how we are faced with risk every single day of our lives – what are the chances of me making that train on time? how likely is it to rain? – it is surprising how unfamiliar the average person is with basic probability. It is a scale running from 0 – where there is no chance of an event occurring – to 1 – a certain future event – with the likelihood of all other potential events falling somewhere in between those points on the probability spectrum.

This article is an expansion of one our helpful videos, which shows how to calculate odds, probability and payouts in just two minutes.

A coin-toss is a great way can to explain how to calculate probability. The coin will definitely land on either Heads or Tails, which taken together provide us with the certain event, which we now know has a probability of 1.

Of course as a bettor what you really want to know is the probability (or chance) of your chosen call, which we will say is Heads. To do this there is a simple equation:

Probability = favourable outcomes / all possible outcomes

A favourable outcome is essentially one that you want to happen because you are going to gain. For your coin toss that is your call – Heads – which you divide by the two possible outcomes – Heads or Tails – to produce a probability of 0.5.

1 (Heads) / 2 (Heads or Tails) = 0.5

In general people are more comfortable with percentages, so by simply multiplying the probability of your event (0.5 for Heads) by 100 you can say that there is a 50% chance of the coin landing on Heads, and you winning your bet.

Now you know how to calculate probability, you can turn this into the form of odds. Decimal odds are the default format used by bookmakers like Pinnacle, and you can arrive at the Decimal odds value for your coin toss choice with the simple equation:

Decimal odds = 1 / probability for your chosen outcome

So the Decimal odds for a coin being Heads is 1 (Certainty) divided by the probability of it occurring which we know is 0.5, producing decimal odds of 2.0. At this point you can equally take odds and reverse engineer the implied probability with the inverse of the equation for turning probability into odds:

1/decimal odds = probability

Moving from implied probability to value

In a short space of time we are getting into interesting territory. Take your newly found knowledge and work out the implied probability for your coin toss with your friend and you’ll see the aggregate implied probability of both outcomes in the coin toss is 100% – (0.5/1+0.5/1)*100 – no surprises as a certain event is 1 (100/100).

However, performing the same calculation for actual odds from your favourite bookmaker will produce a value greater than 100%. So what is happening here? In simple terms the odds don’t reflect the true likelihood – the probability – of the outcomes concerned. The amount by which the implied probability diverges from 100% is the edge your bookmaker holds for that market, and essentially measures the value they are providing. This is an essential piece of information for a value seeking bettor, is easy to calculate but few if any bookmakers publicly share it – other than Pinnacle. It is worth asking yourself why that is?

Calculating odds and probability opens up a whole new world for calculating value but you also want to know what your bet will payout for a bet. For our coin toss example this requires a simple multiplication:

Payout = Your stake X decimal odds

So if you bet $10 on Heads with odds of 2.0 your return including stake is 2.0 x $10 which equals $20 (This includes your $10 stake + $10 profit).

Understanding where odds actually come from is an essential part of evolving as a bettor because it enables you to calculate your own expected frequency for an event – starting to model your own odds – and then compare what you think will happen with what odds are available. Where the two diverge you can potentially turn that edge in your favour, and generate profit, which is whatever bettor should be focused on.

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