What are odds? The right way to look at odds for sports betting

If you still wonder what odds really are and how to really understand it, look no further. We will give you a walk through of what odds are and how this applies to betting in general.

Andrew and Bobby.

Andrew and Bobby.

In most places related to sports and betting you will see the odds of a team winning rather than the probability. The reason you will see odds instead of probability, is because the odds tells you how much you would be winning if you placed a bet on a given odds. E.g. if you bet 100 on 2.00 in odds, you would be returned 200 if you won. One could have used probability instead to describe how likely it was that you would win the bet. But then it would not be as clear how much you’d win if you bet $100. The relationship between odds and probability is that odds = the inverse of the probability (odds = 1 / probability). If one is betting on the true margin free odds of a bet with 2 outcomes, e.g. a coin flip, you would expect to break even in the long run independent of which side of the bet you chose. Let’s use an example to show that this is true. 

We use the example with Andrew and Bobby. Andrew (A) wants to bet with Bobby (B) if he hits the crossbar or not. Historically he hits 4 out of 5 times and misses 1 out of 5 times. This would give the corresponding odds of 1/(4/5) = 1.25 for a hit and 1/(1/5) = 5 for a miss. Andrew wants to bet 100 dollars on himself hitting the bar, so he then asks Bobby what odds he can give him. Bobby knows the math so he says he can give him an odd of 1.25. 

Andrew have now bet 100 dollars on the odds of 1.25 giving him potential return of: 125 dollars or a profit of 25 dollars. 

Bobby have now bet 25 dollars on the odds of 5 giving him potential return of: 125 dollars or a profit of 100 dollars.  

Andrew and Bobby with the crossbar.

Andrew and Bobby with the crossbar.

If they were to do this over a period of time, let’s say 5 times, based on the probability it should go like this.

If they were to do this over a period of time, let’s say 5 times, based on the probability it should go like this.

In a sample size like this of only 5 kicks to hit the crossbar, this would generally not happen because the variance (or standard deviation) is too high. But when you do this over a large sample size, say he is kicking the ball 100 000 times, the variance becomes smaller and the probability that is reflected in the odds correlates much better with the probability for the real events. If this is confusing you should read more about the law of large numbers.

It is important to notice that they would break even only for events where the odds and probability relates to each other 1 to 1.

 

Bobby gets a downgrade in IQ.

Bobby gets a downgrade in IQ.

Bobby now gets a downgrade in IQ, so he does not understand the math. Andrew then asks again what odds Bobby can provide if he wants to bet 100 dollars. Bobby says he would give him 1.5 for hitting the crossbar, essentially giving himself the odds of 3. These odds relate to each other 1 to 1, because the probability in total equals 1:

 

1/1.5 = 0.667 while 1/3 = 0.333

0.667 + 0.333 = 1

 

But, The odds do not relate 1 to 1 with the underlying probability. If the odds were to relate to the probability, we would give the odds of 1.25 and 5 as in the last example. Let’s see what happens with 1.5 and 3 in odds:

 

Andrew is still betting 100 dollars with a potential return of: 150 dollars or a profit of 50 dollars. 

Bobby is betting 50 dollars with a potential return of: 150 or a profit of 100 dollars.  

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As we can see A wins, while B loses in the long term. This is because the odds of him hitting the bar is overvalued (or the underlying probability is undervalued) while the odds of him missing is undervalued (or the underlying probability is overvalued). When the probability is undervalued it means that the event happens more often than the probability suggests as reflected in the odds

How overvalued and undervalued odds and probability works together.

How overvalued and undervalued odds and probability works together.

 

But then you might want to ask: But no sports match is the same, so how is this applicable to the real world? Well, over a vast amount of games there is large evidence for the probability to be reflected in the odds. If you want to read more about it, check this article out

 

Key takeaway

Odds and probability are in theory really just two sides of the same coin, but in practice the case is different. This is because (soft) bookmakers usually offer unfair odds, which do not reflect the underlying probability. This is the way the bookmakers make money, so it is important to understand that the odds at the bookmakers almost never reflect the underlying probability.   

Do you know the different odds types? 

We have written articles explaining them: