Countering the bookmaker’s margin - Part 2: Value betting
14 February, 2020

Our article about how the bookmaker makes money showed that bookmakers try to put some margin into every bet you make. Because of this margin, bookmakers are consistently in a position where they can buy low and sell high. As such, it should be obvious that finding ways of countering this margin is of the utmost importance for anyone aspiring to be a profitable punter.

In the first article about countering the bookmaker’s margin, we examined the benefits of using an odds comparison. We made the case that you can lower this margin by betting with multiple betting companies and shopping around for odds. Even so, for the vast majority of betting propositions, there will remain some margin you will have to overcome in order to be profitable. This means that to be successful at sports betting, you need a way to counter this remaining margin. In our opinion, the next step towards accomplishing that- is to understand the concept of value betting. This is why the focus of this article will be value betting.

The concept of value betting is vital for any punter with intentions of making a profit. Without a proper grasp of it, it is infinitely harder to make it as a non-recreational gambler. The few who are able to show a long-term profit- without a proper understanding of this concept- would almost certainly be able to make a larger profit if they utilized it. Fortunately, this is far from a hard concept to master, even if you are a newbie to sports betting.

Value betting is when you only place wagers on outcomes that, according to your analysis, have a positive value expectation. Positive expected value is found when the real probability of a betting outcome is greater than the probability expressed by a betting company’s odds.

If someone was foolish enough to offer you odds of 2.1 for heads in a coin toss and you knew that the coin did not have a bias for either heads or tails, you would obviously take up this offer. Why is that? The simple answer is that the betting proposition has positive expected value. This can be proven easily. If the coin has no bias, the chances for both heads and tails will be 50%. Remember, odds in the decimal notation are just the inverse of the percentage value. So a 50% chance corresponds to odds of 2.

100/50 = 2

2.1 is larger than 2.0, so obviously there is value to be had here. To calculate how much value is also very easy. All you need to do is to take the odds on offer and divide it by the correct odds.

2.1/2.0 = 1.05

The value in this betting proposition is 5%. If you could make this bet an infinite number of times, your profit should get very close to 5% of your total turnover.

Sports betting differs from coin tosses, card games and other betting propositions where it is possible to precisely calculate the real probability for the different outcomes. This is simply not possible for sporting events. The best any punter can do is to use various tools to estimate what he or she thinks the chance of any given outcome is. Conveniently the same holds true for the bookies, which is the reason why sports betting is an activity it is actually possible to be profitable at, even in the long term.

Even if it is impossible to precisely calculate the probabilities of the various outcomes, it does not mean that you should not try. To the contrary, you should use all means at your disposal and try exceptionally hard to do so. Unless you have a good idea of how likely the different outcomes are, it will be impossible to calculate if the bookmaker’s odds offer value or not.

Let us consider a concrete example. Tottenham played Liverpool in the Champions League final- in Madrid on 1 June 2019. Let us imagine that you are in possession of a brilliant stats driven model which, after careful analysis, arrives at a 23% chance of Tottenham winning, 27% for the draw and 50% for Liverpool winning. Converting this to odds is easy, as decimal odds are the inverse of the probabilities.

Tottenham 100/23 = 4.34782

Draw 100/27 = 3.70370

Liverpool 100/50 = 2.00

Now we will compare your odds with Pinnacle’s closing odds for this match:

Tottenham 4.18

Draw 3.63

Liverpool 1.98

As your odds are above Pinnacle’s for all three outcomes, it means that you do not see value in any of the three-way odds Pinnacle offers for this match. IF your estimations of the probabilities are correct, you would lose money in the long term betting any of Pinnacle’s three-way odds. How much you would lose is easy to calculate. You only need to take the odds on offer and divide them by what you think are the correct odds.

Tottenham 4.18/4.34782 = 0.961

Draw 3.63/3.70370 = 0.9801

Liverpool 1.98/2 = 0.99

The outcome which would lose you the least money for each unit staked – if your percentages for this match are correct – is Liverpool, which should lose you about 1% of your stake in the long term.

Luckily Pinnacle is not the only betting company in the world. When checking with an odds comparison site, it is visible that Coolbet, which ran a promotion offering 100% theoretical payback for this match, offered the following odds at kick-off:

Tottenham 4.45

Draw 3.77

Liverpool 1.96

As Coolbet’s odds are above your odds for Tottenham and the draw, it means that there are two bets that would win you money in the long term, IF your estimations of the probabilities are right:

Tottenham 4.45/4.34782 = 1.0235

Draw 3.77/3.70370 = 1.0179

IF your estimations of the probabilities are accurate, you could get 2.35% value from betting Tottenham and 1.79% value from betting the draw.

If you are very skilled at assessing probabilities, the above scenario is likely to take place regularly. You may not find value with Pinnacle’s closing prices, but you will often find value with some other betting companies. The problem with this is that most bookmakers are likely to severely curtail your betting limits as soon as they realize that you are not completely clueless when it comes to betting, and that it is not a given that you will be a long-term loser. As such, you are unlikely to be able to win substantial amounts from such bookmakers.

In its infancy my betting life was focused on the horse racing track. As a child attending the race track, I grew up in a deterministic betting school. At its core this school emphasizes that the important thing is to find the winner of the race. Value betting is not interesting or something one needs to consider. Champions of this school will make arguments like:

“If I can pick the winners of the races, the odds do not matter, as my bets will win.”

Proponents of this line of thought believe the outcome is already decided before the race has even started, and that there is a 100% probability that a particular outcome will happen. All that is needed is to work out which outcome it will be.

I strongly disagree with this. For me it is obvious that luck will influence the outcome of every horse race and, as a matter of fact, any sporting event.

There are not many certainties in life other than the fact that we will all die. As this is the case, it is of vital importance to adopt a probabilistic rather than a deterministic mindset to your betting.

Consider a race where one horse is far superior to the other horses in the race. Unless something strange happens, this horse is a certainty to win. However, perhaps another horse in the race will have an equipment malfunction and bump into a horse that is considered a certainty to win, causing this “certainty” to sustain an injury and not even finish the race. Maybe this far superior horse starts the race with a bad throat infection, causing it to perform much worse than it normally would, finishing in last place. Another day the race could be truly uneventful and this “certainty” may win by a country mile. These are only a few of an almost infinite list of reasons why we cannot talk about certainties, but rather probabilities for different outcomes.

Similar arguments can be made for all sporting competitions. Even considering how well Yohan Blake was running at the time, most people assumed that the 100-meter final at the Daegu 2011 World Athletics championship would be close to a walkover for Usain Bolt. Until Bolt was disqualified for false starting, that is.

There are not many certainties in life other than the fact that we will all die. As this is the case, it is of vital importance to adopt a probabilistic rather than a deterministic mindset to your betting.

In reality there will always be an element of luck involved, as there are no certainties in your betting life. What you are left with is assessing probabilities for the various outcomes and identifying value bets.

It is not important if you think a team or individual will win, but rather if you think that the betting proposition has a better chance of happening than the odds reflect, and whether you are good enough at assessing the chances of the different betting outcomes to take advantage.

To give an example, if someone offer you odds of 1.25 that both flips of a coin will not be heads and odds of 5.00 that both will be heads. It should be easy to decide what to bet on. The chances of heads both times are 25%.

50% * 50% = 25%

The chance of not-heads both times is 75%.

100% - 25% = 75%

As odds in the decimal format are just the inverse of the percentage, this means that the correct odds for heads followed by heads is 4.00

100/25 = 4

The correct odds for any other outcome are 1.333.

100/75 = 1.333

The expected value of betting heads and heads is a whopping 25%.

5.00/4.00 = 1.25

If you make such a bet you will lose 75% of the time, but the expected value is very good. If you bet and lose several times in a row, you should obviously not be thinking that you bet wrong. What you should be thinking is: how can I keep this going, how can I make the counterparty keep taking my action for this bet? You should also be considering if you are doing proper money management and if there is any chance that the coin can be biased after all. If you know that the coin is fair and that you are employing proper money management, your only concern should be to keep the counterparty playing.

Sports betting of the non-recreational kind is, at its core, a competition to see who can best assess probabilities for the various outcomes. Punters with a deterministic mindset will never understand this. The reality is that a substantial amount of punters are not even trying to assess the probabilities, but rather trying to work out what the result will be.

That it is impossible to establish the true chance of any outcome means that it is easily possible to apply the concept of value betting, but due to incorrect estimations of the probabilities for the various outcomes, to still lose money. This also holds true even in the long run.

However, you are very unlikely to lose money in the long run if you

  1. Estimate the various probabilities for the different betting outcomes - better than the betting companies/betting market
  2. Apply the concept of value betting and utilize some safety margin so that you stay away from the betting propositions that, in your estimation, only offer very marginal value
  3. Perform sound, conservative money management

To make a profit while value betting, you must not only grasp the concept of value betting, but also accurately identify value betting propositions. Unfortunately the latter is much harder than the former. To be able to identify value betting propositions you essentially need to be very good at assessing the probabilities for the various outcomes.

In the short run, value betting may seem rather trivial. It is easy to get caught up in whether the bet won or lost. After all, this is what will have an immediate impact on your bankroll. However, every bet you make will be influenced by random factors. In the short term luck is likely to have a more profound impact on your results than skill. Over time, as the quantity of bets increases, the impact of luck will decrease and the impact of skill, or lack thereof, will increase. This is because, according to the law of large numbers, the results of a large number of bets will likely get close to the expected value. In other words, luck has a tendency, over time and many bets, to even out. It is, however, important to note that many people tend to grossly underestimate variance, and that large samples of data are needed to make it unlikely that luck will not even out.

The concept of value betting on its own is far from enough to make you a winning punter. Even so, it is a very important concept to master as it will put you on the way towards becoming a winning bettor.


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