The experiment was prompted by the outbreak of the coronavirus and the fact that many leagues suspended their games for a period of a few months and afterwards resumed in empty stadiums. We wanted to see whether historical statistics could still be used and what could be observed after this unexpectedly long break.

The General Outcome of 25 Betting Rounds and 77 Bets

The bank grew from an initial figure of 3,000.00 units to an impressive total of 4,617.56 using ratcheted stakes during the course of just one month.

It was very pleasing to see that the Cluster Tables performed so reliably well despite the coronavirus outbreak and the consequent very long pauses in our featured leagues:

Table 1: Corona experiment July-August 2020
Profit/Loss graph after 25 rounds

During this 33-day period a total of 77 bets were placed within the 60% to 80% probability range.

Here’s the distribution of those bets and the Profit/Loss achieved split into clusters of 2% probability increments:

Table 2: July-August 2020 – Over/Under experiment P/L results graph by Probability

From the above chart, you can see that all but one of these clusters produced a profit. However, the number of bets varied in each cluster. For example, there were four bets with a probability between 60% and 62%, and nine bets in the 62% to 64% cluster, and so on.

77 bets is a very small sample size and this becomes even smaller when trying to form conclusions about each of the 2% clusters. However, this is a practical way of maintaining control if you are using the Cluster Tables for your own betting.

Indeed, for monitoring purposes, we recommend that you do sort your bets in small probability clusters and judge the synergy of your portfolio on the basis of its entire performance. You will find it easier to make decisions if there are obvious areas that are letting down the results.

How the Bets were Chosen

The bets were chosen using our Cluster Table tools that are the product of our coursebook teachings. With these tables, you can very quickly determine the expected probabilities of Over/Under bets for any forthcoming match involving the featured teams (i.e. only those playing in at least their sixth consecutive season in that league – identified in the tables).

To help explain how the bets were chosen, here’s an example using the very last pick of our experiment:
Sassuolo vs. Udinese on 02/08/2020

Below is an extract from the Cluster Table used to make this pick:

Table 3: Calculating the Over/Under bets
Sassuolo vs. Udinese 02/08/2020

Sassuolo was the favourite to win the game at odds of 1.95; Udinese was the underdog at odds of 3.84 (odds taken at 06:57 GMT+1 on the day of the match).

With these odds, the HO/AO quotient was calculated:

Using the 2019/20 Cluster Table for Italy, the over and under probabilities for Sassuolo home matches and for Udinese away matches were found using the appropriate HO/AO cluster containing the value of 0.5078.

These percentages were then copied into an extra ‘helper’ spreadsheet (i.e. the two top lines of the tables on the left).

Using the two probability percentages collected from both teams, the average was calculated (Over 0.5 bets example):

This percentage was then converted into the expected Zero odds:

This process was then repeated for all Over/Under bets.

The third line of our helper spreadsheet is for manual entering of the market odds being offered for these bets.

As we were limiting ourselves during the experiment to bets within the 60% to 80% cluster, there was no difficulty choosing the bets for this particular match as there was only one visible within this probability cluster. The bet ‘Under 2.5 goals’ with a probability to win of 68.2% (corresponding Zero odds: 1.47) was being offered at outstandingly good odds of 3.10.

By the way, this bet won as the match ended in a 0:1 result. Of course, there was an element of ‘luck’ involved as on paper it also had a 31.8% probability of losing. Also, the expected ‘Profitability’ as well as the expected ‘Yield’ were artificially high, which would normally have led us to dismiss this bet as viable.

I will summarise these two very important considerations next in the article but if you wish to understand the concepts of profitability and yield in more detail, buying and working through the coursebook is your only option. It simply is too vast a subject to summarise in an article and is not the sort of information I wish to give away for free

Further Reading:
How to Use Soccerwidow’s Over/Under Betting Cluster Tables
5 Simple Steps to Win Over and Under Betting

Profitability (Value I)

Profitability is the relation of profit/loss to the money spent. In other words, profitability is an index for measuring financial success (operational profit) in relation to the costs (money spent) of running the venture.

When applied to gambling, profitability measures betting proficiency in relation to its expenses.

Profitability Formula:

If you wish to learn a little more about what profitability in betting means, here’s an article with the definitions and some example calculations: Stake, Yield, Return on Investment (ROI), Profitability – Definitions and Formulas

The nice thing is that it is actually possible to predict the expected profitability if you have calculated the Zero odds and know the market odds of the bet you are thinking of placing.

You can see the results of these calculations in Table 3 (Sassuolo vs. Udinese calculations) in the row below the market odds. Try to come up with these numbers yourself!

Of course, all these calculations are about probabilities and a future outcome; they aren’t set in stone and results always come with a deviation. I cannot dive deeper into the matter of deviation at this stage but once again recommend the coursebook, where you will find almost a third devoted to explaining this quite difficult topic in step-by-step detail.

However, what we will look at here is the graph of the distribution of Profit and Losses from our Over/Under experiment by expected Profitability.

For those of you who didn’t follow the experiment as it progressed… During July 2020 we published almost daily Over/Under picks with probabilities between 60% and 80%.

Often, there would be only one bet apparent in this cluster (like in the example Sassuolo vs. Udinese) and we would choose this bet without taking any ‘value’ into consideration or worrying about the expected ‘Profitability’ or expected ‘Yield’.

Indeed, the profitability and yield might have carried negative values, but the picks would still be included in our portfolio and published.

The reason for this is that when you calculate Zero odds and consider the deviation, the market odds may be higher or lower but still be ‘fair’.

It seems like a paradox but having negative ‘value’ attached to a bet calculation doesn’t mean that it is a bet without ‘value’.

Table 4: July 2020 – Over Under experiment P/L results graph by expected Profitability

You can see from the graph above that at its beginning the P/L curve wanders around the -200 mark and then starts rising. The starting point for the rise is around 95% and it stops at -40%. This can be used as a knock-out criteria when selecting bets to place:

Advice for those of you who are actively using the Cluster Tables for investment purposes…

If you wish to play a similar system to the picks showcased in our experiment, then please choose your bets by sticking religiously to the 60% to 80% probability cluster and use the expected Profitability as a knock-out criterion.

If you have only one bet in this probability cluster, and it carries an artificially high profitability value like the one shown in this article (Sassuolo vs. Udinese U2.5 goals), then you need to make the tough decision whether or not to play the bet or leave it alone.

Yield (Value II)

Yield is the Profit/Loss ratio applied to the total capital employed (total staked). When applied to gambling, Yield measures betting effectiveness compared to total turnover. (The interest received from securities, i.e. stakes)

Yield Formula:

In football betting, any yield over 7% is considered to be a very good result. Be careful when you hear people talk about their betting strategies or offering betting systems for sale with a high yield. This is intended to impress the reader, but a high yield is always an indication of high-risk strategies employed!

Like with the expected profitability in the section above, it is also possible to calculate the expected yield simply by having calculated the Zero odds and knowing the market odds.

Please have another look at Table 3 (Sassuolo vs. Udinese calculations) in the row below the Profitability. Again, see if you can match these figures with your own formulas or calculations.

Once again, high yield systems mean high risk. Usually, you will need to play many bets to move forwards with systems of this nature. The reason is simple: High risk means low probability and that means a very irregular distribution of winning bets – and lots of losers along the way!

You can see this for yourself in the graph below, which represents the experiment’s distribution of Profit and Losses by expected Yield:

Table 5: July 2020 – Over Under experiment P/L results graph by expected Yield

You’ll see from the curve that expected Yield over 30% didn’t produce any profits and neither did an expected Yield below -15%. That there even was a negative expected Yield is because of deviation.

This factor can be used as a second knock-out criteria when choosing bets:

Advice for those who actively use our Cluster Tables…

Don’t take our guidance here as gospel. Of course, you can choose whichever probability clusters suit your personal acceptance of risk. You don’t need to stick religiously to the 60% to 80% range that we used in this public experiment.

But, ideally, what you then need to do is to select only matches in your chosen clusters (you can do this retrospectively) and analyse their performance by expected Profitability as well as expected Yield. In doing this, you should then be able to build your own knock-out criteria and adjust accordingly.

I really hope you enjoyed this article and learnt something along the way. Please don’t hesitate to ask any questions in the comment section below.

Lastly, keep faith in statistics! Despite the pandemic, every league will continue playing on a professional level and hence, past statistics can be applied to predict future performance. How else do you think bookmakers set their odds?

Note:
And if you need further incentive to investigate our Cluster Tables further, don’t forget that the 169-page Odds Calculation coursebook comes with a free German Bundesliga Cluster Table. Buy the coursebook, snap up a bargain in the process, and begin betting on the over/under markets straightaway!

“I have a question for you since your strategy in the German Bundesliga was Underdog Whole Season, why do you show only Home Underdog bets in the system’s performance?”

So, why?

The answer is very simple: Because the HDAFU Tables identify Value Bet clusters. Although an HDAFU Table may be perceived as a ‘System Betting’ tool the most profitable historical betting clusters are the ones packed with Value Bets. And in the German Bundesliga, in the last five seasons (and beyond) these have mostly been home underdog bets.

It doesn’t matter which angle you approach betting from, to make a stable profit you must always ensure ‘value’ is on your side.

You may now ask Why do certain clusters of the HDAFU Tables contain Value Bets?

To shed light on this you really need to understand…

How do Bookmakers Set their Odds?

The bookmaker trade is a business aimed at making profits like any other business. Although they claim that their odds are ‘fair’ this doesn’t implicitly mean that their odds represent the ‘true’ probabilities of each event occurring.

Something classed as being ‘fair’ means only that it is carried out without wishing to cheat or to achieve an unjust advantage. However, it is neither ‘cheating’ nor ‘unjust advantage’ to optimise profits, is it? Otherwise, you could blame every profit-making company for setting ‘unfair’ prices only because they calculate with high-profit margins.

Take the example of a popular team like Bayern Munich. Playing at home, they win approximately 85% of their matches give or take every season. The ‘true’ average odds should, therefore, be in the region of 1.18 (1/85%). However, with the weight of money (the majority of bets being placed on the most probable winner), the bookmakers can reduce the odds on Bayern to win, say, to 1.15, increasing their profits in the long run, but still offering ‘fair’ odds on a match to match basis.

Of course, this also applies to Bayern’s away games. When playing away, Bayern wins approximately 65% of their matches, which in odds is 1.53 (1/65%). However, the average odds offered by the bookmakers for Bayern to win away are 1.44. That’s a clear and significant reduction. Are you with me?

Now, let’s dive a little bit deeper into odds calculation to help you understand what makes the HDAFU Tables so very special…

Changing One Side Affects the Other Side

To show you the above illustration in numbers we will look in more detail at one of the Bundesliga matches in our 2017-18 Winter League Report.

On the 9th September 2017 Bayern played away against Hoffenheim. Bayern’s ‘true’ chances to win that game were 47.78% (see Value Calculator results below):

The ‘true’ odds corresponding to a 47.78% probability are 2.09 (1/47.78%).

The problem bookmakers probably had with this particular game, especially if they would have offered odds in the region of 2.09, 2.0 or even 1.9 for Bayern to win, is that there wouldn’t have been enough bets on either of the two other possible results, the home win and draw: The book would be unbalanced with the bookmaker facing a huge potential liability if Bayern were to win.

Football followers with a low understanding of probabilities know that Bayern, even playing away, will probably win the match. Regular punters would be expecting odds in the region of 1.5 or 1.6.

Odds around 2.09 would have encouraged far more money on Bayern as punters would have perceived the odds as an opportunity to cash-in on ‘higher than normal’ odds for a Bayern away win.

Therefore, to avoid too many bets on this outcome the bookmakers were literally forced to reduce Bayern’s odds to match public expectations.

So, instead of pricing the odds close to their ‘true’ probability of 47.78% (in odds: 2.09), the bookmakers had to offer the away win close to the ‘expected’ probability (65%). Hence, they offered odds for Bayern to win of 1.46 – an implied probability of 68.5% (1/1.46).

Of course, Bayern’s statistical chances didn’t suddenly increase by 20% to win that match, although the odds offered may have swayed people into believing this.

Probabilities: Home Win + Draw + Away Win = 100%

Statistically speaking, the sum of the probabilities for any match outcome is always 100%; it is either a home win, a draw or an away win.

Therefore, if the odds (applied probabilities) for an away win are changed due to market pressure, it naturally affects the draw and home odds (implied probabilities).

In this example:

• The ‘true’ probability for Hoffenheim to win of 24.5% (in odds: 4.07) was reduced to 14.9% (odds increased to 6.72)
• The ‘true’ probability for the draw of 27.7% (in odds: 3.61) was reduced to 20.3% (odds increased to 4.92)
• The ‘true’ probability for Bayern to win was increased from 47.8% (odds of 2.09) to 68.5% (odds reduced to 1.46)

In this example, the ‘underdog’ at home (Hoffenheim) became even more of an ‘outsider’ and hence a Value Bet (the price offered was much higher than that of its statistical probability).

Just as a side note, Hoffenheim won the game 2-0

The HDAFU Tables Help You to Discover Value Bet Clusters

As shown in the example above there was a clear gap between public expectations and the ‘true’ probabilities, which literally forced the bookmakers to adjust their odds for Bayern, who were shown as a much stronger away favourite than they actually were.

In the EPL the same can be said of the Draw expectation; in Italy, it’s the Away Win and so on. For specifics, you will have to dive deeper into the analysis of the 2017-18 Winter League Report, where the patterns in the leagues chosen for that season are revealed.

Each league has its own betting patterns and punter preferences and the bookmakers react accordingly.

What makes the HDAFU Tables so special is that they highlight where the odds or HO/AO (home odds divided by away odds) clusters are profitable for the bettor if bets are placed constantly and consistently within the parameters of these clusters. The majority of bets made within these clusters are Value Bets.

So, just remember: There is a public expectation of match outcomes and the bookmakers react by reducing or increasing odds and balancing these changes by changing the odds for the other two outcomes. It’s as simple as that.

Time Saving ~ Risk Diversification ~ Value Betting

Value Bettors who calculate each game individually will find it very challenging to identify enough bets for each weekend to diversify risk sufficiently enough. Every match requires time to be analysed.

The calculations for just one match and checking its bets for viability could take as long as two to three hours. If you’re adept at using our Value Calculator, one match might take you 15-20 minutes to analyse. Even then if it takes only 25 minutes per match in total to identify, choose and place a single bet, if you want a Saturday portfolio of at least 15 matches for diversification, it’s going to take you more than six hours to achieve – every Saturday.

With the HDAFU Tables life is much easier. You don’t need to carry out any individual calculations once you have identified the profitable clusters and checked them carefully before you start placing real bets – and you only need to decide upon your systems once (whole season systems) or twice (half-season systems) per season. Once you have prepared a large enough and diversified portfolio of systems from different leagues, you can let the statistics do the work for you.

Of course, an additional finishing touch for those of us with time when compiling the weekly portfolio of bets is to cross-check those highlighted by the HDAFU Tables (portfolio builder) against the Value Calculator (individual match investigator) and ensure that the majority are actual Value Bets on the day.

One thing you can take for granted is if a cluster has been packed with Value Bets during the previous five seasons it’s likely that the same cluster will continue to churn out Value Bets in the following season.

Many thanks, João, for your question and I hope this article helps clarify things for a wider audience!

What does this have to do with betting?

Image: FXQuadro (Shutterstock)

We speak about ‘Inflection Point graphs’ in our HDAFU Profit/Loss simulations because these graphs have turning points. Turning points are points at which a significant change occurs.

In layman’s language – Turning points are the points in the ‘inflection point graphs’ where profits turn to losses or, where losses turn to profits.

For the mathematicians amongst you, we use the term ‘turning point’ although the academically correct mathematical expression would be ‘maximum’ and ‘minimum’.

However, ‘maximum’ and ‘minimum’ in normal language signifies ‘best’ and ‘worst’ but turning points in a curve have nothing to do with any judgement of being ‘good’ or ‘bad’.

Apologies for any academical incorrectness in the use of the terminology, but somehow we have to make ourselves understood by everybody…

Home ~ Draw ~ Away Profit/ Loss Curves

If you have ever calculated your own odds you will certainly have noticed that bookmaker prices often do not show the ‘true’ picture.

In other words, their odds seldom adhere to mathematically calculated values (the statistically expected values).

In the majority of games, odds are either higher than mathematically expected or lower…

Is That Really True? Can You Prove That?

Here’s an image showing the Profit/Loss Curves for betting on the Home win ~ Draw ~ Away win with equal 100 units stakes over a period of five seasons; the straight red line is the bookmakers’ profit trendline:

English Premier League – Profit/Loss curves by ODDS for 2013-14 to 2017-18 seasons

What you can see in the above graph is that if one curve rises, e.g. betting on the away win if the home odds are between 1.7 and 2.15 (orange curve), then another curve falls.

In this example, betting on the draw (brown curve) produces a loss for the bettor and hence, a profit for the bookmakers.

What is most revealing in the above graph is the red curve. It shows how the bookmakers profits vary depending on the home odds, but the most interesting part is the straight line, the red trendline. It is positive for all odds and perpendicular. The interpretation of this is that for the bookmakers it doesn’t matter in which cluster a particular match is in (in the example, home odds), their odds guarantee them the same constant profit across the whole spread.

Why Is This So?

A bookmaker’s aim is to make a profit and they price their odds to ensure that sufficient action is taking place on both sides of a bet, with enough profit retained whatever the outcome.

In addition, bookmaker betting odds are often adjusted according to public opinion to guard against a disproportionately large amount of money being placed on just one side of a bet.

How can the Bettor Make Use of This Knowledge?

The bettor can take advantage of the knowledge that each betting market contains certain odds clusters that are regularly under-priced, whilst other odds clusters are habitually over-priced. But attention, please! These under- and over-priced clusters are different from league to league.

Bookmakers take into account gamblers’ preferences and these vary depending on the cultural background (e.g. risk-aversion) of the locals. This is perhaps because local bettors are the majority takers for any league bookmakers, so bookmakers take local tastes into account.

It is obvious that, for example, Italians will be betting primarily on Italian matches; Spanish people on Spanish matches, and so on.

However, please be aware that the EPL, the most prominent league in the world, naturally has a huge amount of supporters worldwide. This makes the EPL the most unreliable league (system betting-wise) in terms of its odds. Although odds patterns can be spotted easily, it is always a gamble whether or not they will be returning a profit the forthcoming year.

Nevertheless, for this article, we will use the EPL as an example.

The Significance of the Turning Points on the Inflection Point Graphs

Profit turning points can be easily spotted in the Inflection Point tabs of the HDAFU Simulation Tables using visualisations (see example below) in the form of Profit/Loss curves based on five seasons’ data within these tables.

For example, the EPL: Between 2013-18, if you had gambled unemotionally and systematically on all English Premier League matches to be away wins (at the highest bookmaker odds) and placed a constant stake of 100 units per fixture, then at the end of the fifth season, you would not have seen a large change in your bank: -125 units after 1,900 bets.

Huge losses would have been incurred, had you backed all of the away teams to win and limited your betting to the zone of odds between 2.31 and 4.53. Within this zone your losses would have totalled -9,189 units (3,714 plus 5,475).

However, if your strategy had been based on away wins at odds from 1.68 and up to 2.31, after five seasons your profit would have been 3,202 units (7,714 minus 512).

That’s quite a difference, isn’t it?

English Premier League – Profit/Loss curve for 2013-14 to 2017-18 seasons

Just as a side note… Can you see yourself betting on an EPL match targeting odds between 2.3 and 4.5 when backing the away win?

Different Leagues = Different Inflection Points Graphs

The above screenshot shows the Profit/Loss curve for the EPL if back bets on the away win were placed on all 1,900 matches between 17/08/2013 and 13/05/2018 (at 100 unit stakes).

You can see from the graph that the first turning point is located at 2.31 on the ‘away odds’ axis. At this point, the P/L curve reaches a peak of 3,714 units profit before starting to fall again. The decrease in profits continues until away odds of 4,35 are reached (P/L value: – 5,475 units), where the curve turns for a spell but remains negative until away odds of 9.5 are reached. Then it experiences a large jump before falling again.

Now, we compare this to the German Bundesliga Inflection Point graph:

German Bundesliga 1 – Profit/Loss curve for 2013-14 to 2017-18 seasons

You can see at a glance that both graphs are very different.

Whilst the EPL shows a rising curve (profits) until odds of 2.31 the Bundesliga P/L curve starts to drop straight away from odds of 1.4.

This indicates that the bettors on the Bundesliga are probably much more risk-averse than EPL bettors and it seems that they prefer betting on favourites (lower odds). Using this mentality bookmakers can reduce their odds in this group to optimise their profits and hence, the draw odds and/or home odds are likely to be increased.

Once you start working with inflection point graphs you will not only see the various profit /loss curves (whole season, 1st half and 2nd half) and start recognising patterns but you will be also amazed to learn about the different mentalities of bettors in different countries.

Working With the Inflection Points graphs using the HDAFU Tables

Here’s a handy little tutorial:

How to Use the Knowledge of Turning Points

(1) check your betting pattern

Do you recognise your betting patterns within the most common odds clusters; those which show a falling Profit/Loss curve? (For example, betting on odds between 2.3 and 4.5 when backing an away win in the EPL).

If so, perhaps reconsider your strategy and avoid the odds used by the bookmakers to make their profits. Of course, no matter how hard you try, betting in the zones where bookmakers habitually reduce prices (odds) is asking for long-term losses.

It is very rare for people to succeed in any walk of life by swimming against a strong current and you can safely assume that the bookmakers know their job and have for centuries been making a living from manipulating figures.

(2) don’t even try to “beat” the bookies

Swim along with them. ‘Play’ the market the same way as they do. Start looking at strategies which are not in conflict with the market, but in rhythm with it.

(3) be aware that each league has a different market behaviour

Customs and habits of people vary from country to country. Every nation has different culture or cultures. Surely everybody has noticed regional differences expressed in such tangible goods as food or housing. However, these differences extend into how people think and act.

Unfortunately, differences in betting patterns and the subsequent reaction of bookmakers when setting their odds cannot be spotted without taking a mathematical approach. Customer habits, especially in the betting market, remain well hidden from the bettor.

Whichever league you prefer betting on, identify the odds clusters which are utilised by the bookmakers to turn their profits – and then work around those clusters.

(4) use the market turning points for your own benefit

Concentrate on developing your personal betting strategy by taking the market rules into consideration.

(5) find a strategy and identify matches for producing long-term profits

Using the HDAFU simulation tables and finding the various turning points will provide you with the need knowledge of odds clusters you need to produce a long-term profit when backing.

If you already use our Value Bet Detector for calculating odds for individual matches then the knowledge of profitable odds clusters will help you to pick matches which are worthwhile re-calculating.

Of course, bookmakers are in the business of setting odds and determining prices which are offered for certain betting events.

If I had to use just one word to describe how bookmakers think…

Image: Cartoonresource (Shutterstock)

When viewing odds in betting exchanges such as Betfair, Betdaq, Smarkets, or WBX, you should understand that it is neither the exchange platform or the traders using them who set the odds.

The fact is that the bookmakers are used as the market guide for traders on the betting exchanges, and it is the bookies who compile and publish their odds weeks in advance of the events in question (sometimes even months), and certainly well before the exchanges even open their markets for trading.

If you have ever calculated odds you will have noticed that the bookmakers’ offers often do not represent the ‘true’ picture, in other words, the ‘true’ mathematically calculated values (the statistically expected values).

Only occasionally (probably in less than half of all cases) are odds close to the statistical expectations of the betting event. However, in the vast majority of games, odds are either considerably higher than mathematically expected or far lower…

Why Is This So?

You have to appreciate that bookmakers do not really intend to predict an outcome (correctly). If you enjoy statistical analysis, then take a little time to do a simple calculation for any league of your choice. Simply convert bookmaker odds into probabilities and compare them to the actual distribution of the results.

Bookmakers have been around for thousands of years in one form or another. Their main goal is of course to make a profit. They price their odds to ensure that sufficient action is taking place on both sides of a bet.

If a bookmaker’s betting odds are not aligned to public opinion then a disproportionately large amount of money will be placed on only one side of a bet. This would be a gamble for the bookmaker. However, bookmakers are not in the business of speculating on an outcome.

The role of bookmakers is, strictly speaking, rather the function of an intermediary, similar to a stockbroker. They take money from various people on various outcomes and after the game is finished they pay out the winners.

In return for this service, the bookies take a “fee” known as the overround.

The bookmakers’ priority is balancing their books

The closer to the kick-off of a game, the more ‘fluid’ the odds become, as salient information such as team news becomes public knowledge, and this then has a knock-on effect with bettors’ opinions being confirmed or changed on the outcome of the match in question. Thus, the odds tend to change more as the start of the match gets nearer and nearer and more money changes hands.

Always remember

1. Bookmakers set odds based on a mixture of statistical probabilities and public opinion.
2. Bookmakers do not speculate (gamble). Their priority is balancing the books.

In an ideal world, bookmakers would like to see the same amount of money (risk) on both sides of a bet outcome. However, utopia is virtually unknown in the world of bookmaking and firms are rarely able to equalise their level of risk on both sides.

Therefore, you will often see a bookmaker adjusting his odds for an event over time. This fluidity aims to achieve an acceptable money line on both sides of the bet outcome.

Please note! Because it is rarely possible to “equalise” the risk on both sides, bookmakers instead look for an “acceptable” level of risk. This is the only ‘gamble’ bookmakers take.

How do Bookies Manage their Risk?

You will have certainly noticed the plethora of various betting offers used by the bookmakers to woo their customers. Unsurprisingly, these are the bets where they expect to make the highest profits (for example, pushing accumulator bets with offers such as, “If team A (usually a short priced favourite) is the one which lets down your five fold, we will return your stake!”) (how generous of them!!).

Bookmakers apply all kinds of marketing tricks to divert the sports bettor into a direction which is most profitable; for them but not for the bettors!

I risk repeating myself but the truth is that bookies’ odds never aim to predict an outcome of a match with utmost accuracy (therefore the calculated probabilities of ‘true’ odds often do not match the betting odds offered in the market). A bookmaker’s main goal is to balance the books and to do this, public opinion is taken into account.

This is the key to bookmaking success. This is the key to sports betting success.

Of course, each sport is different, but in the end bookmaking methods are always the same. Bookmakers make money with these same methods, regardless of the sport or other type of betting event.

• Their books are not perfect.
• They do not have a crystal ball.
• Bookmakers have a business plan!

The bookmakers’ mantra is very simple:

Calculate the statistical chances of the matches for a weekend and set the odds by taking into account the probabilities and public opinion. Collect enough money to pay off losing bets. Keep the profit.

Learn from the Bookmakers!

Bookmakers are not able to balance their books for each single game. To them, it is always about “acceptable” amounts of money (profits or losses) and spreading risk.

The goal of bookmakers is not to predict the outcome of a game correctly. This means that their odds often do not reflect the expected probability distribution.

Bookmakers’ odds usually reflect public opinion about a match and their primary objective is to ensure a well balanced book.

If you wish to become successful with any form of betting you must understand the way of thinking (the business plan) of the bookmakers.

Why? Because these firms survive and thrive from the money they encourage you to lose through nothing more than your own ignorance of how their ‘system’ works.

Image: archideaphoto (Shutterstock)

‘1X2’ is an abbreviation of the three possible outcomes in a football match: home win (1); draw (X); away win (2).

This market is also known as ‘HDA’ (Home-Draw-Away), or sometimes simply ‘FT’ (Full-Time match result).

The act of 1X2 betting is referred to as “betting on the full-time result”, “match betting”, or can be termed a “three-way bet”.

Definition of ‘Full-time’

Full-time is reached in a football match at the close of the second half of 45 minutes’ regulation time plus the time added-on by the officials for stoppages. When the added-time has elapsed, the referee’s whistle signals the end of the game.

All 1X2 (HDA) bets relating to the result of the match then begin to be settled by the bookmakers.

In a fixture requiring an outright winner, in the event of a draw or tied aggregate scoreline at the end of the regulation match time, two periods of extra-time may then be played to break a deadlock.

It is important to reiterate that full-time 1X2 bets are closed and settled on the result at the end of a regulation period of 90-minutes’ play (2x 45 minute halves, plus added time), and after this, new markets will then appear in most bookmaker platforms for extra periods of play (extra-time) or penalty shoot-outs.

Placing a Bet

It is possible to place a match-result bet either before the kick-off (ante-post bet), or whilst the game is in progress (in-play bet).

In the English Premier League (EPL) match shown below (screenshot courtesy of Betdaq betting exchange), we have elected to back the draw at odds of 3.5. (Decimal or ‘European’ odds).

In this case, the bet was requested by clicking on the yellow-highlighted square bearing the odds of 3.5 in the ‘Back All’ column.

(Click on the image below to enlarge it in a new tab):

Betdaq: Example Bet Slip

Having clicked on the draw price, a bet slip opens up to the right of the screen, ready for insertion of our stake. Here, we have entered a figure of £10.

The profit due from our wager should the match indeed end in a draw is shown as £25.

In order to strike this bet, the next step would be to click the purple button ‘Place Bet(s)’.

What do Bookmaker and Betting Exchange Odds mean?

Just as a side note… When we write articles showing mathematical calculations we always prefer to use European odds, also known as decimal odds.

It would go too far to explain in this article the whole concept of betting odds but here’s an article on that topic if you are interested in learning more: Understanding Betting Odds – Moneyline, Fractional Odds, Decimal Odds, Hong Kong Odds, IN Odds, MA Odds

In short, betting odds show how much you will be paid out if your bet wins.

However, odds can also be converted into their ‘implied’ probabilities and here’s the formula:

Betdaq’s prices for our example match (at the time of the screenshot grab) were:

Theoretically, because there are only three outcomes to a match (home, draw or away), the probability percentages of each should add up to 100%.

But, in reality, the percentages on any one match with any single bookmaker will always be above 100%; using our example odds, it’s 101.09% (35.21% + 28.57% + 37.31%).

Why should this be?

Bookmaker vs. Betting Exchange Overrounds

The percentage difference over and above the 100% base probability figure is known as the bookmaker ‘overround’, ‘margin’, or ‘vigorish’ (or ‘vig’). This represents the bookmaker’s expected profit.

In its simplest form, for every 101.09 units the bookmaker accepts as wagers on the odds of our example match, if the wagers remain stacked in the same proportions as the implied probability percentages, then the bookmaker will pay out only 100 units, thus ensuring a profit regardless of the match result.

However, our example here is a betting exchange. Like all other exchanges, it guarantees a profit from every match by charging commission on all winning bets. Here, Betdaq’s commission rate is 2%.

The overround calculations now become slightly different because the commission amount has to be factored in.

You can see that at the same odds, the implied probabilities now add up to 102.45%. Because of the commission element, exchanges tend to have a larger overround than bookmakers, even if it seems at first glance that exchanges have better prices. In fact, rewards are generally higher with a bookmaker.

Here’s the formula to convert odds in an exchange into their ‘real’ odds (after commission) in order to compare directly with bookmaker odds:

So, in our example match, the ‘corrected odds’ were as follows:

What do the Implied Probabilities mean?

The important thing to remember is that converting odds into their implied probabilities is not an accurate indicator of the percentage chances of each outcome. Bookmakers adjust their odds (prices) due to demand, which leads to distorted ‘implied’ probabilities. These are normally very small and not easy to spot but enough for the bookmakers to stay in business and make consistent profits.

Implied probabilities reflect much more the public perception of the likely outcome (not the statistical likelihood), being a measure of the volume of money wagered on each outcome rather than its real chances of success.

And odds fluctuate throughout the ante-post and in-play markets according to the weight of money placed and other factors such as time elapsed in the match.

It is, therefore, not advisable to rely on the market odds (at any moment in time) as a totally accurate benchmark of the event probabilities.

In order to more accurately gauge ‘true’ probabilities, it is advisable to take a purely mathematical approach using historical results and statistics.

The very nature of selecting two variables in what is effectively a combination bet or ‘double’ means that the odds are multiplied creating an opportunity for higher returns than backing each outcome individually.

The attraction of higher odds and the perception that most games in modern football are free-flowing attacking affairs where both defences are likely to be breached have created a market for these types of combination bets.

You may also think that by ‘doubling’ the home or away result and BTTS, the wager is shrewder than simply picking the correct score of the match where the odds are higher but far disproportionate to the probability of a return?

Let’s take a look at these points in more detail.

Table 1: Winning & Losing – FT Result + BTTS Double

Goal-scoring Statistics

We have previously looked at FT score distributions using a sample of almost 11,000 matches from nine different leagues.

If you open the screenshot there you will find that clean-sheet victories (1-0; 2-0; 3-0; 4-0; 0-1; 0-2; 0-3; 0-4, etc.) by either the home or away team accounted for 38.22% of all results.

Draws (0-0 through to 4-4) made up a 25.33% quota of all results.

However, for the sake of this article, we are interested in home and away wins where both teams scored. When tallied, these accounted for precisely 33% (19.76% + 13.24%) of all results:

10,723 Match Sample: Home or Away Wins where both teams scored

A sample size of 10,723 matches is a statistically significant amount and a fair benchmark to gauge other leagues by.

In comparison, of the 1,900 English Premier League (EPL) games that took place in the five seasons from 2012/13, there were 646 matches (34%) when betting on one of the teams to win and both teams to score could have returned a winning bet.

From these indications, there will be ‘around’ a third (33%) of matches in a season in any top-flight league where the combination of BTTS and a decisive match result occur.

But, of course, this assumes that the right teams were selected to win. Without taking account of any assumed preference for the favourite, the probability is as low as 16-17% (50-50) for a winning return across those games.

Win and BTTS Odds on Offer

Typical odds in the market for the Win (home or away) + BTTS can be anything between 3.00 and 6.00 depending on the teams involved, but the average odds are around 4.00.

So, roughly speaking, there is a 1 in 6 chance (16% = 1 in 6.25; 17% = 1 in 5.88) of making a winning selection, which will, at average odds of 4.00, return winnings of three times your money.

But how does this compare with simply backing the correct score?

Correct Score Analysis

The EPL is considered one of the most exciting leagues in the world, but the most common result type, as it is in every league, is actually a (not very exciting) one-goal game (1-0 or 0-1).

One goal games accounted for 348 (18.32%) of the 1,900 EPL matches between the five seasons during 2013-18.

The second most common result is 2-1 either way. During the same five season period, the EPL recorded a 2-1 home win 142 times (7.47%), and a 1-2 away win 123 times (6.47%), equating to 13.94% of all results.

In comparison, adding the 2-1 and 1-2 occurrences in Table 2 above gives a total of 15.94%, but it is safe to say that, across the board, 1-0 and 2-1 score lines are generally the most common results.

Again, taking out any preference for favourites, and using the 50/50 measure to predict the right team winning the match 1-0 or 2-1, the probability of correctly predicting 1-0 either way are around 9% (half of 18.32% in our EPL example), and around 7% for predicting a 2-1 (half of 13.94%).

So, mathematically at least, there is a slightly lesser chance of winning with these bets. However, looking at the disparity in odds, the potential winnings in the Correct Score market are far, far greater.

Conclusion

Taking a typical weekend’s EFL Championship betting fixtures as an example, even allowing for favourites and serial 1-0 winners, the odds for correctly predicting a 1-0 win range from around 6.00 to 34.00, and average out at odds above 11.00.

So whilst there is statistically a 1 in 11 chance (9%) of making a winning 1-0 correct score selection, either way, the bet will on average return winnings of more than ten times your money, and potentially as high as thirty-three times the original stake.

All things considered, betting on the correct score market provides a much larger reward than betting on the combination of match result and BTTS.

A vast amount of gamblers never achieve betting returns high enough to crossover to the exclusive group of people who make a living from betting. Even worse, the majority of sports betting practitioners consistently lose more money than they win.

Punters learn the hard way that they lack knowledge and understanding of probabilities. They constantly overestimate their skills in judging the chances of predicting an outcome.

Collage of Shutterstock images: 3Dmask

Bookmakers remain in business and thrive at the expense of the majority of gamblers who possess two perfect flaws in their thinking:

This particular human behaviour guarantees bookmakers their profits but, it’s devastating for the bank balances of bettors. Does this sound familiar to you?

Good Knowledge and Understanding of Probabilities Required

To make money with sports betting, determining the probability of a bet outcome and calculating the corresponding odds for it are unavoidable.

Comparing the betting odds offered in the market with the expected fair price is a constituent part of discovering whether the odds offered for a bet are too high (containing value) or, too low (without value).

Here is an example:

The screenshot below shows an excerpt from Soccerwidow’s Value Calculator for the EPL game on 25/10/2014 between West Ham and Man City.

1×2 Odds Calculation via Soccerwidow's VC: West Ham vs Man City on 25.10.2014

The statistical probability of a Man City win was 49%, corresponding to ‘true odds’ of 2.04 (100/49).

Translated into layman’s language the chance of Man City winning this match was approximately 50/50. Of course, this meant West Ham had a 50/50 chance of avoiding defeat (i.e. West Ham winning or drawing the game).

However, at kick-off the highest odds on offer for Man City to win were only 1.65, equating to a 60.6% chance (100/1.65).

Everyone who bought a bet on Man City to win placed their bets at the price corresponding to a 60.6% chance, whilst in truth City’s chances were only 49%.

Without a satisfactory knowledge and understanding of betting odds and probabilities, there were probably tens of thousands of punters backing Man City, clearly priced as the favourite in this match, at massively under-priced odds.

People who bet like this over and over again shouldn’t wonder why they lose more money than they win over the course of a season.

In contrast, the bookmakers make a good profit from bets of this nature. In this particular example, offering odds of 1.65 equates to a mathematical advantage over the punter in excess of 20%, meaning that their profit on a whole portfolio of bets like this is, in the long run, at least 20% or above.

Are you still with me?

You need to understand that the ability to calculate probabilities and odds is crucial and will enable you to better judge if odds are over- or under-priced (i.e. worthwhile or not).

Sports Betting Odds – How to Know that Odds are Fair

Betting odds which correspond to the theoretical calculated probability are called ‘fair odds’.

Image: alexkatkov (Shutterstock)

The West Ham v Man City match is by no means a one-off or even a rare example.

The market odds offered on any event very seldom represent fair odds. They are regularly either over- or under-priced.

Considering that there is always ‘error’ present in statistical calculations (deviation of predicted distributions to the actual observed results), any betting odds within a corridor of +/- 5% of the calculated probability can be called ‘fair’.

Soccerwidow’s Value Calculator has an error rate of approximately 3%. Translating this to our example, consistently betting on teams with a 49% chance of winning will produce an expected hit rate for similar matches of somewhere between 46% and 52% (49% +/- 3%).

As we have seen, the highest odds available for Man City to win prior to kick-off were based on a 60.6% probability. This was way outside the acceptable probability corridor and, therefore, the 1.65 betting odds were hugely ‘unfair’.

Laying Man City in this case would have been a ‘value bet’, certainly not backing them to win.

Compulsory Maths Lessons for Bettors

I am really sorry but, for anyone seriously interested in betting for a profit, a thorough and practical understanding of betting odds calculation is absolutely necessary.

Sadly, maths, statistics and probabilities have never been the most popular subjects in schools.

If you want to be a winner you need to make a stark choice: either force yourself to learn everything you can about probabilities and betting odds or, accept the fact you are gambling for entertainment purposes only with a strong prospect you will lose more than you will win.

If you value the money in your pocket there is no sense to continue betting on gut feelings alone waiting for the next ‘lucky streak’.

So long as bettors remain ignorant of betting odds calculation, bookmakers will continue to grow their businesses whilst bettors will continue to pay for it.

Conclusion

Betting odds are the prices for bets which very rarely represent the true probabilities of an event actually occurring. For the majority of bets offered in the market, odds are either over- or under-priced.

The ability to compare odds and buy bets at the best available prices is crucial for betting success, as is a deep understanding of probabilities and odds calculation. Without these attributes bettors are doomed to lose more money than they win.

However, before you decide to delve deeply into learning betting odds calculation, please consider carefully whether it is in fact a good use of your time. If you are not put off by the maths involved I can certainly assure you that the learning curve ahead is very, very steep and long.

Perhaps you can think of other things to concentrate upon and make money in a profitable, but more socially acceptable way?

If I haven’t persuaded you otherwise and you are still serious about wanting to make money with betting, then it is certainly worthwhile reading my other articles on this topic (see selection below) – and consider buying our Over/Under Betting Course and/or Value Calculator to help you master this subject.

Check out our store for more educational products on betting odds calculation: Soccerwidow’s Products

Here’s a selection of relevant and free explanatory articles delving deeper into the subject of betting odds calculation:

How do Bookmakers Tick? How & Why do they Set Their Odds as they do?
How Bookmakers’ Odds Match Public Opinion
What is Value? What is Value Betting?
What is the Ideal Sample Size for Accurate Predictions?
Probability, Expectation, Hit Rate, Value, Mathematical Advantage: Explained

They rely on dividing historical data (previous five complete seasons) into clusters according to the “HO/AO quotient” to provide a reliable comparison with future matches under analysis.

Betting odds are a mixture of statistical fact and public opinion (people voting with their money) as to what the likely outcome of an event will be.

Introducing the HO/AO quotient allows us to to ‘cluster’ groups of past matches and with that, to quantify the mutual relationship between the number of goals scored in matches and the strength of the teams involved. (The HO/AO quotients are a practical application of corellation).

This allows us to put an upcoming game into perspective.

In other words, we use the group of past matches bearing HO/AO quotients most similar to the match under analysis in order to make more accurate assessments about its likely number of goals.

The number of goals scored↔team strength relationship is a hugely strong correlation known to the bookmakers and used to a greater or lesser degree when setting their opening odds.

However, as public opinion (market pressure) leads to ‘errors’ in market pricing (odds), using the knowledge of the correlation allows us to spot ‘value’.

Following on from our Betting with Cluster Tables introductory article, here are the four simple steps needed to calculate pinpoint zero odds for intelligent value betting decisions in the Over/Under ‘X’ Goals market:

We shall look at each of these steps using the English Premier League as example.

Let’s look in fine detail at the EPL match: West Ham vs. Southampton from 31st March, 2018.

Step 1 – Find the Home and Away Odds

One of the most important components of the Cluster Tables is the HO/AO quotient (home odds divided by away odds), hence the need for both odds before referring to the tables.

To find the latest, up-to-date odds for any fixture you can employ bookmakers or betting exchanges of your choice, or make use of an odds comparison site. For the sake of our example, we are using OddsPortal.com as they are the only site showing time-stamped odds to support our illustrations.

Oddsportal Ante Post Odds Composite Screenshot – West Ham vs. Southampton 31/03/2018

The screenshot on the left is a composite image showing both the home and away odds just before this game started. Click on the image to enlarge it in a new tab.

Betsafe offered a price of 2.90 on West Ham six minutes before kick-off, whilst 5Dimes gave best price of 2.73 on Southampton seconds before the start.

Despite the multitude of odds movements throughout the entire ante post market, you will find in the vast majority of cases that the relationship between the home and away odds will stay pretty much the same throughout the ante post market.

Usually, the HO/AO quotient locates the match firmly between the two ends of a cluster, and the quotient tends to remain in that same cluster group no matter how the odds move during the lead up to kick-off.

This means that the timing of the analysis is not critical; you can perform it at any period during the ante post market before the match kicks-off. And of course, bet placement timing then also becomes just a matter of finding market odds containing value.

Timing only becomes an issue in the very rare event that the HO/AO quotient places the match very close to one of the ends of the cluster range for either team. It is then always wise to check odds close to kick-off to ensure that you have the match in the right HO/AO clusters for both teams.

Most of our tables are based on Pinnacle bookmaker odds, and for these leagues, you need only find which odds Pinnacle is offering at that time.

A small number of our tables use the highest audited bookmaker odds from a select panel included at Oddsportal. For these leagues, you will need to find the highest home and away odds being offered from a small range of bookmakers at the time.

Okay, we have our home and away odds – onto the next step…

Step 2 – Calculate the HO/AO Quotient

Easy! Take a calculator or enter the figures into a spreadsheet and just divide the home odds by the away odds to provide a quotient.

In this case, the quotient is: 2.90 divided by 2.73 = 1.0623 (rounded-up)

Step 3 – Identify the Relevant Cluster and Percentage Result

Cross-checking any team’s HO/AO quotient against their statistical percentages for any of the over/under 0.5 to 6.5 options in any match under analysis is extremely easy.

Within the Cluster Table for the appropriate league, click on the Betting Tables tab. This reveals a one-touch spreadsheet for obtaining both team’s results.

Here is the table of figures for West Ham (click on the image below to enlarge it in a new tab – and then use the magnifier to enlarge again if necessary):

Over/Under Cluster Table – Betting Table Screenshot

To change the team, simply click on the orange team name in the top left-hand corner to access the drop-down menu of all teams with five-season data sets.

By clicking on the team you are looking for, the figures in the table will automatically revert to those of that team.

The first half of the sheet contains the home figures: Summary at the top, Over ‘X’ Goals, and then Under ‘X’ Goals. The bottom three panels are the away results.

For this example, let’s decide to go for the most popular ‘Over 2.5 Goals’ bet.

For West Ham’s home figures, using the second panel from the top, you can see on the left-hand side in dark blue, their dedicated HO/AO clusters.

The HO/AO quotient we have calculated is 1.0623 and this fits neatly into the third cluster down. Looking under ‘Running Total Probability’, we simply record the percentage figure, in this case, 73.9%.

Here are West Ham’s top two panels with the relevant cluster row and percentage result for Over 2.5 Goals highlighted:

Over/Under Cluster Table – Betting Tables Tab – West Ham’s Cluster Row Highlighted

And after changing the team name, here are Southampton’s away figures in their fourth and fifth panels:

Over/Under Cluster Table – Betting Tables Tab – Southampton’s Cluster Row Highlighted

You will also note that the HO/AO quotient fitted very firmly inside the relevant cluster group of both teams, and not too close to its edges (West Ham’s cluster group was 0.7301-1.9345, whilst Southampton’s was 0.8211-1.3880).

Again, you will rarely encounter situations that will need monitoring – most games will see the same cluster groups used despite the odds movements throughout the ante post market. This means that neither analysing nor placing the bets is time-sensitive, and both exercises need not be performed at the same time either.


Next Page: Step 4 – Do the Maths!

In conjunction with the course and based on its teachings, Soccerwidow also publishes a set of dedicated Over/Under Goals Cluster Tables (summer and winter leagues), which are a one-touch solution to identifying value within the over/under ‘X’ goals market for individual matches in a particular league.

What is a Cluster Table?

A Cluster Table is an Excel spreadsheet containing an interactive data set, which displays goal distributions in a particular league during the five complete seasons immediately prior to the season currently in play.

Results are split into four equal-sized groups, or ‘clusters’, according to the historical home and away odds of each match within the five-season-data-set (highest odds at close of ante post market), which act as a gauge of public opinion (perceived strength of the teams), for the match under consideration.

Here are two cluster examples taken from a game in the English Premier League (EPL) during the 2017-18 season. The screenshots come directly from the EPL 2012-17 Cluster Table.

Click on the images below to enlarge them in new tabs:

Man Utd Home – Over ‘X’ Goals Cluster Table 2012-2017 – Over 2.5 Goals Highlighted

Liverpool Away – Over ‘X’ Goals Cluster Table 2012-2017 – Over 2.5 Goals Highlighted

As you can see, the four clusters representing 95 respective home and away games over five seasons are divided into almost equal sets (3x 24 games; 1x 23 games), which determines the division of their HO/AO quotients (Home Odds divided by Away Odds).

Two rows are highlighted: these are the corresponding rows for the match between these two teams on 10th March, 2018.

The home odds of Manchester United were 3.30. Liverpool’s away odds were 2.61. The HO/AO quotient was therefore 1.26 (3.30 divided by 2.61).

How to Interpret the HO/AO Figures

The HO/AO clusters for all teams are different from one another. But why?

Odds are determined according to a team’s historical (statistical) strength (success), or lack of it, and no two teams perform exactly the same, which will of course produce different quotient figures.

How then is it possible to compare two teams in this fashion?

The home odds and the away odds are set by the bookmakers according to historical distributions (statistical results) and therefore provide a constant benchmark to a team’s past performance (looking backwards).

By the time the ante post market closes, they also contain a deal of public perception in terms of demand for the bet in question (looking forwards).

Therefore, the HO/AO clusters take the correlation between the ‘perceived’ strength of the teams involved (based on historical results) AND the market pressures (demand and supply) faced by the bookmakers when setting their odds.

The HO/AO quotient is therefore an ideal method of comparing two teams by selecting from their historical results the nearest batch of equivalent games against teams of a similar perceived strength to the opponent under analysis.

If United are 3.30 to beat Liverpool and Liverpool are 2.61 to beat United, it makes sense to look at comparable results where both teams carried similar prices in their respective home and away games in the past (i.e. the closest United home games to their price of 3.30 in this game, and the closest Liverpool away games to their price of 2.61).

Splitting five seasons’ worth of games into four clusters does not divide exactly. Each team plays 19 games at home and 19 away per season. This makes a total of 95 home and 95 away games for each team, hence why for United’s home games and Liverpool’s away games (and any other team) there are three clusters of 24 games grouped together, and one cluster of 23.

In our example, it is coincidental that the most relevant clusters for both teams to the calculated HO/AO quotient of 1.26 each contain 24 games over the last five seasons.

What the Clusters say about the Comparative Strength of Teams

When looking at the tables in the EPL for any team, the following categories become apparent when dividing games into ‘perceived strength’:

1. HO/AO: up to 0.2248
   The home team is the clear favourite with a very good chance of winning (the weight of money makes the home team the overwhelming favourite)
2. HO/AO: 0.2249 to 0.4902
   The home team is definitely stronger than the away team, but there is also a good chance of a draw in the game (fluctuating opinion between home or draw)
3. HO/AO: 0.4903 to 0.7730
   It is not really clear in which direction the game will develop (no overwhelming favourite)
4. HO/AO: 0.7731 to 1.6922
   The chance of a draw is quite high as both teams are perceived to be of equal strength (no overwhelming favourite)
5. HO/AO: over 1.6923
   The home team is weaker than the away team; it could be an away win (the perceived favourite is the away team)

Why are ‘Zero’ odds important?

After the setting and publishing of opening odds for sale, the price of a bet is then influenced by:

• The popularity for that bet amongst punters (demand)
• A balancing act of monies received between the outcomes carried out by the bookmaker via price fluctuations to create its margin/profit (supply)

The price fluctuations (changes in the odds) from the opening of the market right up until the end of the event are therefore driven by both demand (punters) and supply (bookmakers), and contrary to popular belief, not dictated solely by the bookmaker.

If the zero odds of an event are known it is possible to identify temporary or lasting pricing ‘errors’, large and small, caused by these fluctuations in demand and supply. These errors can then be used to ensure that every bet placed contains ‘value’, the essential element in making long-term profits from gambling.

As a reminder:

• Prices offered above zero odds represent value back bet opportunities
• Prices offered below zero odds represent value lay bet opportunities

Zero odds are those at which, if every bet were placed at this price, the overall outcome of any number of bets would be a ‘zero’ sum game.

Finding ‘value’ is therefore about determining the implied (actual estimated) probability of an event (based on historical results), and obtaining odds representing a lower probability (i.e. higher odds) if backing, or a higher probability (lower odds) if laying.

Of course, the higher the odds obtained above zero odds are, the more profitable your long-term back bet portfolio should be and the lower the odds obtained below zero odds are, the more profitable your long-term lay bet portfolio should be.

Manchester United vs. Liverpool

The HO/AO quotient was 1.26, suggesting that public perception of the event was that the draw was probably the most likely outcome.

In the images above, the Over 2.5 Goals bet type is highlighted.

HO/AO 1.26 sits in the fourth cluster of United’s cluster table, and the percentage chance of Over 2.5 Goals for their home games within this cluster was 37.60%

HO/AO 1.26 sits in the third cluster of Liverpool’s cluster table, and the percentage chance of Over 2.5 Goals for their away games within this cluster was 62.40%

Calculate the average of these percentages: 37.60% + 62.40% = 100.00% / 2 = 50.00%

Calculate the zero odds: 1 / 50.00% = 2.00

It just so happens that the highest Over 2.5 Goals odds on offer for this event were also 2.00, providing no value in backing or laying.

The result was 2-1 to United, meaning that public perception of the event most likely being a draw was proved to be wrong. Public perception of likely outcomes and the eventual reality are very difficult to reconcile, which is why odds movements should never be relied upon as a guide to potential outcomes.

You should also note that the most popular games to bet on are usually those most intensely analysed (United vs. Liverpool is just about the most high-profile club game in the world). Because of this, the highest pre-match odds available for many of the different bet types are usually very accurate compared to the statistical likelihoods. In this case, we calculated 2.00 as the zero odds and indeed, 2.00 was the highest pre-match price available.

Once again, we reiterate just how accurate the Cluster Tables are in calculating probabilities.

Try the Power of the Cluster Tables for Only £2

The Cluster Tables are an extremely powerful tool for checking market odds against ‘true’ odds in order to select bets containing ‘value’ for long-term profit.

The tables can also be utilised for predicting odds movements before kick-off and much, much more, but we will write about these benefits in other articles.

A German reader once commented that he couldn’t believe we were selling the Cluster Tables because to him, “these five season tables are something like a ‘money printing machine’!“.

If you wish to play around with the table used in our example above, you can purchase the EPL Cluster Table for the 2017-18 season here for just £2:

This table comes with the added bonus of a £5 discount voucher applicable to the Fundamentals of Sports Betting Course – Over/Under Goals.

You can use this table for backtesting the 2017-18 EPL season. Randomly select any weekend and carry out the calculations as demonstrated in this article. Try experimenting a little and perhaps compile different portfolios such as:

• Choosing only Under 3.5 Goal bets
• Choosing bets which have at least a 60% probability to win
• Choosing bets with a strong home favourite only
• … and so on! Use your wits and imagination to find a system that actually works for you!

Once you understand how the Cluster Tables work and have found a system to focus on, picking bets for a weekend becomes truly very easy!

Please note that after the 2017-18 EPL season finishes this sample table will expire and should not be relied upon for betting purposes after that. Sorry, you will have to buy the 2018-19 replacement table. However, the 2017-18 version will certainly give you a good idea of the table’s full functionality.

If you have any further questions on how to use the cluster tables, please use the comments section below.

Thanks for reading and good luck with your value betting!

Although the rules for roulette tables are designed in such a way that the bank makes money in the long run, it must be said that roulette is a pretty fair game. If you play with only small amounts (relative to your chips), then you can gamble for a long time at the roulette table whilst having a lot of fun.

This article shows you how to calculate probabilities in roulette, including the odds for each type of bet, allowing you to analyse all the possible variations.

Probabilities – A Brief Introduction

Collage of Shutterstock images;
Foreground: donskarpo,
Background: Nata789

The calculation of roulette wheel probabilities is very simple.

Let us take the classic example of a dice with the numbers one to six. How large is the probability that the next throw is the number five?

Of course, it is 1/6 or 16.67%: only one side of the dice has the number five, one of six numbers in total.

And how big is the probability of getting a number that is at least four?

The answer is 50%: there are three possible throws (numbers four, five and six), meaning a three in six chance, or 1/2.

If you have understood these simple examples then you will also be able to understand the probabilities expected in roulette.

Roulette Probabilities

Roulette has a total of 36 numbers, one to 36. The 36 numbers are divided into the following equal sized ‘sets’:

• 18 red numbers (Rouge) and 18 black (Noir)
• 18 even numbers (Pair) and 18 odd (Impair)
• 18 numbers in the lower half (Manque) and 18 in the higher half (Passe)

Lastly, there is an additional stand-alone number, which is the green “zero”, making 37 numbered zones in total. The zero is not included in any of the three sets above.

So, if you are gambling on any of the three sets, in other words;

• red or black
• odd or even
• low or high

then your likelihood to win is 18/37 = 48.65%. If your bet wins, your stake is returned plus 100%. In effect you double your money as each of these sets is an ‘evens’ bet.

Assuming the frequency of results is uniform (i.e. each number appears once during every 37 rotations), the bank will win all bets placed on the three sets every 37th round, when the green zero arrives. Thus, players lose an average of 1/37 of their stakes (assuming that they always play with the same stake per round).

Putting this another way, imagine you are betting on both the “red” and “black” sets at the same time. On average, 36 out of 37 times, the roulette ball will land on a number from one to 36. You are backing all 36 numbers and will lose one bet each time but receive full compensation on the other. (A zero sum game). But you will make a total loss (lose both bets) when the ball lands on zero, and this is precisely the case in 1/37 of the games.

So you can say that with simple chance you should expect returns of 36/37 of your stake money, which is the expected value in roulette (97.3%). In other words, for every 100 units staked you will receive back an average of only 97.3 units.

There are some casinos which are a little fairer to players who rely on simple chance. In such a casino when betting on, for example, red, if a zero appears your stake is not lost immediately but is left to ride on the next spin of the wheel.

In this case, the stake is returned to you (without winnings) if the next spin is “red”. The expectancy value for this type of house increases a gambler’s chances to 98.65%, or 98.65 units returned per 100 unit stake. Wagering with 100 units in a session will cost an average of 1.35 units (the house “edge”). You’ll find further maths and explanations in Wikipedia here.

Probability Table for Roulette Table Bets:

Expected Sequences for Simple Probabilities

If you witness “red” five times in a row, what do you think should come next? Red or black?

Many will believe that the chances for “black” are now higher. Black has not appeared for a while so it must surely arrive again soon to ‘balance out the frequency’.

Unfortunately, this thinking is incorrect. Following a series of “red” five times in a row, the probability for black always remains the same: 18/37 = 48.65%. Just remember the roulette wheel has no memory – it simply does not know what the last number was.

This is why it makes no sense to write down the sequence of red and black. (Surely you must have observed gamblers in casinos engaging in this habit?). It is impossible to detect even the smallest patterns in the roulette wheel because the ball has no memory and will always churn out numbers completely at random.

However, it is unlikely that “red” will appear six time in a row. The chance of six reds in a row is
(18/37) ^ 6 = 1.3% (i.e. 48.65% x 48.65% x 48.65% x 48.65% x 48.65% x 48.65%). (For more explanations see also our combinatorics article). By the way, this is approximately half the chance that any one single number appears (1/37 = 2.7%) and, of course, it is just as unlikely that there will be red numbers five times in a row followed by a black number; the probability for this sequence is also 1.3%.

Examples of Probabilities

To give you a better feel for roulette probabilities, here are a few examples. Here we use “r” for red and “b” for black:

• r or b: 18/37 = 48.65%
• rr or bb: 18/37 x 18/37 = 24% (two reds in a row or two blacks in a row)
• rb or br: 36/37 x 18/37 = 47.3% (one colour followed by the other)
• rrr or bbb: 18/37 x 18/37 x 18/37 = 11.5%
• rbr or brb: 18/37 x 18/37 x 18/37 = 11.5%
• rrrr or bbbb: 18/37 x 18/37 x 18/37 x 18/37 = 5.6%

Never confuse these probabilities with the “conditional probabilities”. The chance of red four times in a row is 5.6% but if you come to the table immediately after a red number has appeared, the probability that you will witness a further three reds (making a total of four times in a row) is 11.5% – purely because you will be observing only a series of three rounds.

The Law of Small Numbers

The law of small numbers was first conceived in 1898 by Ladislaus Bortkiewicz (1868-1931). His book is still available in German, free of copyright, and can be downloaded as a PDF or Kindle version. An English language introductory text is also available.

The Law of Small Numbers is not exactly bedtime reading material, but here is a brief summary. As roulette is a game of repetitions the “law of a third” and the “law of two-thirds” should become evident as play continues.

If there are exactly 37 rotations performed at roulette (as many as there are different numbers), according to the book:

• approximately one third of the numbers (around 12-15 numbers), will not be hit at all
• approximately one third of the numbers will appear exactly once
• approximately one third of the numbers will appear twice or more
• approximately two thirds of the numbers will appear at least once

The Law of Large Numbers

The law of large numbers states that with an increase of repetitions the actual observed frequency comes closer to the theoretically calculated probabilities.

Although it is possible to observe on one particular evening, for example, red numbers coming up 60 times in a row, and another evening 40 times black, ultimately, when you observe the distribution of red and black over a longer period, the frequency will be closer to 50:50.

Therefore, there is no roulette system with which you can beat the probabilities. It may seem for a short time that a certain system functions but, in the long run, you will lose money with every system because roulette rules are designed in a way that the casino earns money. Period. Bear this in mind when you play roulette, but it is still fun!

We hope that this article about roulette and its probabilities has helped you. Now it’s time to enjoy. All you need is a serious and decent online casino where you can test your newly acquired knowledge. Choosing a suitable casino is best done via a comparison site. Here is one: Australia Online Casinos – Check it out, choose your casino and then put your roulette theory into practice!