Case Studies – Soccerwidow Football Betting Maths, Value Betting Strategies Tue, 14 Aug 2018 13:47:47 +0000 en-US hourly 1 Judging the Risk of a Football Betting Portfolio Tue, 24 Jul 2018 18:30:20 +0000 more »]]> Understanding how risk can be controlled when betting is sometimes quite a challenge. Learn today how risk can be reduced & controlled when betting on football. Risk management of a portfolio should be an essential part of your betting strategy.

Please note that this article addresses system betting (= a predetermined selection of bets to bet on the same criteria over a longer period of time).

System betting simply means that you are not judging the risk of any individual bet prior to placing it (this would be ‘value betting’). System bettors identify an overall ‘edge’ or ‘advantage’ that is likely to persist over a longer period of time and then follow-through from the start to the finish of a campaign. Of course, there is ‘value’ involved (a ‘mathematical advantage’), otherwise it wouldn’t work.

The examples in this article are our actual picks for the 2017-18 season that were identified using the HDAFU Tables.

What Exactly is a Portfolio?

A portfolio is a package of bets where extensive analysis has determined the choices (picks). Diversifying the portfolio is an essential part of betting strategy with the aim of reducing the risks of losing.

Please do not confuse the term ‘portfolio’ with ‘best timing of placing bets’. A portfolio is planned well in advance of a weekend (or round, or even season) and determines the assortment of bets that are to be placed later.

A portfolio of bets is therefore a varied group of individual bets, not just one particular match on a particular day.

To judge the success of any particular betting portfolio it is necessary to evaluate the performance of all of its systems together as one, not just the individual group members (bets in just one league or system).

What is Diversification?

Diversification is a technique that reduces risk by allocating bets among various leagues, bet types, and other categories such as times or seasons. The rationale behind this technique contends that a portfolio constructed of different kinds of bets will, on average, pose a lower risk than any individual bet (system) found within the portfolio.

Diversification strives to smooth out unsystematic or anomalous risk events (outcome of matches/leagues) in a portfolio so that the positive performance of some bets (winnings) neutralizes the negative performance of others (losers).

The questions that probably arise right now are: How big should my portfolio be? How much should I diversify?

I will answer these two questions at the end of the article but for the time being let us first look at our portfolio for the 2017-18 Winter League season. I will explain step-by-step how I came up with the choices and what my thinking was behind them. This will probably already answer many of your questions.

Our Portfolio for the 2017-18 Season

For the sake of brevity, I am showing only the first 10 European leagues we used in alphabetical order: Austria, Belgium, Denmark, England, France, Germany, Greece, Italy, Netherlands and Poland.

The overall results you will see would have been similar whichever 10 leagues we chose to illustrate with.

For betting, it doesn’t matter which leagues you choose so long as you have easy access to all of them with the bookmakers available to you. A well-balanced portfolio normally delivers the results as expected.

Here is our portfolio for 2017-18:

Image 1: Portfolio of bets for the 2017-18 winter league season

As you can see it is a conservative portfolio with a good number of low risk and medium risk systems.

As a side note, this article isn’t about how the individual systems (within a portfolio) are picked. However, for the 53 bets in the EPL, you will find a detailed explanation in this article: Finding a System Using the HO/AO Quotient

For the other nine leagues you will just have to trust that the systems were picked in a similar manner to the EPL example.

Probability / Expected Hit Rate / Risk

The terms probability, expectation and hit rate are all closely related, and express more or less the same thing. The main differences are that before a game starts (or a whole system of bets/portfolio is played) the terms ‘probability’, ‘expectation’ and ‘prediction’ are used but, once results are known, these terms are supplanted by actual ‘hit rate’.

The observed distribution of the past (as displayed in the HDAFU Tables) becomes the probability for the future (= expected hit rate).

Referring to image 1 above, there was an expected hit rate of 80% in the Greek Super League. This meant that from every 10 bets placed, on average, 8 were likely to win. Therefore, the longest losing streak when placing 50 bets in a row was 2 (see article: The Science of Calculating Winning and Losing Streaks). This individual system within the portfolio was evaluated as being ‘low risk’.

On the other hand, the expected hit rate of 31.58% in Germany meant that from every 10 bets placed, on average, 7 were likely to lose. The longest losing streak expected when placing all 57 bets in a row was 11. This is an example of low probabilities, or ‘high risk’ classification.

Losing Streak Observed vs. Maximal Losing Streak Expected

The ‘longest losing streak expected’ is not necessarily the ‘longest losing streak observed’.

For example, in the EPL 2012-17 the observed longest losing streak was 6 in a row and this happened 3 times during the previous 5 seasons.

Image 2: EPL HO/AO group 0.603 to 1.396 – Backing the Draw 1st Half

Nevertheless, to judge the risk for the future you have to allow for the worst-case scenario even if it hasn’t happened for a very long time – one day it will happen, believe me!

It is always safer to prepare for the worst rather than relying on luck.

At the end of this article (image 6) you will see that 2 of the 10 systems (Austria, EPL) reached their expected longest losing streaks, and one system even outstripped its calculated (predicted) expectations (Denmark).

Calculating the Expected Maximum Longest Losing Streak

Here’s a screenshot from the EPL 2012-17 HDAFU Table representing the HO/AO quotient cluster group (0.603 to 1.396) for backing the draw. The expected total number of bets and expected hit rate for the forthcoming season are circled in red.

Image 3: EPL 2012-17 HO/AO group 0.603 to 1.396 – Backing the Draw 1st Half

To calculate the longest expected losing streak use the following formula:

Formula longest losing streak

n = number of trials (i.e. total number of bets expected)
ln = natural logarithm
P = probability / expected hit rate (for losing streaks: expected losing rate)
| .. | = absolute value or ‘modulus’

Here’s the formula in action for the EPL example:

The winning probability of 39.62% means of course that the losing probability is its inverse:

100% minus 39.62% = 60.38%

To calculate the longest losing streak use in Excel the following formula:


Read more about the above formula, its use and interpretation in our article: The Science of Calculating Winning and Losing Streaks

The result of our calculations meant that for the 2017-18 EPL season, when backing ‘Draw in the first half’ within an HO/AO Quotient between 0.603 and 1.396, the expected maximum losing streak was 8 losses in a row.

Furthermore, sorting the 2012-17 data falling within this HO/AO Quotient group into rounds revealed that there weren’t more than 4 available bets in any round of matches; sometimes there was only one, and occasionally there were none.

With a losing streak of 8 bets possibly spanning a period of 5 to 6 weeks (= 1.5 months), this system was not likely to be easy on the nerves.

To guard against nerves becoming mass panic, you will need to ensure that your portfolio does not contain too many systems with lower probabilities. Although not very likely, it is quite possible that they may all experience their longest losing streaks at the same time (2017-18 being a case in point, where the season began badly across the board).

Rules of Thumb to Judge Risk

A high yield ALWAYS indicates high risk!

High Yield (over 30%) = High Risk (normally)

…Until it doesn’t!

I have included in the example Netherlands Eredivisie (Backing the Favourite 2nd Half) because the analysis came out with a 75% probability of winning. However, the expected yield of 32.23% was exceptionally high for this probability group and there were only 15 bets expected.

Normally, high probability of winning and high yield do not go together. Therefore, it may have been just an observed anomaly because of the small number of matches on average each year in this group.

Nevertheless, because only 15 bets were expected (of over 500 in the whole portfolio) and with an expected high hit rate, the overall judgment for this particular pick was ‘medium’ although the high yield would have normally marked this system as ‘high risk’.

Moral 1: There are no rules without exceptions.

Next rule:

Low Probability (expected hit rate under 35%) = High Risk

In Germany, the expected hit rate was 31.58% (high risk), whilst expected yield was 29.38% (medium risk)

The combined expectations of hit rate and yield here would perhaps have labelled this system as ‘high risk’ but downgraded to ‘medium risk’ as expected yield was under 30%.

Calculating the overall Probability / Expected Hit Rate / Risk of the whole portfolio

Portfolio compilation and decision-making involved the balancing act of achieving as high an expected hit rate as possible, together with an acceptable yield.

  • The overall expected hit rate of the portfolio should be in the region of ± 50% (of course, if you can get it higher, the easier it will be on your nerves)
  • An acceptable yield is anything in the region of ± 20%

To calculate the overall expected hit rate of the whole portfolio, list your systems like I have done in image 1 (Portfolio of bets for the 2017-18 winter league season)

  1. First you multiply the number of expected bets with the expected hit rate for each system, e.g.

    Austria: 72 times 31.94% = 22.9968
    Belgium: 30 times 86.67% = 26.001
    Denmark: 36 times 41.67% = 15.0012
    …and so on

  2. Then add them all up:

    22.9968 plus 26.001 plus 15.0012 plus etc., etc. .. = 243.2526

  3. Now divide the result by the total number of bets expected:

    243.2526 divided by 505 = 0.4816883 ≫≫ 48.17%

To calculate the overall expected Yield the same calculation applies.

The portfolio example in this article had 505 expected bets over the period of a whole season, with an expected Hit Rate of 48.17%, and an expected Yield of 22.22%.

It was therefore a ‘medium risk’ portfolio.

‘Medium risk’ means that you must be prepared for bumpy rides – substantial ups and downs in your betting bank. But with a sensible staking plan, this shouldn’t mean bankruptcy before the situation picks up again.

Three Scenarios of the same Medium Risk Portfolio with 500 Bets

Despite a ‘high’ hit rate of 48.17% (which isn’t as ‘high’ as you may think) you may experience a betting campaign like this one if you don’t get off to a good start:

Image 4: Profit/ Loss Scenario I for an expected hit rate of 48.17% and 22.22% yield

However, you could get a good start and a very smooth curve over the whole season.

Please note, these screen captures relate to the same portfolio of bets. Nothing has changed: 48.17% probability of winning; 22.22 % expected yield.

Image 5: Profit/ Loss Scenario II for an expected hit rate of 48.17% and 22.22% yield

Scenario 3 has an extremely good start (up to bet number 80) and then gives way to a bumpy ride to the end of the season:

Image 5: Profit/ Loss Scenario III for an expected hit rate of 48.17% and 22.22% yield

Have a think about these profit/loss curve simulations.

The first (unlucky) scenario even has an average hit rate of 52%, much higher than the second and third. However, the second and third are much smoother on the nerves and both have a better financial result at the end.

What I’m trying to say is that you must always remember that you are gambling. Although you are using sound statistics for compiling your portfolio, never lose sight of the fact you are still gambling!

The two very simple rules to negotiate a season with a profit at the end are:

  • If you have a sound portfolio do not give up too quickly.
  • If you have at the beginning a very good start don’t become over-excited and start increasing your stakes more than originally planned.

Always remember, gambling has a lot similarities with rolling a dice; you may have to wait for ages until the sixes start popping up or you have them all at the beginning and then for a long time none.

The Final Performance of the Portfolio

At the end of the season, the portfolio produced the expected result (the overall hit rate was more or less as predicted) although the leagues themselves within the portfolio performed erratically with peaks and troughs during their seasons.

Image 6: Final performance of the 2017-18 winter league portfolio

All three ‘high risk’ systems produced, as expected, very long losing streaks: Austria, EPL, Poland.

Denmark produced a longer losing streak than expected. It started on the 26/8/2017 and continued until 29/10/17 – more than 9 rounds of games! Nevertheless, they recovered to finish with a positive return, although far lower than expected.

I will write more about the final performance of that portfolio in another article where you will also be able to download the whole monitoring spreadsheet including staking and ante post odds movements.

How big should my portfolio be? How much should I diversify?

Betting, in general, is a very unreliable venture and to be able to ‘control’ risk (reduce on losing streaks) a good number of high probability bets is required.

However, the big challenge with football betting is that especially the lower odds (up to 2.5) are often reduced because market demand forces bookmakers to reduce prices for favourites and increase the prices for the opposite bets (underdogs and occasionally draws).

You will therefore find plenty of draw and underdog strategies in the HDAFU tables but unfortunately, these two bet types come normally with very low probabilities of winning (= low hit rate expectation/high losing rate expectation).

And, if you have too many low probability bets in your portfolio and experience several weeks in a row where the favourites are mostly winning, your betting bank may become distressed beyond your comfort levels.

As I have shown you in the example, to get a balanced portfolio of 500 bets requires approximately 10 leagues. If one league doesn’t play according to statistics (e.g. Denmark) another league will hopefully make up for it (e.g. Germany).

Of course, the larger your portfolio, the better.

The more ‘low risk’ you can identify the better.
Reduce on ‘high risk’ as much as you can.

Image 7: Relationship between a systems expected hit rate and its yield

Pay attention that you don’t have too many systems with just 10 to 15 bets in your portfolio as they are much more volatile than systems with 50 bets or more.

However, in the example portfolio, there were only 5 systems with 50 or more bets. It’s not always easy to stick to every rule.

The Rule of Thumb is: 50 is the magic number!

  • At least 50% ‘medium risk’ strategies.
  • At least 50% of the systems within the portfolio with at least 50 bets (for the whole season/year).
  • An overall expected hit rate of the portfolio of around 50%.
  • A minimum of 500 bets in the portfolio = an average of 50 bets in 10 different systems

If you can achieve more than 50 – the magic number – in any of the above equations, then your portfolio should have an even stronger chance of succeeding.

Good luck with your betting!

I hope this article has answered the questions we receive about judging the risk of a system identified with the HDAFU Tables, and will help you to construct a well-balanced portfolio. However, if you are still not clear, then please feel free to ask any questions via the comment section below.

>>> buy your hdafu tables <<<

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How to Use Soccerwidow’s Over/Under Betting Cluster Tables Wed, 06 Jun 2018 07:09:38 +0000 more »]]> Soccerwidow’s Cluster Tables are an essential tool for identifying value bets and creating a profitable portfolio in the Over/Under ‘X’ Goals market.

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:

  1. Find the Home and Away Odds
  2. Calculate the HO/AO Quotient
  3. Record the Cluster Table Results
  4. Perform the Final Calculations

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 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

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.

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

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

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

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

As you can see, Southampton’s Over 2.5 Goals percentage for an HO/AO quotient of 1.0623 in their away games is shown as 33.3% in the second cluster down.

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!

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Over/Under Goals Market – Betting with Cluster Tables Sun, 22 Apr 2018 18:30:16 +0000 more »]]> The Fundamentals of Sports Betting Course has long since been Soccerwidow’s flagship product. It is the most comprehensive guide available anywhere explaining the mysteries of bookmaker mathematics and how to profit from understanding the concept of ‘value’.

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.

>>> cluster table discount codes <<<

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

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

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:

>>> epl cluster table 2012-17 <<<

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!

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HDAFU Tables: £20k in 214 days with the Winter Leagues Wed, 02 Aug 2017 00:38:12 +0000 more »]]> Following up the successful 2016 Summer League Campaign, here is our complete report on the 2016-17 Winter League Campaign, based on 18 different top flight leagues.

300x300 Illustration: 2016-17 Winter League Profit Curve2016-17 Winter League Profit Curve

We will try to avoid repeating what was said in the summer league article so that it is all new information for you here.

For the sake of completeness, you should still read and digest both reports for a full idea of our strategies and thought processes.

And you will find the current stock of available HDAFU tables via this link.

2016-17 Campaign Report

Measures of Risk

Before beginning to plan any portfolio or placing bets, you will need to review your analyses and rank the systems you have found according to risk exposure based on the values of the upper inflection point odds.

This will allow you to compile a portfolio with a healthy balance of risk, which is essential to the success of any investment plan.

Here is our rough guide:

  • Low Risk (Probability 45.00% or more; upper inflection point maximum odds of 2.22)
  • Low-medium Risk (Probability 44.99%-35.00%; upper inflection point maximum odds of 2.85)
  • Medium Risk (Probability 34.99%-22.50%; upper inflection point maximum odds of 4.44)
  • Medium-high Risk (Probability 22.99%-16.00%; upper inflection point maximum odds of 6.25)
  • High Risk (Probability 15.99% or less; upper inflection point odds above 6.25)

Discretion is used if a system does not fit these parameters or crosses two or more classifications – In these cases, the harmonic mean odds of all the games in the set is used as the benchmark to guage risk. The Excel formula for a range of odds in cells A1 to A100 would be: =HARMEAN(A1:A100)

Measures of Success

You will also need a definitive framework to be able to judge the final results.

For us, the final results of any league fall into four distinct categories:

  • Systems that achieve a six-season-high (i.e. profits larger than any of the previous five seasons). (Over-Achievers).
  • Those that make a profit over and above the size of the initial stake (£100 in our case), but fall short of six-season-high results. (Achievers).
  • Strategies that break-even or, record a tiny profit or loss up to the size of the initial stake (£100 in our case). (Zero-Sum).
  • Leagues that make a loss over and above the size of the initial stake. (Losers).

You can already see that two of these outcomes are favourable, one is neutral, and only one is detrimental.

2016-17 League-by-League Review

Let’s have a brief look at each league to see how our 22 systems fared. (Alphabetically according to the tab codes in the workbook):

1. AUS1 – Austria Bundesliga – Whole Season System

Risk: Medium-high

Only eight of 28 bets won, but this was enough to see a profit of £882.00. Hit rate and yield were both below the calculated averages and the resultant profit figure was lower than any of the five previous seasons’ figures.

Result: Achiever

2. BEL1 – Belgium Jupiler League – Whole Season System
Up to, but not including Europa League and Championship Group splits

Risk: Medium

Both the estimated hit rate (33 out of 97 bets won) and yield figures were surpassed by wide margins, leading to a six-season-high profit figure of £3,108.00.

Result: Over-Achiever

3. CZE1A – Czech Republic 1. Liga – First Half Season System
Up to the 04/12/2016 winter break

Risk: Medium

Nine out of 22 bets won, and whilst the hit rate and yield both outstripped expectations, the profit figure settled at £1,247.00, the fourth largest in the last six seasons.

Result: Achiever

4. CZE1B – Czech Republic 1. Liga – Second Half Season System
From 18/02/2017 start of the second half of the season

Risk: Low

This one suffered its worst result in the last six seasons, but the resultant loss was minimal at -£310.00.

Result: Loser

5. DEN1A – Denmark Superligaen – First Half Season System

Risk: Medium

This was the only system employed in this league purely because the format of the second half of the 2016-17 season was to change from previous seasons.

Although hit rate and yield were both below estimates, the system still recorded its third highest total for six seasons at £1,238.00.

There were twice as many bets than expected (largely due to the fact that around 40% more games than usual were played in the first half of the season to accommodate the new second half season format).

Result: Achiever

6. ENG1 – England Premier League – Whole Season System

Risk: High

This system suffered the longest losing streak we have ever encountered, almost 14% worse than expected, for a very painful 36 straight losses. (A six-season-low).

However, the situation was mostly recovered by three big winners all carrying odds of over 12.00, for a final loss of just -£32.00.

The last six bets of the season lost, but had only one of these been a winner, this system would have returned a profit. Small margins.

Result: Zero-Sum

7. FRA1 – France Ligue 1 – Whole Season System

Risk: Low-medium

Hit rate and yield were both below par, but the league turned in a steady performance for a profit of £1,634.00, ranked fifth largest in the last six seasons.

Result: Achiever

8. FRA2 – France Ligue 2 – Whole Season System

Risk: Low-medium

The same story as France Ligue 1, but with a profit of £2,801.00, for its third largest profit figure in six seasons.

This one was unusual for a much higher number of bets than expected. (215 vs. 119 estimate – Profit was at £2,523.00 after 119 bets).

Result: Achiever

9. GER1A – Germany Bundesliga 1 – First Half Season System
Up to 21/12/2016 winter break

Risk: Medium-high

Another below par system, but one that still achieved a profit of £1,098.00. (Fourth largest in six seasons).

Result: Achiever

10. GER1B – Germany Bundesliga 1 – Second Half Season System
From 20/01/2017 start of the second half of the season

Risk: Medium

The very rare inclusion of a system with two non-profitable seasons (the oldest two) in the previous five.

It featured one more bet than expected, which won, to total one more winner than expected. Hit rate and yield both exceeded estimates for a profit of £1,294.00. (Fourth largest in six seasons).

Result: Achiever

11. GRE1 – Greece Super League – Whole Season System

Risk: Low-medium

The hit rate here was almost 8% below estimate and resulted in the worst performance for six seasons, and a loss of -£819.00.

Result: Loser

]]> 223
5 Simple Steps to Win Over and Under Betting Mon, 10 Jul 2017 05:40:23 +0000 more »]]> In the world of sports betting, most punters focus on 1×2 match results. Punters are driven to find a system for Home-Draw-Away bets, but regrettably, this bet type is actually one of the most difficult to master and to reap reliable profits from. It takes some time until bettors start to consider other markets such as Betting on Over Under Goals.

To teach you how to make reliable profits with Betting on Over Under we have written a Fundamentals of Sportsbetting course which is accompanied by Cluster Tables.

This article explains some of the mechanics behind the Cluster Tables.

Punters are driven to find a 1x2 system but Over Under betting is much easier

To demonstrate how the cluster tables work and that their use enables you to easily pick a successful portfolio of Over/Under bets for any weekend, we are going to analyse a random EPL weekend with the matches played between 12/5/2017 and 16/5/2017.

For detailed calculations and explanations we are going to be looking at the Tottenham vs. Man United match, played on 14/05/2017.

5 Simple Steps Guide on How to Win Over and Under Betting

  1. Calculate the HO/AO Quotient
  2. Pick the Correct Row in the Cluster Tables for the Match
  3. Calculate the Probability for all Over/ Under Goals Bets and Covert Them into ‘Fair’ Odds
  4. Compare your Calculated Fair Odds with the Market Odds & Identify the Value Bets
  5. Decide whether To Lay or To Back

The Cluster Tables have been developed to allow you to quickly calculate the true probabilities/odds for a match that you wish to bet on and then compare the true odds with the actual market prices. To find ‘value’ in the market you need to find the pricing ‘errors’; the bets which are overpriced and the bets which are underpriced.

The truth of the matter is that these are not really ‘errors’, but rather a result of the bookmakers making use of public opinion to maximise their profits. They reduce the prices of bets if the demand is high, and vice versa.

You too can account for ‘public opinion’ as a correction factor when calculating the true odds. This is done via the HO/AO quotient which is explained further down in this article.

Another important detail that you may notice when reading this article and using the Cluster Tables is that we don’t use any goal counts (or ‘form’ considerations, or news) from the current season.

We are going to analyse a round of matches from May 2017, but will be applying the Cluster Table encompassing the seasons 2011-12 to 2015-16 .

The example is purposely set late in the season to demonstrate that for true betting success you don’t need to worry about ‘current form’, ‘suspensions’, ‘weather’.

Have fun, enjoy & win!

(1) Calculate the HO/AO Quotient

This step is very simple.

Find the match – Tottenham vs. Man United (14/05/2017) – and using any odds comparison site look up the odds for the 1×2 bets.

The evening before the match, the home win (Tottenham) was priced at 1.85, and the away win (Manchester Utd) at 5.50.

For the HO/AO quotient you then simply divide the home odds (HO) by the away odds (AO).

1.85 divided by 5.5 = 0.336

For those who like odds closer to the game, the highest bookmaker odds just before kick off were: Tottenham: 1.7 and Manchester Utd: 6.3.

1.7 divided by 6.3 = 0.269

We need this quotient for the next step, but first we will take a look at what this quotient actually means.

In the next step you will also see that both HO/AO quotients – 0.336 and 0.269 – fall in the same cluster group. This will actually (almost) always be the case as the clusters span quite a wide range of corresponding odds. Therefore, it really does not matter WHEN you carry out the calculations!

Bookmakers seldom price their odds to represent the true probabilities. They set odds that follow the public opinion.

We are making use of this public perception as a ‘correction factor’ when trying to find value bets.

This is where the HO/AO quotient comes in handy as a very simple solution. It is possible to find the 1×2 odds for any match played in the past and to calculate their HO/AO quotients.

With the help of the HO/AO quotients it is then possible to cluster matches into groups which represent the ‘perceived’ strength of teams at the time of the match.

For example, a match perceived by the public as being between two equally strong teams at the time of the match will have a quotient between 0.9 and 1.1 (home/away odds, both, in the region 2.5 to 3.0), while strong home favourites may have quotients of 0.04 or 0.05 and so on.

Just tinker around with that, until you get the idea.

Here’s a video to show you the EPL Cluster Table in action.

Now we are going to looks at some of the calculation from the video in more detail…

(2) Pick the Correct Row in the Cluster Tables for the Match

After having calculated the HO/AO quotient we are only one step away from picking the Value Bet(s) for this match.

For the sake of the shortness of this article and to keep it sweet and simple, we are only looking at the Over/Under 2.5 Goals bets.

In the match between Tottenham vs. Man United match, played on 14/05/2017, the Over/Under odds for this match were very close: The bet on Over 2.5 goals was priced at 2.00, and the Under 2.5 bet was priced at 1.98.

Which one of the two was the value bet? What should we have picked without listening to our gut feelings?

Remember, the HO/AO quotient was:

The evening before the match: 1.85 divided by 5.5 = 0.336
The closing odds before kick-off: 1.7 divided by 6.3 = 0.269

Here are the screenshots for the distributions for both team (I marked in orange the cell you have to look up the probabilities to calculate the game in the next step).

Tottenham at Home - Distribution

Manchester Utd at Home - Distribution

In the above screenshots, the goal distribution of Tottenham playing at home and Manchester United playing away can be seen.

Please note that, for Tottenham we had to pick the second to last row to be in the correct cluster group whilst for Manchester United it was the last row. This is something, that when you start using the Cluster Tables, you will have to be very careful about – to always pick the correct row which corresponds to the calculated HO/AO quotient.

(3) Calculate the Probability of Over/ Under Goals and Convert Them into ‘Fair’ Odds

With the above two tables we can now calculate the probabilities for this particular match.

The calculation is as follows:

Tottenham Home: 56.5% plus Manchester Utd Away: 54.4% = 110.9%
110.9% divided by 2 = 55.45% (rounded: 55.4%)

Expected ‘Fair’ Odds: 1 divided by 55.4% = 1.81

Just as a side note, we are calculating with European odds through this website. If you don’t know how to convert probabilities into odds and vice versa, here’s the formula:

Probability into European odds

If you need to calculate with odds other than European, here’s the article on the topic:
Understanding Betting Odds – Moneyline, Fractional Odds, Decimal Odds, Hong Kong Odds, IN Odds, MA Odds

Next Steps:
(4) Compare your Calculated Fair Odds with the Market Odds & Identify the Value Bets
(5) Decide Whether To Lay or To Back

Wish to play around with the Cluster Table?
Try the EPL Cluster Table for Only £2

]]> 14
HDAFU Tables: £10k in 178 days with the Summer Leagues Thu, 06 Jul 2017 21:27:49 +0000 more »]]> They say that the proof of the pudding is always in the eating.

Here is how a straightforward backing system made up of a portfolio of nine leagues from our Summer League HDAFU tables made over £10,000 in 178 match days from £100 level stakes during 2016.

2016 Campaign Odds Range

FREE Download!
2016 Summer League Campaign Workbook:

Full details of the 2016 Summer League portfolio are included in a dedicated Excel workbook, which you can download here for free. This workbook details every bet placed in all nine leagues, together with a chronological summary, the winning and losing streaks, and the parameters of each system employed.

It’s a must-have simply as a monitoring sheet template, and you will need it to understand much of what we talk about below.

Click on the following link to receive your free download via email:

>>> 2016 summer league campaign <<<

Just click on the button above and then on “Continue Checkout” in the pop-up box. Enter your name and e-mail address and our store will then deliver the file to you via e-mail, free of charge. The size of the Excel file is 278KB. (Warning: Please do not apply these systems to future seasons – the parameters will certainly have changed, with each league requiring a complete re-analysis).

Note: When downloading this spreadsheet you will also receive a coupon code offering a discount of £5.00 GBP, redeemable against the purchase of any individual HDAFU Table. This allows you the opportunity to experiment and explore your first HDAFU Table without paying the full price for it and before you commit to buying more. Test drive and formulate strategies for any current season ‘on the cheap’!

Overview of the Monitoring Workbook

Summary Tab

Here you will see the 15 separate systems derived from the HDAFU tables that were pooled together as a single campaign; a well-balanced mixture of backing home wins and favourites (six systems: low risk/low return) and away wins and underdogs (nine systems: higher risk/higher return).

At the time of analysis, although there were viable systems for the draw apparent, other systems took preference. (However, several draw systems were employed in the subsequent Winter League portfolio).

You will also see that in certain leagues, we different systems were run in the first and second halves of their seasons. In other leagues, the system chosen was a better fit for the whole of the season (U.S.A., Finland and Japan).

Analysing the HDAFU tables is now a much faster exercise than ever before despite the fact that each league now comes with three separate workbooks: one to demonstrate the five full seasons approach; one limited to games in the first half of each season; one limited to games in the second half of each season.

As frequently happens, there is more than one opportunity to analyse in each of the three workbooks, but only the most promising system per league is considered for inclusion, or two if the league is split into half seasons. Read more about this approach here.

Running more than one system per league in the same market (in this case, the 1×2 market) causes confusion with conflicting betting decisions. It also means relying on something that is not the most promising in that league to help support the portfolio as a whole. With portfolio betting it is essential to field the strongest team from the start without involving any also-rans.

To mix the best performing systems with lesser ones would be like mixing apples with pears. The sweet tasting apple pie we hoped to bake would be contaminated. Always better to compare and match apples with apples.

On the whole, the time taken to analyse and then decide upon which system to support was no more than a couple of hours per league, sometimes a little more, sometimes less.

For the nine leagues represented, less than 20 hours was spent coming up with the 15 systems.

(1) Expectations Prior to 2016 Season

In columns F-P, you will see a complete breakdown of the figures the 15 systems forecasted for the 2016 season in each league.

You will also see a box entitled Possible Yield Range (Row 30). The Average Yield and Lowest Yield expected are highlighted: between 23.86% and 1.58%. This is the more realistic threshold the final result was expected to occupy.

The Highest Yield expected of 46.05% is an arbitrary figure. It is virtually impossible to achieve for the following reasons:

  • It represents a cherry-picking exercise because the 46.05% figure is a synthesis of each league’s single highest profit season from the five analysed. Which season is the ‘best’ is also unlikely to be the same one in different leagues. For example, it might be the 2015 season in Japan and 2016 in Sweden.

    Although there is a tiny possibility that all nine of our leagues simultaneously experience their best season in the last six in the bet types we are targeting, the statistical chance is negligible.

  • The HDAFU tables are based on highest market odds at the close of the ante post market and it is extremely unlikely that you will obtain the highest odds available with every bet you place. The more realistic expectation is therefore always going to be less than the Highest Yield forecast.
  • Some of the 15 systems were bound to fail although guessing which ones would was impossible to answer. This was known before the campaign began. There are several reasons for this:
  1. Systems were chosen which showed a historical profit in at least four of the five seasons analysed. Even with a system based on five seasons’ profit, there would still be chance of it failing in the sixth season.
  2. The league may experience a lower than average hit-rate in the new season. In fact, the coming season may be an anomalous one altogether. For example, it records the worst hit-rate for home wins in the last 10 seasons. Without the need for a complicated mathematical calculation it can be said right away that there is a basic one in 10 chance of this occurring, and 10% is 10%, not zero.

    The more leagues and systems used, the more times this chance is faced and 10-year record highs and lows have to be set sometime. Of course, if we narrow things down and say that the league records its worst set of home wins in the next season (the sixth: the one after our five seasons’ analysis), the chance of the new season being the worst of the last six is a basic one in six (16.67%).

    Likewise, for a bet type to record its best results for 10 seasons, the chance is again 10%, and 16.67% in the last six seasons.

    Of course, the reality of the overall performance is likely to be somewhere in the middle (a standard distribution bell curve). Not all systems will fail and not all will over-achieve but by picking the sweet spots in the historical results, the chances of overall success are enhanced.

  3. Bookmaker odds across the board may be slightly lower than usual in response to repeating trends in the match results. There are definitely some seasons where the odds setting for a particular bet type is markedly different from previous seasons. It’s not often, but it does happen. This may not influence whether a profit is made, but it will affect the size of it.

  4. (2) Results of 2016 Season

    The forecasts and the results achieved were very close.

    The average forecast suggested a scenario of 849 bets with a hit-rate of 44.99%. The total eventually recorded was 825 bets (without missing a single betting opportunity) at a hit-rate of 43.52%.

    But even with these fractional shortfalls, a yield of 12.17% (cell V28) equated to a profit of £10,038, with all four bet types in profit – The higher risk/higher return away wins were the star performers with a profit of £7,097 (cell Y25).

    A yield of more than 12% is an excellent return. Anything over 5-6% is good. There are no savings plans that we are aware of that deliver such a large return in such a short space of time.

    And if you need reminding, the money in betting is not in perennially backing home wins and favourites.

    Only four of the 15 systems achieved yields in excess of their average expectations (V column cells filled in green). Three of these (plus another two) achieved hit-rates in excess of the five season average (T column cells filled in green).

    Overall, it was not an exceptional performance (it didn’t need to be), but it was a carefully planned one. It flew the mission, hit the objective and came back in one piece. The system avoided the bookmakers’ radars with a relatively small stake of £100 per bet. (Limited by the size of our initial bankroll).

    A 10k return and a bankroll which was luckily in profit from bet number 1 (and remained so until the end – see Chrono tab), was immensely satisfying, and when all was totted-up the earnings came to around £70 tax-free per hour of time invested in the project. Everything will be quicker and slicker next time…

    Aftermath – Why did Some Systems Fail?

    Going back and trying to figure out why things went wrong is an integral part of any betting system. It helps allay fears that perhaps you did something wrong – if you did, hopefully you’ll find the error. It’s not about creating excuses for failure; it’s more about peace of mind and learning lessons for the future. Life is all about continuing to learn.

    Getting the calculations correct when formulating the systems is fundamental. If theories are based on misleading information to begin with, you are sunk before you start betting.

    Here is the post-mortem:

    Brazil – Série A

    It was a strange season in Brazil.

    The crowd plays a hugely important role in football matches. We’ve all heard of ‘partisan atmospheres’, especially during local derbies.

    Following the undoubted rise in popularity in the game caused by hosting the World Cup in 2014, average attendances rose to a six year high of 17,160 per match in 2015 and then instantly fell by almost 10% to 15,809 in 2016. Increasing crowd violence and rising admission prices were held to blame.

    It is difficult to say how much of an influence the crowd effect has on a season, but it was certainly an anomaly in 2016.

    On top of this, results were also skew-whiff. The 2016 season saw 53.30% home wins. During 2011-13, this figure was around 48%; 2014 = 51.84%; 2015 = 52.63%. The differences between these figures do not seem great, but in 2016 there were 202 home wins, almost 20 more than in any of the seasons 2011-13.

    Whilst the first half season system based on home wins brought a profit, the home win anomaly detrimentally affected the underdog system in the second half of the season. The away win percentage (mostly underdogs) only hit 21.9% in the second half of the season, a six season low.

    However, the fact remains that the second half season underdog system was only one win away from turning a profit. If any one of the 21 lost bets had come in, there would have been profits across the board in Brazil.

    Instead, it was just a case of bad luck. The majority of expected home wins were in the second half of the season, when the preference was for the other way around.

    Norway – Tippeligaen

    The second half of the season was miserable. It was tempting to pull the plug on this system at one stage, especially when it became obvious that this system would fail.

    But, the point of all of these systems is to hold firm and play them through to the end. Compare what happened in Norway with the last round of games in Japan where all five bets won. This is another example of synergy – the Norway losses were recovered elsewhere in the grand scheme of things.

    Norway recorded its lowest home win rate for six seasons and by more than 2%. This equates to six wins short of the lowest total in any of the previous five seasons, which in a 240 game season, is a big deviation.

    In the first half of the season, the incidence of home wins was 50.51%, with only 26.26% away wins. In the second half, when home wins were targeted, the rate dropped to a miserly 41.13%, whilst away wins were 31.21%. Like Brazil’s two systems, Norway’s results were precisely the wrong way around again.

    Norway was certainly anomalous as it produced the lowest home win rate in 2016 of any season since 2004. That 10% chance mentioned earlier came in here.

    You’ll see from the HDAFU tables (if you buy them!) that the Norwegian mid-season break (like Sweden) is around a third of the way into each season. The fact is that the season halves are disproportionate. Most of our bets were in the larger second half programme.

    Perhaps in future it will be a better idea to use a whole season analysis (i.e. dispense with the split season approach) in all leagues where the season halves are disproportionate.

    Singapore – S-League

    This was a lesson in gut-feeling. This system was taken on board largely due to previous successes in this league.

    The 2015 S-League had turned-in a yield of 37% and profits of £4,659. It was almost in homage to this result that underdogs were chosen again in both halves of the 2016 season.

    The league format in Singapore has changed dramatically recently. 2015 saw only 9 teams take part in the league, which was repeated in 2016. There were 13 teams in 2013.

    The statistics used to formulate the systems here were therefore disparate. In splitting the league into halves for the first time, a mixture of apples and pears was unwittingly analysed.

    The tiny loss incurred across the board was therefore a matter of luck. Okay, it was only 26 bets in total during 2016, but a small negative result wasted time that could easily have been avoided. Greed probably got in the way of the decision-making process as did the feel-good factor of winning well in previous seasons.

    2017 will probably see a return to the whole season approach in this league too.

    Next Page: Other Workbook Tabs and Conclusion

    ]]> 46 1X2 Betting System – Staking the Underdog Wed, 12 Aug 2015 03:11:03 +0000 more »]]> Every year we publish HDAFU simulation tables (Home, Draw, Away, Favourites, Underdogs), which model profit & losses for five seasons in each featured league for developing profitable betting systems.

    Today’s article discusses the question what would have happened when backing the underdog playing away from home in the German Bundesliga?

    Such a match was played in this league on 23/05/2015 between Moenchengladbach and Augsburg. The best bookmaker odds for the full-time 1×2 market at kick-off were: 1.57 Home; 5.00 Draw; 7.30 Away.

    Moenchengladbach were the clear favourites at 1.57; Augsburg the rank outsiders. However, the men of Augsburg won the game, 1-3, defying their long odds.

    How regular do such things occur? Is it profitable to bet on outsiders?

    Here’s a screenshot from the ‘Backing by Odds’ tab in the simulation table for this league:

    BL1 Simulation Table – Betting on Away Win 2010-11 to 2014-15German Bundesliga – ‘Backing by Odds’ tab – Five Seasons 2010-15

    In the table above you can see that from a total of 306 matches during 2014-15, the away team won 79 times. (Click on the table to enlarge it in a new browser tab).

    79 of 306 is 25.8%, and this percentage shows that the away team won, on average, slightly better than once every four matches.

    Profit and Loss Sectors when Betting on the Away Team

    Looking at the profit/loss (P/L) summaries in the ‘Totals’ column, adding together the first six rows of odds clusters produces a loss of -2,564 units, based on a flat stake of 100 units per bet.

    Essentially this means if the away team was priced as a clear favourite or close to the home team’s prices, they won less frequently than the probabilities indicated by their odds. The last of these first six cluster groups closes at away odds of 2.90.

    Look at the second row of the table. The odds cluster between 1.66 (implied probability 60.2%) and 2.00 (implied probability 50%) contains 83 matches and, if the odds had been ‘fair’, 55.1% (60.2% + 50% / 2) of the away teams priced in this group should have won.

    As you can see, this was not the case! Of 83 games in five seasons only 43 were away wins (51.8%).

    Therefore, punters who regularly backed away favourites in the Bundesliga during 2010-15 surrendered ‘value’ in their bets to the bookmakers. When this happens, only one side of the deal wins in the long-run; invariably it isn’t the bettors!

    Okay, let’s take a look at the away underdogs…

    BL1 Betting on Away Win - 2010-11 to 2014-15German Bundesliga – ‘Inflection Points’ tab – Five Seasons 2010-15

    This screenshot shows a steep rising curve starting at odds of 4.40 and continuing until odds of 17.0.

    Over five seasons, 462 matches fell into this group (Moenchengladbach vs. Augsburg being one of them). The away underdog won 88 times = 19% hit rate!

    In these odds clusters the away team won, on average, once in every five matches. The average betting odds were 6.40, representing a probability of 15.6%.

    The curve shows, as well as the calculations (19%/15.6% = 121.7%), that the mathematical advantage was on the side of the gambler!

    The P/L curve registered 653 units profit at the start of our selected segment and finished at 13,727 units. This is a difference of 13,074 units of profit located solely within the away odds cluster group from 4.40 to 17.0.

    Why does this advantage exist? How does it happen?

    Backing Low Odds Favourites – Downfall of any Betting System

    Most bettors prefer betting on the more popular and ‘emotionally safer’ shorter-priced favourites, but please ask yourself the following two questions:

    • How does a profit-oriented company (i.e. bookmaker) set its prices?
    • Should the prices (odds) for favourites rise or drop?

    Both common sense and business acumen prevail in this situation:

    Many customers = High demand = Higher ‘prices’ for the product!

    The market dynamics are the following: The more bets expected to be placed on a particular outcome, the more bookmakers reduce their odds. Reducing odds mean that the bettor must risk more money (stake more) to achieve the same financial outcome. The punter therefore pays a ‘higher price’ (gets lower odds) for the same product:

    Odds 2.0 → stake 50 = win 50
    Odds 1.5 → stake 100 = win 50
    Odds 1.25 → stake 200 = win 50

    Falling odds means:

    ⇒ Rising stakes
    ⇒ Potential to lose more money
    ⇒ Lower percentage returns should the bet win!

    Although this relationship may seem paradoxical, falling odds means rising prices!

    Bookies adjust Favourite & Underdog Odds to Public Expectations

    To reiterate: Falling odds for an outcome is a clear indicator that this is a favourite. Warning! Dropping odds do not indicate that the statistical probability for the favourite winning the game is improving; purely the fact that the outcome is becoming more and more favoured by bettors. This is a betting fundamental, which many gamblers are totally unaware of.

    Falling odds mean bookmakers are effectively raising the price for the product! The product itself does not change in the slightest (i.e. betting on the favourite), but it becomes more expensive to buy. The bettor has to risk more money in order to win the same amount. In this case, you do not get ‘more for your money’, but considerably less!

    Let’s use a different example. A confectionery company launches a new chocolate bar, which becomes an instant success. Demand increases; the company naturally takes advantage of the situation by raising the price. You can certainly make the statement that if the price of the chocolate increases it is a ‘favourite’, but the product itself never changes – it’s still a 100g chocolate bar!

    The last word here is that since the books have to be ‘balanced’ (i.e. the payout of all three 1×2 bets combined needs to add up to around 100%), whilst the ‘prices’ for favourites are lowered to take advantage of the demand, on the opposite side, the odds for the underdogs rise.

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    Combinatorics and Probability Theory in Football Betting Fri, 17 Apr 2015 08:09:38 +0000 Introduction to Combinatorics and Probability Theory

    This article is a step-by-step guide explaining how to compute the probability that, for example, exactly 4 out of 6 picks win, or how to calculate the likelihood that at least 4 of 6 bets win.

    To help your understanding of this topic you will need to comprehend the basics of football result probability calculations, which I explained in detail in the article Calculation of Odds: Probability and Deviation.

    The Basics of Probability Computation in Football Betting

    The following picks table contains 6 value bets including the calculated probabilities for each bet to win:

    English Premier League - Value Bets - 22.3.2011

    English Premier League - Example Picks 22.3.2011

    Of the 6 published picks, 4 won and made a profit of 19.9% on the 50.00 € betting bank. I will now attempt to explain the mathematics behind the above selections.

    The calculation of the probability that all 6 Picks will win is relatively easy and requires no knowledge of difficult formulas. You simply multiply together the given probabilities, thus:

    61.1% x 63.2% x 77.0% x 56.4% x 52.6% x 71.0% = 6.3%

    The result of 6.3% is the probability that all 6 picks in the portfolio win.

    Of course, the other end of the scale is that all 6 picks will lose. Again, this is a straight forward calculation: simply multiply the opposing probabilities to those used in the ‘win’ scenario, thus:

    38.9% x 36.8% x 23.0% x 43.6% x 47.4% x 29.0% = 0.1973%

    The result of 0.1973% is the probability that all 6 picks lose.


    • Probability that all 6 Picks win: 6.3%
    • Probability that all 6 Picks lose: 0.1973%

    If you divide 6.3% by 0.1973% the result is 31.93. This means the probability in this particular portfolio that all 6 picks win is almost 32 times higher than the probability that all 6 picks lose.

    Practically speaking, there is a 32 times higher chance of winning all 6 bets and cashing 40.90 € profit than losing all 6 bets together with the entire 50.00 € starting bank.

    Accumulated Betting Odds

    • To win all 6 picks: 15.9 (1 divided by 6.3%)
    • To lose all 6 picks: 506.7 (1 divided by 0.1973%)

    These odds express that on average all 6 selected bets should win once in every 16 rounds and only once every 507th round should a total loss of the portfolio occur.

    A single season’s football league betting will usually comprise approximately 80 rounds of matches (midweek and weekend betting). This means that statistically a total loss may happen once every 6.3 years betting on a similar portfolio to the example above each time. Of course, it could happen more often as wins and losses have a nasty habit of not lining up as cleanly as statistical theory says they should. For example, 2 total losses could occur in the first 2.6 years and then no more for another 10 years.

    What is the probability that exactly ‘X’ picks win or lose?

    Further interesting questions include what are the probabilities that exactly 5 of the selected 6 picks win, or at least 4 of the picks win, and following this, it is natural to ask whether it is viable to make long-term profit on this type of portfolio and if so, how much?

    An easy starting point for assessing whether a portfolio is ‘worthwhile’ is by calculating the ‘expectancy’, in other words, how many of the picks are likely to win. This is simply the average of the win probabilities of the selected picks:

    (61.1% + 63.2% + 77.0% + 56.4% + 52.6% + 71.0%) / 6 = 63.55%

    This value means that by betting on the above portfolio a success rate of 63.55% is ‘expected’, which would correspond to a hit rate of 4 from 6 picks (i.e. 6 [picks] times 63.55% = 3.81 [roughly 4 picks]). This means that on average this portfolio should usually bring around 4 successful picks. However, it is obviously necessary to check if the combination of 4 successful picks and 2 failed ones will produce a profit:

    Football Betting Profit Calculation - Permutation Any 4 from 6

    Profit Calculation: Exactly 4 out of 6 Selections Win

    The above illustration shows that every combination of 4 picks from our 6-match portfolio would have returned a profit of between 7.02 € and 16.71 € depending upon the combination.

    Important Note

    Please note that the average value (expectancy value) does not mean a 63.55% probability that exactly 4 picks will win every betting round. The average value indicates that if you bet on this type of 6-match portfolio often enough, an ‘average’ of 4 hits can be expected.

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    1×2 Football Betting – How to Compile a Winning Portfolio Fri, 05 Dec 2014 14:00:34 +0000 more »]]> This article moves away from betting on individual teams, and pushes strategic thinking further up the knowledge ladder.

    The method described below explains how to use our HDA simulation tables for recognising profitable 1×2 betting strategies and building a portfolio from a selection of major European leagues.

    Conceptual image of 1x2 football bettingImage: archideaphoto (Shutterstock)

    Profitable betting on football is about compiling successful portfolios and understanding the underlying market economics.

    The following analysis portrays just one successful scheme in detail – Have fun learning about market behaviour and deriving a betting system from it! 🙂

    Understanding the Betting Market

    It is impossible to predict with total accuracy the outcome of one particular match; however, it is possible to identify and use historical distributions of data to judge the future in general.

    If you do not know what the term ‘distribution’ means, check out this article for an introduction:
    Goal Distribution Comparison – EPL, Bundesliga, Ligue 1, Eredivisie

    However, understanding distributions, odds calculation and probabilities is only the first step.

    The next step is to understand the market economics. Just in case you missed them here are two articles describing how the bookmaker market works:-

    How do Bookmakers Tick? How & Why do They Set Their Odds as They do?
    How Bookmakers’ Odds Match Public Opinion

    The main message of these two articles:

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

    Comprehending Market Economics to Elect a Strategy to Investigate Further

    Remember your basic economics lessons in school or college which were about supply and demand.

    Adapt this to the football betting market: In which situations will bookmakers reduce their prices (odds), and which prices will increase as a result? Which bets are traditionally the most popular?

    The fact is the majority of punters prefer betting on favourites up to odds of 2.5. Just look at online odds comparison sites which show the percentage distribution of bets on a certain outcome. It is frequently above 60% on the favourite (independent from the offered odds), if not higher.

    On the other hand, consumer demand for bets on the underdog is often much lower than the actual chance of it winning.

    Bookmakers are aware of this market behaviour and try their best to predict trends, time the market, and choose the best outlets for their odds. Customer behaviour is well analysed and used to generate various marketing strategies aimed at balancing the books and boosting sales.

    Therefore, for the bettor, it is safe to assume that many favourites will be under-priced to win, and draws and/or away wins will be over-priced to “make up and balance the book”.

    For example, a traditionally strong team like Bayern Munich playing away will, of course, attract a good deal of punters betting on them to win rather than any weaker opponent playing at home. However, most punters are normally ignorant of the fact that even teams such as the mighty Bayern Munich win approximately just 50% of their away games.

    In these game constellations bookmakers, simply by following market economics, have to reduce their prices for the (away) favourites massively and balance this by increasing the price of the less fancied home team.

    Investigating Distributions: Profit/Loss Inflection Points

    From what has been explained in the previous chapter it should now be obvious that favourites are often under-priced to win, and draws and/or away are frequently over-priced. Therefore, it should be possible to find a workable strategy using this knowledge.

    Now comes some maths… hang in there! 🙂

    In the last five seasons, a total of 1,900 matches were played in the English Premier League (EPL), of which, 46.74% finished in a home win:

    Table showing EPL Full-time 1x2 distribution - Five seasons 2009-14EPL: Full-time 1×2 distribution – Five seasons 2009-14

    The home team was priced the favourite in 1,351 of these matches (home odds lower than the away odds), and a total of 763 games did indeed end in a home win, equating to 56.48%.

    Table showing EPL: Favourite home wins - Five seasons 2009-14EPL: Favourite home wins – Five seasons 2009-14

    The balance of 549 matches saw the home team priced as the underdog (home odds higher than the away odds). From these games, 125 finished in a home win for the underdog, equating to 22.77%.

    Table showing EPL: Underdog home wins - Five seasons 2009-14EPL: Underdog home wins – Five seasons 2009-14

    Now convert these favourite and underdog win percentages into odds:

    Home wins (Favourite): 56.48% = 1.77 [European odds]
    Home wins (Underdog): 22.77% = 4.40 [European odds]

    The above two odds are “inflection points”, the points on a curve at which the curvature or concavity changes from plus to minus or, from minus to plus. Translated into layman’s language… the pivot points along the profit/loss curve where profits turn to losses or, where losses turn to profits.

    However, these are purely the mathematical inflection points and do not take market forces into consideration.

    Therefore, please do not start betting on every favourite at home priced below 1.77 in the EPL, or on every underdog playing at home priced above 4.40. (Although following this simple strategy would have produced quite a profit!).

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    The Gambler’s Ruin Explained – Fair Coin Flipping Wed, 24 Sep 2014 08:26:01 +0000 more »]]>

    One of the phenomenons of probability is Gambler’s Ruin. The most common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected zero value to both sides) will eventually go broke against an opponent with infinite wealth.

    In other words, the maxim of gambler’s ruin is that if you play long enough you will eventually go bankrupt and have to quit the game prematurely.

    Woman holding bank notes close to her face with a calculator and bills in the background / Frau hält Banknoten an ihr Gesicht mit Taschenrechner und Rechnungen im HintergrundCollage of Shutterstock images; Foreground: wacpan, Background: Lisa S.

    The World of Sports Betting

    The truth is that in the world of sports betting, the common gambler has far less money than a bookmaker or casino, and there will inevitably be a time when he will simply be unable to continue playing and, of course, the house will not be giving credit.

    “Long enough” may be a very long time though. It mainly depends on how much money the gambler starts with, how much he bets, and the odds of the game. Even with better than even odds, the gambler will eventually go bankrupt. But, this may take a very long time indeed.

    Please note that we are talking here about a “fair” game; e.g. each bet with zero value. The practice of bookmakers and betting sites to offer odds with an overround in their favour makes this outcome just much quicker.

    Fair Coin Flipping

    To make the dilemma of gambler’s ruin a little easier to understand imagine coin flipping with a friend. You each have a finite number of pennies (n1 for yourself and n2 for your friend).

    Now, flip one of the pennies (either player). Each player has a 50% probability of winning (head or tail). If it’s a head you win a penny and if it’s a tail you surrender a penny to your friend. Repeat the process until one of you has all the pennies.

    If this process is repeated indefinitely, the probability that one of you will eventually lose all his pennies is 100%. In fact, the chances P1 and P2 that players one and two, respectively, will be rendered penniless are:

    Formula Gamblers Ruin

    Now let’s populate these equations with real numbers:

    Gamblers ruin example 50-50 - same pennies

    The above example is based on both players starting with the same amount of pennies (100 each). In other words, you and your friend have both an exact probability of 50% to end up with all of the pennies after many, many coin flips. This means that after an unknown number of coin flips either you or your friend will finish banking all the pennies. At the start, your chances are equal, and it is impossible to say who may win.

    However, if one of you has many more pennies than the other, say you start with 100, and your friend with 10,000, then your chance of finishing with all of the pennies (yours as well as your friend’s) is as low as 1%, whilst your friend’s chances are 99% to win this unequal match.

    Gamblers ruin example 50-50 - player 2 advantage.jpg

    Bankruptcy Probability Table – Gambler’s Ruin

    To visualize the gambler’s ruin problem further, here is an overview of the probabilities of finishing with N amount of pennies.

    Player 1 starts with 5 pennies. Player 2 has an infinite amount of pennies.

    The top row shows the number of flips. The left hand column shows player 1’s current amount of money. The numbers in the table are probabilities (click on the image to enlarge; opens in a new tab):

    Visualisation gamblers ruin

    Overview of the probabilities to finish with an N amount of pennies after X flips

    Reading the table (examples):

    After the first flip player 1 has a 50/50 chance of ending up either with 4 pennies (i.e. he lost the first coin flip), or with 6 pennies (i.e. he won the first coin flip).

    In 10.4% of the trials player 1 will be broke (penniless) after the tenth flip of the coin. This means that every 10th experiment of this nature player 1 will have been forced to give up after the 10th flip of the coin due to a run of “bad luck” whilst player 2 is not affected by “bad luck” purely because he has plenty of coins to sit through and survive any such spell.

    82.04% of the players will still be in the game after coin flip 15. However, 17.96% of the gamblers will already have retired due to exhausted funds.

    You can download the above table including all of its formulas, should you wish to experiment with different probabilities:


    In return for this freebie we would appreciate if you could share this article or give us a ‘thumbs-up’ with a ‘love’ or ‘like’ via Twitter or Facebook or any other social network site 🙂

    Of course, you will now probably surmise that player 1 started with only 5 pennies, and by staking 1 penny each bet he was risking 20% of his starting bank on each coin flip, which is way too much. Player 1 should ideally have started with a much larger pile of pennies, and risked a far smaller percentage of his bank with each coin flip.

    Anyway, eventually the same thing will always happen, albeit just much more slowly. Player 1 will still go broke sooner or later, if player 2 has an infinite amount of pennies. It’s just for the sake of the above table and illustration that we choose to show the calculations with a starting bank of 5 pennies only.

    Go to the next page, to see some more examples and illustrations…

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