Case Studies – Soccerwidow Football Betting Maths, Value Betting Strategies Thu, 18 Jan 2018 09:03:48 +0000 en-US hourly 1 5 Simple Steps to Win Over and Under Betting Wed, 30 Aug 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.

After reading this article you may wish to give it a try and use some of the ‘free bets’ offers from a bookmaker of your choice.

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
1×2 HDAFU Tables User Guide: 4 Easy Steps to Find the most Lucrative Betting Systems Tue, 08 Aug 2017 21:29:59 +0000 more »]]> Our HDAFU tables have evolved tremendously over the years – the 5th Generation of Summer Leagues is now available for sale.

They are a complete statistical analysis of historical performance over the previous five seasons of the Home win, Draw, Away win, Favourite win and Underdog win (H-D-A-F-U). They serve to identify the most profitable odds ranges in each bet type.

To help you understand why we value this product so highly, here is our Definitive Guide for using the tables to their maximum potential.

If you wish to work along with the example in this article you can download the relevant HDAFU table FOR FREE here.

Please note that this is a basic, abridged version but includes everything you need to work through this User Guide).

The size of this Excel .XLSX workbook is 864 KB.

>>> free hdafu table download <<<

It’s difficult for us to put into words how important the HDAFU tables are to us and our own betting adventures. But what we can say is that we have complete confidence in them to do their job. And from testing them in a live setting, we know that they are an extremely reliable method of building lucrative betting portfolios.

Quite simply, they are the best and most user-friendly tools available for nailing down value betting systems in every league you apply them to.

They reveal the DNA of a league, and provide a hidden level of detail that makes finding and exploiting the sweet spots so easy and so rewarding.

The next four steps will probably change the way you think about betting…

Step 1 – Observation

The first thing you will see when opening the Data Tab in any of the HDAFU tables is the financial summary of each bet type.

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

HDAFU Table Data Tab: Whole Season Results Summaries

HDAFU Table Data Tab: Whole Season Results Summaries

The totals along the top row show the effects of betting on every match over five seasons. In our example league the totals are (from left to right) Home win (-7,329), Draw (-835), Away win (+8,236), Favourites (-2,594), and Underdogs (+3,501).

You can see from this graphic that away wins look the most promising backing system with a profit of 8,236 units from 100 unit stakes.

To customise the stake amount enter what you want in the Fixed Stake box at the top of each bet type in the Data Tab.

The image above shows the full five season cold analysis. If you enter a different stake amount the financial values will change, but the percentages will always remain the same. This being the case, we have fixed these percentages as a benchmark to better gauge the improvements we will make with our filtering exercise later.

The Odds Toggle is for testing the effects of the odds you are getting when playing the systems for real – you can ignore it during your analysis.

You can also leave the betting exchange commission rate at zero. Again, use it for backing system monitoring purposes when you start betting on or paper testing your systems of choice.

Okay, we fancy away wins in this particular league but let’s now have a look at the Inflection Points Tab to see if this backs-up our observation.

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

HDAFU Table Inflection Points Tab: Inflection Points Overview

HDAFU Table Inflection Points Tab: Inflection Points Overview

Away wins are certainly financially the most profitable bet type but the profit curve doesn’t really begin rising until odds of 3.30 are reached. Overall profit at this point is 463 units and this rises to a peak of 13,502 units around odds of 8.60.

These two points on the graph would therefore be our two inflection points: Odds of 3.30 where the curve begins to rise; Odds of 8.60 at the pinnacle, the point at which profits begin to fall again.

However, notice there is a big portion of the away wins curve which is a zero-sum game. This ‘hole’ in our profit curve begins around odds of 3.75 (6,653 units). At this point, the curve falls away again, encounters what we call ‘statistical noise’, and only recovers at odds of around 6.52, when the profit figure surmounts its previous high at 7,184.

HDAFU Table Inflection Points Tab: Inflection Points Odds Intervals 3.75 - 6.52

HDAFU Table Inflection Points Tab: Inflection Points Odds Intervals 3.75 – 6.52

In between these two points is the potential for a lot of wasted effort and not a lot of gain.

We can see the extent of this by scrolling down and looking at the inflection point intervals.

(Click on the right-hand image to enlarge it in a new tab):

This image shows the start of the 3.75 odds sector at the top and the end of the 6.52 odds sector at the bottom.

The yellow column indicates the running total of matches up to each cluster of matches.

We can see that our two odds of 3.75 and 6.52 encompass roughly 330 matches – the difference between 1,115 indicated at the 6.52 break-off point and 785 at the starting point of the 3.75 cluster.

That’s 330 bets over a five season period that are simply not worth making; or 66 bets in a season.

HDAFU Table Inflection Points Tab: Inflection Points Odds Intervals 3.30 - 8.60

HDAFU Table Inflection Points Tab: Inflection Points Odds Intervals 3.30 – 8.60

We can see this clearer by looking at the same snapshot between our original inflection points of 3.30 and 8.60.

:(Click on the left-hand image to enlarge it in a new tab)

In this odds range, we have roughly 587 bets (1,221 minus 634). We now know that more than 56% of these (330 bets) are not worthwhile making.

This leaves only 257 bets but the away win profit sectors between the inflection points seem to be split into two areas of the curve: from odds of 3.30 to 3.75 (medium risk system, accounting for around 160 bets), and then from odds of 6.52 to 8.60 (high risk system; around 100 bets).

If we were to continue our analysis of away wins we would eventually see that the three elements (the medium risk sweet spot, the high risk sweet spot, and the statistical noise in-between) combine to give us a bumpy ride.

Our expected hit-rate will be tempered by that area of noise, and yield will be lower because of the size of the zero-sum area and the number of pointless bets within it.

This means a lot of unpaid work to perform, placing many bets that maintain the status quo and not much else. On top of this, the losing streaks will be greater.

Therefore, why not split into two systems in this league?

The synergy we have mentioned before about many systems supporting each other is what makes the HDAFU betting systems so viable.

However, we also mentioned that you should find the single best system in a league to play alongside the other best systems in the other leagues within your portfolio.

In our away win example, we would need to choose the better of the two systems we have identified. Either backing away wins at odds between 3.30 and 3.75, or between 6.52 and 8.60. Choose one or the other, not both.

We recommend never to play multiple systems in the same bet type. The synergy effect is diminished as ultimately, one of the two systems is not the best we can find.

Ideally, we are looking for synergy between the absolute single best systems in each league within our portfolio, without creating a situation where one system supports another within an individual league.

With different bet types in the same league (e.g. 1×2 market and over/under goals market) this is not an issue, but we would go as far as avoiding the conflict of interest between HT and FT 1×2 systems in the same league, for example.

Away wins initially looked great but is there something better?

Have a look once again at the Inflection Points graphs to try and see what it is.

As is typical of an underdog backing profile, the high risk/high return nature of this bet type produces a noisy curve, one full of jagged peaks and troughs. There are only small rising areas to analyse. Anything you can analyse into promising profits will contain few betting opportunities in a season, with long runs of losing bets to cope with.

Backing the favourite has one area between odds of 1.90 and 2.10 but we can see at these odds not a huge profit is created over five seasons (less than 3,500 units).

The home win is a misery for backing. Again, the sweet spot is between 1.90 and 2.10 but the profit is less than 2,000 units.

That leaves us with backing the draw. There is a large, rising area in the curve beginning at draw odds of 3.32 (-2,008 units), and peaking at 3.65 (7,170 units). It represents a potential profit chunk of 9,178 units over five seasons.

This is better illustrated by superimposing our inflection points onto our graph – We are interested in only the portion of the curve in-between the red arrows:

HDAFU Tables: Inflection Points Graphic

The shape of this curve is what you should be looking for when identifying the first system to analyse in your leagues of choice.

It is the classic, gently rising curve from bottom left to top right. It is relatively smooth, with a far smaller amount of statistical noise.

Therefore, this is the bet type we will analyse as our example.

Next Page: Step 2 – Hiding, Sorting & Filtering

]]> 76
How we made £20k in 214 days with the Winter League HDAFU Tables 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.

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

Sadly, the length of time it has taken us to put together this article and the accompanying spreadsheet means that we are not able to offer it for free.

Indeed, the information contained in the following spreadsheet is far, far more extensive than the Summer League free download, and is a betting education in itself.

And we are sure that you will feel the nominal £6 charge is worth every penny: It will double as an ideal template for your own portfolio structuring and monitoring processes.

The size of this .XLSX Excel file is 553KB:

>>> 2016-17 winter league campaign <<<



  • The spreadsheet details every bet in every system used and is totally customizable, including a stake toggle (Chrono tab cell N1838) to allow you to see the effects of different levels of flat staking.
  • Includes a separate tab for each of the 22 systems used, detailing the systems themselves and the individual bet results.
  • The Chrono tab brings the 22 systems together in one tab for collective detailed analysis.
  • The Inflection Points graph tab shows the profit curve’s adventures based on the full range of odds bought. (This is a static table relevant only to this portfolio).
  • The most important addition is the Stake Ratchet and Stop-loss simulation (an example of a medium-aggressive progressive staking plan: Chrono tab), which will provide you with the ideas and tools to manage your money professionally and make it work at optimum levels in order to maximise profits.


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.

]]> 204
How we made £10k in 178 days with the Summer League HDAFU Tables Thu, 06 Jul 2017 21:27:49 +0000 more »]]> They say that the proof of the pudding is always in the eating.

Here is the story of how we made over £10,000 in 178 match days from £100 level stakes during 2016 with a straightforward series of backing systems made up of a portfolio of nine leagues from our Summer League HDAFU tables. (Click Here: 14 leagues for 2017 now available for sale).

FREE Download!
2016 Summer League Campaign Workbook:

Full details of our 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).

Overview of the Monitoring Workbook

1) Summary Tab

Here you will see the 15 separate systems we decided to play with; 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, we do employ several draw systems in our Winter League portfolio).

You will also see that in certain leagues, we ran different systems 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 our 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 we take only the most promising system per league, 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.

If we were to start mixing the best performing systems with lesser ones then we would be 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, we spent less than 20 hours coming up with the 15 systems.

i) Expectations Prior to 2016 Season

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

You will also see a box entitled Possible Yield Range (Row 30). We have highlighted the Average Yield and Lowest Yield expected, which you will see is between 23.86% and 1.58%. This is the more realistic threshold we expected our final result 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 our 15 systems were bound to fail although guessing which ones would was impossible to answer. We knew this before we even started. There are several reasons for this:
  1. We chose systems 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 we can say 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, our chances of overall success are enhanced.

  3. Bookmaker odds across the board may be slightly lower than usual. We have definitely seen evidence in the data we have collected over the years that there are 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. It may not influence whether you make a profit, but it will affect the size of it.
  4. Next Page: Season Results and Post-Mortem

    ]]> 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.

    ]]> 51
    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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    Football Roulette – 2012-13 Correct Score Simulation And Conclusion Tue, 11 Jun 2013 20:27:15 +0000 In this final article on the Football Betting Correct Score Roulette System we will take the initial paper test one stage further and add what would have happened in the 2012-13 season if we had continued the system with the seven teams failing to register a 2-0 home win during 2011-12.

    We will also investigate the proposed stop-loss point at the end of the calendar year, and try to project what practical uses the theory behind this system may have in a different arena.

    2012-13 Paper Test

    As we have seen, this is a progressive system with each stake individually calculated to claw-back all previous losses and to collect a net £100 win when the desired correct score line arrives.

    In this way, the staking plan becomes exponential as we saw in the first of our three articles.

    Taking the same staking system into its second season and, still assuming that each bet can be placed at odds of 11.0, the table for match rounds 24-46 is as follows:

    Correct Score Roulette Staking Table - Rounds 24-46

    Correct Score Roulette Staking Plan Table

    NB. The new season begins on the above staking plan table for non premier league teams, but for the top-flight teams, match 20 on the original staking plan table represents the first game of the 2012-13 season (as Premier League teams play only 19 home games in a season).

    You can see on the table above how quickly the stakes grow from game to game for teams continually failing to register the elusive 2-0 home win score line.

    At some stage it will become difficult to get stakes of this size placed with any one market and therefore the system may have to rely on split stakes placed with more than one bookmaker or betting exchange to achieve full coverage of each match.

    Looking ahead, staking may become more and more tricky in order to force this football betting system to its final conclusion; pursuing this course is dependent on having a very large betting bank and having the desired result arrive before bankruptcy.

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    Football Roulette Correct Score Betting Strategy – 2011/2012 Season Paper Test Results Fri, 07 Jun 2013 19:00:58 +0000 What’s The Score?

    After describing the Football Roulette – Correct Score Betting system, it is time to reveal the results of our first paper test.

    30 teams were picked according to a popular selection process:

    • 8 from the English Premier League (top 8 from the previous season)
    • 7 from the English Championship (the 3 relegated sides from the Premier League plus the top 4 sides that didn’t get promoted into the Premier League)
    • 7 from English League One (the 3 relegated sides from the Championship plus the top 4 sides that didn’t get promoted into the Championship)
    • 8 from English League Two (the 4 relegated sides from League One plus the top 4 sides that didn’t get promoted into League One)

    Our chosen score, was a 2-0 home win.

    The system sounded good enough to put to the test and the following tables show the results from the 2011/2012 English League season (click on each table to open in a new tab and then place mouse pointer over the table and use magnifier to enlarge):

    2011-12 Results of the Top Eight English Premier League Teams from 2010-11

    English Premier League Results 2011-12

    2011-12 English Championship Results: three relegated Premier League sides and the four highest placed Championship sides not promoted from 2010-11

    English Championship Results 2011-12

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