Photo: Dario Sabljak (Shutterstock)

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. 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 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:

Now let’s populate these equations with real numbers:

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.

In fact, if you want to back the draw in a game, over 95% of the games we have analysed this season would have had financially greater benefits available in the bookmaker market.

Taking into consideration the standard Betfair commission rate of 5%, the bookmakers who wish to compete have to offer something more attractive but this is a balancing act if they want to avoid the risks of an arbitrage situation. The margins are therefore very fine but over the course of a season, you will undoubtedly be at least 5% better off placing your back bets in the bookmaker market rather than at Betfair.

Comparing Bookmakers’ Odds with Exchanges’ odds

Below, is a tiny extract from a huge Soccerwidow exercise comparing Betfair prices across many European top-flight football leagues with the best available odds offered by a selection of online bookmakers:

German Bundesliga Matches 2nd-4th November, 2012

For consistency, our exercise uses odds available 24-hours in advance of each match.

The calculations above take into consideration Betfair’s 5% commission charge, and you can see straight away that just one event marked red in the extreme right-hand column provided a better financial return with Betfair (the possibility of Augsburg winning at Hannover). Otherwise, 26 out of 27 events (96.3%) were better off backing in the traditional bookmaker market.

The extent of the bookmaker advantage in all of the 1X2 match event possibilities is also shown and here are a few examples:

• Freiburg to beat Moenchengladbach was priced at 3.50 in the bookmaker market, thus providing a financial advantage of 11.98% over Betfair’s price. In effect, for a 10 unit stake the bookmaker return is 2.68 units better off than with Betfair.
• The draw in the Bayer Leverkusen vs. Fortuna Dusseldorf was priced 9.25% better with the bookmaker market offering 3.25 units more return for a 10 unit stake.
• Backing Werder Bremen to beat Mainz provided a return 7.21% better with the bookmakers rather than with Betfair.

With the spread of results during this round of matches in the Bundesliga, it is evident that every HDA result which happened (cells highlighted in dark blue) was more profitable as a back bet in the bookmaker market. Even with some exchanges offering lower commission charges than Betfair, bookmaker prices are on the whole still more financially rewarding.

Successful Gamblers ‘Plan’ to Win – They Never ‘Hope’ to Win

An amount as small as 5% may not sound large, but 5% is a huge amount when considering factors such as eventual yield and return on investment.

If you have found what seems to be a successful selection system but lack the discipline not to attend to details when running your betting venture then we suggest that you are not serious enough about it. It follows that if you are not serious enough about your gambling then be honest with yourself and please do not bet.

Remember, the bottom two teams at the end of the season are automatically demoted to Bundesliga 2, whilst the 16th placed team enters a play-off with the 3rd placed Bundesliga 2 team to decide which will play in the top tier the following season…

Photo: Carlos Yudica (Shutterstock)

Many seasoned followers of top-flight German football will have developed a feeling over the years that the likelihood is pretty high that newly promoted teams do not tend to survive their first season in the Bundesliga 1.

However, the exact probabilities are probably something that not many bettors can quickly produce and Soccerwidow has therefore looked at the statistics in detail to provide answers.

Last Season’s Top 5 Automatic Relegation Outlook

It may be a slight surprise to learn that the probability of automatic relegation (bottom 2 finish) for a team having finished in the top 5 of Bundesliga 1 during the previous season is not zero; in fact it has happened 3 times in the last 49 seasons:

• In 1967-68, FC Nuremberg won the Bundesliga 1 title only to be relegated the following season.
• During 1968-69, Alemannia Aachen battled to a 2nd place finish but found themselves a year later playing in the second tier.
• The last memorable slide to oblivion of this nature was not so long ago: In 2008-09 Hertha BSC gained a creditable 4th place, the reward for which was Europa League football in 2009-10, but in the latter season they were demoted to Bundesliga 2, having finished 18th out of 18 in the top-flight.

Therefore, statistically speaking, the probability that any one of last season’s top 5, Borussia Dortmund, Bayern Munich, Schalke 04, Borussia Mönchengladbach or Bayer Leverkusen, are automatically relegated at the end of the 50th Bundesliga 1 season is 6.1%.

The statistics suggest that on average in Bundesliga 1, surprises such as this happen once every 16 years.

Newcomers’ Automatic Relegation Perspective

The probability is as high as 39.8% that a newly promoted team will not survive their first season in Bundesliga 1, but there is no guarantee that the automatic relegation positions at the end of the season will contain any of these teams.

Eintracht Frankfurt, Fortuna Düsseldorf and Greuther Fürth share a 37.5% chance that none of them will finish either 17th or 18th at the end of this season.

In 49 seasons, all of the newly promoted teams have avoided the bottom 2 positions on 18 occasions.

Last season FC Cologne (10th in 2010-11) and FC Kaiserslautern (7th in 2010-11) ended the season in the automatic relegation spots, 17th and 18th respectively, rather than either of the newly promoted teams FC Augsburg or Hertha BSC (although Hertha eventually succumbed in a play-off to Fortuna Düsseldorf).

Only 7 times in the history of Bundesliga 1 have newly promoted teams been automatically relegated in both the bottom 2 positions the following season. Last time this happened was 2007-08 when both Hansa Rostock and MSV Duisburg, finished 17th and 18th respectively after just a single season in the league.

The statistical chance of 2 of the 3 newly promoted teams (Fortuna Düsseldorf, Eintracht Frankfurt or Greuther Fürth) filling the bottom 2 positions at the end of 2012-13 is 14.6%.

The chance that just 1 of the 3 finishes in the bottom 2 spots is however fairly high at 47.9%.

So, the probability that 1 or 2 of the new arrivals do not survive longer than the 50th Bundesliga 1 season is 62.5% (47.9% plus 14.6%). The corresponding odds for this statistical probability are 1.6.

Conclusion

The market is currently offering the following odds for relegation:

• Fortuna Düsseldorf = 3.0 (33.3%)
• Eintracht Frankfurt = 5.0 (20%)
• Greuther Fürth = 2.8 (35.7%)

A “Dutch” back bet (weighted stakes for equal risk/return) on all 3 teams calculates to 89% (“Dutch” combined odds: 1.12)

The acid question is therefore whether it is better to “Dutch” back or “Dutch” lay all 3 of the newly promoted teams, Fortuna Düsseldorf, Eintracht Frankfurt and Greuther Fürth, in this the “Golden Jubilee” Bundesliga 1 season?

For a change we’ll let you decide…

Defending champions, Borussia Dortmund, will be bidding for their 3rd championship on the bounce but defending a title is never easy in Germany, attested to by 5 different teams having won Bundesliga 1 in the last 10 seasons…

Photo: KENCKOphotography (Shutterstock)

Meat & No Veg: Hamburger SV

Hamburger SV are the league’s longest servants, ever-present since its formation in 1963. Their record of 3 title wins, 5 runners-up finishes, and twice 3rd in 49 years hasn’t really troubled the statisticians, and 15th place last season was a narrow escape from possible relegation.

Never in the history of Bundesliga 1 has a team finished so lowly in a preceding season and then gone on to win the title. This fact is perhaps reflected in the bookmaker odds with Stan James currently offering best price at 201.00! This might be worth taking in the hope that Hamburg start the season well enough to trade out for a profit.

Not A Sausage: Kaiserslautern

Looking more at the stats, it can be further surmised that the likelihood of a team finishing 11th or lower improving enough to win the championship the following season is extremely low, although not absolutely zero, as are the chances of a team arriving from Bundesliga 2 and then immediately winning the top-flight division.

1. FC Kaiserslautern are the one team who have most recently defied this rule of thumb, winning the title in 1990-91 after a 12th placed finish the previous season, and more impressively triumphing in 1997-98, when they became German champions having spent the previous season in Bundesliga 2. Many commentators still attribute the latter success to the inspired leadership of Otto Rehhagel, one of Germany’s most famous and successful managers who took on the challenge of turning an unfashionable team into championship winners.

However, when all is said and done, Kaiserslautern will not have a chance for glory this time around due to their relegation last season…

Sauerkrauts: Hoffenheim, Mainz, Freiburg, Augsburg, Fortuna Düsseldorf, Eintracht Frankfurt and Greuther Fürth

So, back to the theory of teams unlikely to win the league having finished 11th or lower last season or who spent last season in Bundesliga 2. This would rule out the following teams:

• Hoffenheim currently best priced at 201.00, with Stan James.
• Mainz are 380.00 with Betfair.
• Freiburg at 1,001.00, again with Stan James.
• Augsburg seemingly have no chance at a price of 1,501.00, once more through Stan James. As they say, Augsburg have 2 hopes of winning the league: Bob Hope and no hope.
• The 3 newly promoted teams are likewise given little chance by the bookies and you can get odds of 1,001.00 on Fortuna Düsseldorf, Eintracht Frankfurt and Greuther Fürth from both Paddy Power and Blue Square.

Wurst Not First: Stuttgart, Hannover, Wolfsburg, Werder Bremen and Nuremberg

There is a 16.7% statistical chance based on the previous 49 seasons that a team finishing in 6th-10th place last season will win this season’s title. It has happened on 8 occasions since 1963.

This means that Stuttgart, Hannover, Wolfsburg, Werder Bremen and Nuremberg should all have improved chances of claiming the prize than any of the aforementioned teams.

16.7% means that on average, Germany heralds an unexpected champion every 6 years. In 2006-07 Stuttgart came from 9th the previous year to win the top-flight; in 2003-04 Werder Bremen won the league after placing 6th the previous season.

• Odds of 62.00 are available via Betfair for Stuttgart to claim this season’s crown.
• Wolfsburg can be backed with Betfred at a price of 81.00.
• The odds for Werder Bremen are best with Stan James at 151.00.
• Hannover are 171.00 with Betfair.
• Nuremberg are the rank outsiders of this group at a best price of 501.00 with Stan James.

Top Beer: Schalke, Borussia Mönchengladbach and Bayer Leverkusen

The statistical likelihood that a team finishing in 3rd to 5th position in the previous season wins the next is as high as 29.2%. The clubs in this bracket are Schalke, Borussia Mönchengladbach and Bayer Leverkusen.

If we had a soft spot for any of them it would be for Schalke to finally claim their maiden Meisterschale at only their 45th attempt.

• Schalke are the favourites from this group priced at a modest 26.00 with Betfair.
• Bayer Leverkusen can be backed at 67.00, also with Betfair.
• Borussia Mönchengladbach are 81.00 with Stan James.

This group of 3 can certainly be considered for a “Dutch” back bet and we will tell you why below…

Über alles: Borussia Dortmund and Bayern Munich

Top of the shop are of course defending champions Borussia Dortmund and Bayern Munich.

On 15 occasions, the defending champions have successfully defended their title, however 9 of these triumphs are firmly lodged in the record books of Bayern. Disregarding this for a moment, the pure statistical chance of Dortmund winning in 2012-13 is as high as 31.25%, but in 45 seasons they have managed a ‘double’ only twice, and have never won the title 3 times in a row.

Photo: Florian K. (Wikimedia Commons)

Bayern have accumulated 21 titles in their 47-year league history and their success rate is therefore a massive 44.7%; roughly speaking they win the Bundesliga once every 2 years.

To calculate the exact mathematical odds there are several approaches but these are beyond the scope of a short article such as this. Nevertheless, the fact is that no matter how the calculation is performed, Bayern and Dortmund have a statistical likelihood combined of around 50% of winning the 50th Bundesliga title, which of course means 50% any other team.

For those of you seriously considering a season-long investment on the Bundesliga winner, we advise to avoid backing Bayern or Dortmund as their odds carry hefty negative values. Bayern’s best odds are currently around 1.87 and Dortmund’s are at 2.90. However, realistically speaking, both should be somewhere in the region of 4.0.

Combining the market’s prices of these two teams produces a whopping 87% chance that one of the two will win the Deutsche Meisterchale in 2012-13. This is more than 40% below the long-term value, and therefore in the long-run more bets of this nature will be lost than won.

A nice alternative would be a “Dutch” lay bet on Dortmund/Bayern, risking 1.50 units to win 10 units with a 50/50 chance of success. Now that’s what we call a true ‘value’ bet!

Conclusion

The group probabilities for winning the 2012-13 Bundesliga season:

• Dortmund and Bayern – 50% combined
• Schalke, Mönchengladbach and Bayer Leverkusen – 29.2% combined
• Stuttgart, Hannover, Wolfsburg, Werder Bremen and Nuremberg – 16.7% combined
• The other 8 teams – 4.1% combined

It’s certainly going to be an exciting season ahead and a battle royale for the “Jubilee” title. If you are wagering money on the final outcome then please be aware that the findings above are purely based on statistics and not on any major changes in team personnel over the close season.

Never bet more than you can afford to lose and thanks once again for reading!

Congratulations to those ‘mad’ scientists at the International School of Management (ISM) in Frankfurt and the German Sports University in Cologne whose predictions we followed throughout Euro 2012.

Photo: byheaven (Shutterstock)

Those of you who also followed suit reaped the benefits of their statistical predictions realising a yield of between 19.7% and 25.5% depending upon which style of staking plan you employed (either fixed stake or fixed risk/win).

However, some of their prophecies did not materialise…

For example, co-hosts Poland did not make the semi-finals.

There were plenty of goals in the England v. Sweden match but not a huge goal difference for England and in the end they struggled to win at all.

Alas, the scientists’ beloved Germany did not get a chance to dethrone the defending champions in the final despite saying, “chance, luck and statistics are favouring zis”.

Never-ze-less, ze predictions from ze Frankfurt and Cologne think-tanks produced handsome profits.

As mentioned in our original article not all predictions will win. Indeed, it would have been miraculous if they had all won as the mathematical likelihood was just 0.00000031% (326 million to 1 – that’s definitely the way to bankrupt the bookies!).

Soccerwidow’s pre-tournament profit/loss estimation of the scientists’ predictions using a fixed risk/fixed win staking plan:

Total risk of all bets (stakes): 106.55 Units
Maximum potential profit: 140.52 Units
Realistically expected profit (10%-15% yield): 10.66 to 15.98 Units

However, things turned out better than expected with profits of 27.22 units (25.5% yield) based on our favoured fixed risk/fixed win staking plan:

Euro 2012 Simulation: Staking Plan Fixed Win / Fixed Risk

Euro 2012 Simulation: Staking Plan Fixed Stake

The second table represents the same bets using a fixed stake staking plan.

We feel that a Fixed win/Fixed Risk staking plan is the most solid and reliable form of staking for maximised profits and minimised losses, and we have just found this article Raceadvisor.co.uk: Fixed Profits or Fixed Stakes? which includes a mathematical experiment comparing a fixed stake with a fixed risk/win staking plan. It’s an interesting read and a similar outcome to our own findings.

However, the Fixed Stake Staking Plan tends to be a more popular method and although this would have also brought a nice profit of 22.65 units (19.7% yield), the Fixed win/Fixed Risk staking plan remains ‘smarter’ in our humble opinion.

Staking Plan Excel Spreadsheet for Download

If you would like to analyse these calculations in a little more detail you can download our Excel spreadsheet which complements the above tables, free of charge. However, please return the favour and either Twitter this article, like it on Facebook, or Google+ it.

SHARE TO DOWNLOAD!
Please share to download via Twitter, Facebook or Google+ The download link will them appear, as if by magic!

Famous Last Words

In our original ‘mad scientists’ article we recommended a fixed win/fixed risk staking plan and as we have seen, this method performed better than a fixed stake staking plan.

However, both staking plans produced fairly similar results due mainly to the fact that betting odds between 1.5 and 3.5 were in play. Especially at the lower odds the differences between the stake amounts in both plans were not huge, which ultimately led to similar results.

Whichever staking plan you choose is down to you and it then remains to follow it religiously without emotion and to never chase losses…

If you now have a great void in your life following the completion of Euro 2012, instead of developing withdrawal symptoms or falling into post-Euro 2012 depression, remember that you always have therapy available by reading this blog from cover to cover. Then, if you are very brave you may wish to dive into Soccerwidow’s betting course in order to learn the skills of professional odds calculation and prepare yourself for next season!

If the prognosis of scientists from the International School of Management (ISM) in Frankfurt and the German Sport University Cologne is to be believed, then Euro 2012 will be nothing more than a re-run of the 2008 finals, with few surprises along the way.

According to the results of their statistical analyses, co-hosts Poland will make it to the semi-finals, but Netherlands will fail in the group phase. England’s chances rely on victory over Sweden to reach the quarter-finals on goal difference.

Photo: Augusto Cabral (Shutterstock)

Of course, without any bias whatsoever the German scientists have predicted their countrymen to reach the final and beat Spain to claim the title.

Prediction: Germany will beat Spain in the Euro 2012 final

Of the 24 group games, there are only 7 matches with big favorites, and 17 matches between more well-matched teams. Of these 17 games, the underdogs will prevail in 7.

Among the 17 more balanced encounters there are three key matches:

Poland against Russia (victory Poland)
Portugal against Netherlands (victory Portugal)
France against England (victory France)

There will be a surprise in the match between England and Ukraine (only a draw), but England will qualify for the quarter-finals due to a better goal difference.

The top two in each group from the simulation are Poland & Russia, Germany & Portugal, Spain & Italy, and France & England.

The quarter-finals are less spectacular:

Germany knock-out Russia and Spain beat England. France get lucky and narrowly defeat Italy.

Semi-final predictions:

Brave Poland finally meet their match against Spain. Germany beat France, but this match will probably be the tightest game of the tournament.

Final heartbreak for holders:

Germany get lucky and beat Spain.

Here’s the complete forecast (in German though!).

What Value this Prognosis?

This is a statistical simulation, and as with all such predictions, pretty clear statements of the likely outcome are often produced, but particular events (i.e. individual matches) do not necessarily comply with the bigger picture.

Unfortunately the report does not specify the expected probabilities (expectations) for each individual event and only presents the final findings. Of course, there is the chance that the scientists will get lucky and every match will enter the history books exactly as predicted in the simulation, but this is probably just wishful thinking!

How do the betting odds compare? It can certainly be expected that some of the predictions from Cologne and Frankfurt will happen exactly as predicted, but not all. Also, do the market odds contain enough value to make it worthwhile following the forecast? Again, this is left up to the reader.

It is however interesting to follow such predictions, which must have been time-consuming to compile. We have therefore added a little to the analysis by checking the odds and bets on the forecasts. The 1st July will be the day of reckoning!

Bets on individual group phase matches (fixed return 10 Units per bet)

Group A – Poland to beat Russia: 4.76 Units at odds of 3.1 at BetVictor
Group B – Portugal to beat Netherlands: 4.00 Units at odds of 3.5 at BetVictor
Group D – France to beat England: 6.67 Units at odds of 2.5 at William Hill
Group D – England to draw with Ukraine: 4.17 Units at odds of 3.4 at Bet365

Bets on which teams progress to the quarter-finals

(A) Dual Forecast (fixed return 10 Units per bet):

Group A – Poland and Russia: 4.44 Units at odds of 3.25 in Coral
Group B – Germany and Portugal: 3.33 Units at odds of 4.0 at Ladbrokes
Group C – Spain and Italy: 10.00 Units at odds of 2.0 at Paddypower
Group D – France and England: 5.32 Units at odds of 2.88 at Paddypower

(B) Single bets on teams to reach the quarter-finals (fixed risk – “Dutch” 10 Units per group)

Group A – Poland: 5.54 Units at odds of 1.8 at Ladbrokes
Group A – Russia: 4.46 Units at odds of 1.45 at BWin

Group B – Germany: 6.41 Units at odds of 1.29 at Ladbrokes
Group B – Portugal: 3.59 Units at odds of 2.3 at Bet365

Group C – Spain: 6.03 Units at odds of 1.14 in Coral
Group C – Italy: 3.97 Units at odds of 1.73 in StanJames

Group D – France: 5.11 Units at odds of 1.5 at BetVictor
Group D – England: 4.89 Units at odds of 1.57 at Bet365

Bets on teams to reach the semi-finals (fixed risk – Dutch 10 Units):

Poland: 0.96 Units at odds of 6.0 at BetVictor
Spain: 3.67 Units at odds of 1.57 at Ladbrokes
Germany: 3.45 Units at odds of 1.67 at BetVictor
France: 1.92 Units at odds of 3.0 at Ladbrokes

Bets on teams to reach the final (fixed risk – Dutch 10 Units):

Germany: 4.78 Units at odds of 2.6 at Ladbrokes
Spain: 5.22 Units at odds of 2.38 at Coral

Bet on the winner of the Euro 2012 (fixed return 10 Units):

Germany: 2.86 Units at odds of 4.5 at Betfair

Total risk of all bets (stakes): 106.55 Units
Maximum potential profit: 140.52 Units
Realistically expected profit (10%-15% yield): 10.66 to 15.98 Units

You’ll need a good staking plan if you wish to follow the German scientists’ predictions and it is also important to follow through with all their forecasts rather than cherry-picking (this is always important when betting on statistical predictions). We have specified the stakes (units) using the mathematically sound and risk-averse staking plan of fixed risk/fixed win. The odds displayed are the highest odds in the market at the time of writing this article.

Should you decide to follow these predictions and need to sign-up at any of the above bookmakers, it would help Soccerwidow.com if you would do so via the links provided above. For us to continuously offer free content to our readers, advertising revenue is needed and this is generated via your clicks and purchases (i.e. registrations at bookmakers).

Good luck with your Euro 2012 betting, and don’t forget that your family may not care so much for football as you do. Please find some time for your loved ones in between the excitement of what is considered to be the best quality international football tournament in the world…

Because bookmakers are profit-making enterprises who offer bets on the market, it is understandable that they build-in a winning margin to their odds computations. This margin is called overround.

Photo: Elnur (Shutterstock)

The overround differs from bookie to bookie and can be at its lowest around 2.5% (e.g. Pinnacle pride themselves on being the bookmaker with the highest odds and the lowest margins) but can reach 12% or even higher (e.g. Ladbrokes, and most of the other high street bookmakers).

The overround is the bookmaker’s mathematical advantage and ensures in the long run that they will collect more money (stakes) than they will have to pay out to bettors.

It should be obvious that a bookmaker needs this margin in order to pay staff and running costs, and of course to make a profit.

In an accumulator bet, the overround is exponentiated, which increases the profits of the bookmaker by multiples.

Exactly how does this work?

Here’s an example: If the overround is, for example, 6%, then in a five-fold bet the compound interest is 33.8%.

The above calculation means that a five-fold bet containing individual bets each with an overround of 6% generates a profit margin of 33.8% for the bookmaker. But what does this mean in reality?

Bookmakers overround example

Here is a table for five cup finals in mid-May 2012 (Swiss Cup, Scottish Cup, UEFA Champions League, Portuguese Cup, Coppa Italia), and the odds offered by the bookmaker, Tipico:

Table 1: Bookmakers betting odds (Tipico)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)

You will find the mathematically correct probabilities calculated for these five cup finals in our article The Permutations of 5 Cup Finals in 5 Days, and the following table shows the corresponding true odds (or ‘zero’ odds):

Table 2: Calculations Soccerwidow - conversion probabilities to true odds (without an overround)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)

Comparing the above tables, you can see straight away that the true odds differ dramatically from the bookmaker’s odds. For example, Basel’s true odds of winning their match were 1.89, but the bookmaker offered this bet at 1.67. The draw in the Swiss Cup final had true odds of 4.05, whereas the bookmaker offered only 3.80, et cetera.

Sometimes bookmakers odds are higher than the true odds. Using our example again, betting on Bayern to win was available at 1.8, although their true odds were nearer 1.54. However, of the 15 home, draw and away bets only five were offered at higher prices than the true odds, and 10 were lower.

Tipico’s average overround was between 4.13% and 6.22% per match:

Table 3: Bookmaker odds converted to probabilities (1 divided by odds)
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)

On 10 of the bets, the overround (profit margin) was between 6.28% and 38.89% (red). Five bets were offered at negative ‘value’ which ranged between 4.31% and 16.21% (green).

Table 4: Bookmaker overround for each bet
(Swiss Cup, Scottish Cup, Champions League Final, Portuguese Cup, Coppa Italia, 2012)

Why do bookmakers love accumulators or parlay bets?

In the article The Permutations of 5 Cup Finals in 5 Days I explained:

To compute the overall probability of a certain combination of results, simply multiply the individual probabilities together. Thus, the combined probability that all five favourites won was:

52.8% x 45.9% x 64.9% x 54.7% x 43.7% = 3.76%

Effectively speaking, the 3.76% combined chance of all five favourites winning means this would statistically happen only once in every 25 seasons.

The above calculation is based on the REAL chances.

If you take Tipico’s probabilities (Table 3) then the equation is as follows:

The accumulator’s odds for all five favourites to win would have been (Table 1):

This means that a winning accumulator would have paid the bettor 17.63 times his stake as a return.

However, based on the true probabilities, all five favourites win only once in every 25 betting rounds (3.76%), which means that the bettor will lose his stake 24 times. Winning 17.63 times his stake just once in 25 attempts is just not a prudent investment!

The overround (profit margin of the bookmaker) in this example is 42.8%:

Interpretation: The exponentiated overround for an accumulator as in this example (five-fold multiple bet on five favourites to win) gives the bookmaker a profit margin of more than 40%. Of course it happens now and then that the bookmaker pays out, because a chance of 3.76% is not zero. Tipico then publishes its lists of the lucky winners to encourage even more people to put their hard-earned cash into multiple bets, where the odds are definitely stacked in favour of the bookie.

Conclusion: Bookmakers just LOVE accumulator and multiple bets, but people with dollar signs in their eyes continue to play..!

Amen.

It has been a busy week in the world of football with the conclusions of many major tournaments across Europe, including the jewel in the crown, the UEFA Champions League final between Bayern Munich and Chelsea.

Photo: Kristo-Gothard Hunor (Shutterstock)

Having previewed many of the recent important cup games we decided to take a retrospective look at the pre-match expectations and compare them with what actually happened.

The table below summarises five of the matches we previewed and shows the probabilities we calculated using historical statistics.

For example, in the Swiss Cup final, we computed that FC Basel had a 52.80% chance of winning in normal time, but the game ended 1-1 after 90 minutes. In comparison, our spreadsheets showed the draw had just a 24.70% likelihood.

The only match which finished as expected was the Scottish Cup final, where Hearts defeated poor Hibernian, 5-1. In the other four matches, either the underdog won (Académica in Portugal and Napoli in Italy), or the games ended in a draw (Bayern v Chelsea and Basel v Luzern).

Cup Final Dreams

To compute the overall probability of a certain combination of results, simply multiply the individual probabilities together. Thus, the combined probability that all five favourites won was:

Effectively speaking, the 3.76% combined chance of all five favourites winning means this would statistically happen only once in every 25 seasons. This is a fairly bleak insight for those of you who like accumulator or parlay bets!

Taking this train of thought further, if Basel, Hearts, Bayern and Sporting all won, but the Coppa Italia ended in a draw, then the probability calculation would be as follows:

The probability generally that four favourites won and the fifth match ended in a draw or a victory for the underdog, was 17.78%.

Calculating this is quite simple and is purely a question of multiplying the probabilities for every permutation of this event and then adding together the results. In this case there are 10 possible permutations, summarised in the table below:

10 Possible Permutations

We can now say that in five cup finals with similar probabilities, the likelihood that either all the favourites will win, or at least 4, equates to 21.54% which means this will happen on average approximately every five years:

Again, we mention accumulator bets, which perhaps don’t seem so attractive once you know the actual statistical chances of succeeding with, in these examples, a five-fold.

As an aside, the probability in our five cup finals in general for only one favourite winning, two games ending in draws, and two victories for the underdog was 4.86%. This combination of events was therefore more statistically likely than the 3.76% chance that all the favourites would win.

Read more about this subject in further detail in our article: Combinatorics and Probability Theory in Football Betting.

We hope you enjoyed this article and also hope it has added something to your knowledge base. Please always gamble responsibly and never more than you can afford to lose.

The probability of a Bayern win was somewhere between 56.9% and 64.9% probability, depending how the match odds were viewed. If you elected to give Bayern the full 100% home advantage then the draw in regular time had a mathematical chance of only 20.7%. If this match had been played on neutral ground then the mathematical probability computed to around 23.2% for the draw.

Of course this means that statistically speaking the draw would be expected just once in roughly every fifth match in a similar odds constellation.

Bayern v Chelsea - home advantage

Bayern v Chelsea - neutral ground

Yesterday’s final shows once again that despite such a heavy chance of between 56.9% and 64.9%, this did not mean Bayern’s win was 100% guaranteed.

Congratulations to ‘The Lions’ of Chelsea FC. They certainly deserved their first European champions crown!

An interesting article about the computation of probabilities for this match can be found at: Are Bayern Munich at Home in the UCL Final?

Soccerwidow’s statistical preview (in German) includes an Excel spreadsheet for download with the calculations (which you don’t need to understand German to read!): Bayern München v Chelsea FC: 19.5.2012 UEFA Champions League Finale – komplette Spielanalyse und Excel Tabelle


So, two seasons in a row without a trophy for Germany’s most famous team and who would have predicted that? The hoodoo continues as still no team has ever won the Champions League or European Cup final in their own stadium.

Meanwhile, triumph for the team from West London with only a caretaker manager. Who would have foreseen they would beat the mighty Barcelona to reach the final, let alone win it in Bayern’s own stadium? You see, nothing is certain in football!

We look forward to next season’s UCL final at Wembley Stadium in London. Will Chelsea be travelling just a few miles up the road to defend their title? We’ll just have to wait and see…

Judging purely from statistics, watching French league games must be rather boring as there are never many goals.

Photo: Koya979 (Shutterstock)

The Dutch, on the other hand, tend to have at least five goals in nearly 10% of their matches.

From a betting perspective however, the French league is a more sound proposition because its results are statistically more reliable and predictable.

In this article we explore the “goal habits” of four major European leagues and compare them using simple line graphs.

English Premier League: 20 teams; 380 games per season

French Le Championnat: 20 teams; 380 games per season

German Bundesliga 1: 18 teams; 306 games per season

Dutch Eredivisie: 18 teams; 306 games per season

Photo: Vinicius Tupinamba (Shutterstock)

As you can see, the above graphs look fairly similar for all leagues: the curves rise steeply up to the threshold of two goals per game, peak around this figure, and then begin slowly dropping. This spread is called Poisson Distribution, which in maths, also determines things like radioactive decay (and the lingering strength of a Frenchman’s breath, no doubt!).

A radioactive particle disintegrates over time and the rate of decay can be calculated using the Poisson Distribution method. Such a distribution always begins at a known value, runs quickly up to a maximum, and then slowly drops as it approaches larger values.

The ‘peak’ threshold in football games to look at when betting is the average number of goals per game, analysed as we have here, over five years.

Dependant upon the league in question, the middle of the distribution always lies somewhere between two and three goals (hence the popularity of ‘Over & Under 2.5 Goals’ markets with both bookmakers and betting exchanges).

In our examples, the average numbers of goals per game are: Premier League: 2.6; Le Championnat: 2.3; Bundesliga 1: 2.8; Eredivisie: 3.0.

Mathematically speaking, the area in each graph between the horizontal axis (the ‘X’ axis) and the Poisson lines themselves always equates to ‘one’ purely because the probability that one of the results will happen is always 100% (i.e. it is 100% certain that the game must contain either zero, one, two, three goals, et cetera). Using the concept of ‘one’, exact probabilities can be calculated by using the “Euler’s Number” together with “K!” (faculty), and thus odds can be developed. But this is a higher level of mathematics than you need to know at this stage.

Photo: Smileus (Shutterstock)

There is a very descriptive and well explained article on Poisson Distribution (together with all the formulae) in the article What have a football team and a radioactive source in common? (www.weltderphysik.de).

However, this article is written in German, but easily translated using Babel Fish or Google Translate, for example.

Now, a closer look at our graphs above reveals the following trends:-

• Bundesliga 1 exhibits the most regular goal distribution (all five seasons’ curves follow similar paths). This is despite having fewer games per season (306) than both the English Premier League and French Le Championnat (380 games per season). This is paradoxical because a more even distribution should be expected from a larger sample size.
• There is a fairly consistent number of Dutch games finishing 0-0 each season.
• Most of the French top-flight fixtures finish with less than six goals (i.e. the ‘Under 5.5 Goals’ market).
• Within the two goal threshold (i.e. the ‘Under/Over 2.5 Goals’ market) all leagues show larger variances than in any of the other goal event categories.

Nota Bene: Spend a little time comparing the graphs and see what other discoveries you can make!

Relative Deviation

In order for you to understand the term ‘Relative Deviation’ it is necessary first to grasp the concept of ‘Absolute Deviation’.

For example, analysing our data set to quantify the average number of times that two-goal game events occur in a season is fairly easy. This is just a matter of adding up all of the two-goal game events over ‘X’ number of seasons and then dividing by ‘X’ to reach the average per season (where ‘X’ is the total number of seasons represented in the data set).

Photo: Andresr (Shutterstock)

Absolute deviation is the difference (or ‘deviation’) each season’s data set shows from the average for that data set. Effectively it is a simple way of comparing ‘apples’ (the average) with ‘pears’ (the deviation).

Relative deviation takes this idea one stage further and allows the comparison of different events with different results within the same data set.

It is difficult to envisage a direct comparison between, for example, two-goal events and three-goal events over a period of five years if they both have different frequencies and therefore different averages. Relative deviation analysis allows an ‘apples’ with ‘apples’ comparison of this information to be made.

A very quick and simple example to illustrate: Say a season contains 100 matches and over five seasons the average containing over 2.5 goals is 50. One of those seasons contains 52 matches over 2.5 goals. The absolute deviation for that season is 2% (i.e. 52% is 2% different from the average), whilst the relative deviation is 4% (52 divided by 50 and then shown as a percentage).

Say the average number of games per season containing over 5.5 goals is only five. The same season we are analysing contains seven such matches. Again, the absolute deviation is 2%, whereas the relative deviation is much larger at 40%. This means that the ‘error’ or deviation relative to the norm in this season was far greater for over 5.5 goals than for over 2.5 goals and thus, just tiny fluctuations in events with smaller average expectations have a greater tendency to ‘upset the apple cart’ when it comes to betting.

Taking the same information we used to build the first set of four graphs, we can now produce graphs showing the relative deviations (the average figure over five seasons), which will shed more light on the statistics from a betting perspective:

English Premier League 2006-2011: Over/Under 'X' Goals - Relative Deviation

French Le Championnat 2006-2011: Over/Under 'X' Goals - Relative Deviation

German Bundesliga 1 2006-2011: Over/Under 'X' Goals - Relative Deviation

Dutch Eredivisie 2006-2011: Over/Under 'X' Goals - Relative Deviation

Looking at the graphs above you will see that the ‘over’ and ‘under’ goal event curves again intersect somewhere between two and three goals in all four leagues.

The meaning of this is that bets on ‘over 0.5, 1.5 and 2.5 goals’ have a smaller variance (error), and are therefore “safer” bets than ‘under 2.5, 1.5 or 0.5 goals’, which show greater fluctuations in distribution over the five seasons.

Photo: Michiel de Wit (Shutterstock)

After the curves cross the situation changes and the under ‘X’ goals curve shows a diminishing relative deviation (error). Again, this means that bets become “more reliable” (they have a smaller and smaller variance) the higher the under ‘X’ goals event category climbs.

You can easily produce graphs like the ones presented above in whichever league you wish to analyse. Simply add-up all the zero goal matches plus the games with only one goal to produce the ‘under 1.5 goals’ result for a season; zero goals, plus one goal, plus two goals produces ‘under 2.5 goals’, and so on. Then, calculate the average of each respective over and under event category by dividing the sum in each category by the number of seasons you have analysed. After this, compare the observed results of each year with the average and compute the relative deviations (see also my article Calculation of Odds: Probability and Deviation). The final step is to build the average of the relative deviations (errors) for each year and you’ll come up (hopefully) with something similar to the above graphs.

Here’s another graph showing a comparison of relative deviations (errors) for the over ‘X’ goals market in all four leagues:

Relative Deviations (Errors): Over ‘X’ Goals - German Bundesliga 1, French Ligue 1 Le Championnat, Dutch Eredivisie, English Premier League

Interpretation:

• French Ligue 1 (Le Championnat) and German Bundesliga 1 show the smallest deviation on over 2.5 goals; it might be worth developing a system to bet on over 2.5 goals in both these leagues. However, from the perspectives of the English Premier League and the Dutch Eredivisie, betting on over 2.5 goals should be avoided because the results show an average variance of around 6.7% per year. This means the results are statistically unreliable and fluctuate/vary up to four times more than the French and German counterparts.
• German Bundesliga 1 gives the most consistent impression and except for the ‘over 5.5 goals’ threshold (where the Dutch show the smallest deviation), the Germans have their noses in front in all the other over ‘X’ goals betting categories making this an ideal league for consistently accurate over ‘X’ goals forecasts.
• Exactly the opposite occurs in the English Premier League (which has the highest deviations) and avid followers will also agree that results in this league are never easily predictable, with regular surprises and ‘upsets’.

To complete the story, here’s the combined graph for the under ‘X’ goals market:

Relative Deviations (Errors): Under ‘X’ Goals - German Bundesliga 1, French Ligue 1 Le Championnat, Dutch Eredivisie, English Premier League

Interpretation:

• Under 0.5 goals (i.e. 0-0 results) show the Dutch league with the lowest deviation and therefore producing the most regular and reliable results.
• In the under 2.5 goals market the French have significantly less deviation than any of the other three leagues. We have already seen they are worth a punt on the over 2.5 goals market, so concentrating your analytical resources on over/under 2.5 goals in Le Championnat is the way to go, but again, avoid the Dutch and the English.
• For more “reliable” bets (i.e. higher probability, but obviously lower odds offered) you should consider looking at the under 3.5 and/or under 4.5 goals categories and, no surprise, just stick to the French or German top-flight leagues.

Summary
Betting on the German Bundesliga 1 and/or French Le Championnat on over 1.5 goals (or even over 2.5 goals) as well as under 3.5 goals (and/or under 4.5 goals) seems to be statistically rather a ‘sure thing’, so long as you are planning a strategy around securing long-term profits using a proper staking plan. You will also need a mathematical advantage or ‘edge’, which means never betting under ‘value’. The latter part of the equation is probably the biggest challenge!

Betting ‘under’ value will lose in the long run as described in the article Calculation of Odds: Probability and Deviation.

However, if you need to learn how to evaluate and process raw data, calculate odds, probabilities and recognise VALUE, please look no further than Socccerwidow’s basic course.

Further reading about statistical goal distribution:
Goal Production In Six Leagues, Or: Are the Eredivisie and Ligue 1 Different?
Goals Per Game Ratios

As ever, thanks for reading and best of luck with all your football betting!