This article summarizes the advanced Poisson methods, which, unlike older ones, take into account the mutual dependency between the opponent teams.

The well known method of Maher (1982) introduced the Poisson model, which uses attack and defense skills and home ground advantage in soccer predictions. Maher’s model assumes the Poisson distributions of the opponents are independent. In other words, the number of goals to be scored by each team depends only on the skills of this team and doesn’t depend on the opponent’s skills.

However, it is clear that when a strong team plays against a weak one, there exists the effect of underestimating the opponent. And vice versa, a weak team usually plays better against a team stronger than itself. This mutual dependency between the opponents was taken into account in the latest publications and will be discussed in this article.

Mark J. Dixon and Cole (1997) were the first to introduce the correlation factor into the Poisson model for games where the number of goals scored by each team was one or zero. The correlation was high for draw cases and low for matches with one score difference. When a team scored more than one goal, the correlation was equal to zero. The latest improvement of the correlation method was achieved in the works of Lee (1999) and Dawson at al. (2007). They assumed that the number of goals scored in a soccer match comes from a bivariate Poisson distribution and not from independent univariate Poisson distributions like it has been assumed in previous methods. Technically, the bivariate Poisson distribution is defined and implemented using the advanced Copula method. This method allows defining bivariate Poisson distributions, which use either a positive or a negative correlation unlike the standard bivariate Poisson distribution that supports only negative correlation factors.

The improvement of this method compared to the older Poisson-related methods is in using the mutual dependency between the opponent teams for soccer predictions.

Still, the Poisson methods have another drawback: the model doesn’t consider the time-dependent changes in team skills. This issue will be discussed in the next article.

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This article summarizes the Poisson methods for soccer predictions that were developed in the early 90s, their advantages and disadvantages.

The pioneering work of Moroney appeared in 1956 and defined the Poisson model to be the best suitable model for soccer score predictions. This model had a number of drawbacks. Firstly, it didn’t take into consideration the effect of the opponent’s strengths on the final match score. Moreover, the model didn’t distinguish between attack and defense skills of the teams; didn’t consider the changes in team strengths over time; and didn’t refer to the influence of home ground advantage on the final score.

Only in the early 90s the new developments appeared, improving significantly the Moroney’s method. The most known method that used the Poisson model in this period was the method of Maher published in 1982.

According to this method, the goals scored by the opponents during the game are drawn from the Poisson distribution. The mean of this distribution is defined by the difference between the attack and defense skills of the sides. Moreover, the home field advantage factor was added to the mean of home team distribution. Assuming x and y to be the number of goals scored by the home and away teams respectively, then according to this model x and y come from independent Poisson distributions with means HM and AM respectively. In this case, the expected number of goals is proportional to HA-AD+HG and AA-HD for the home and away teams respectively. HA and AA are home and away attack strengths, HD and AD are home and away defense strengths and HG is the home ground advantage. If the parameters above are calculated correctly, the match outcome can be successfully predicted.

The main improvement of this model compared to the older one is in distinguishing between the attack and defense skills of the opponents and, of course, in taking into account the influence of home field advantage.

The model has two main drawbacks: it doesn’t consider the time-dependent changes in team skills and doesn’t refer to the statistical dependency between the Poisson distributions of the playing teams.

Later on, Maher’s Poisson method underwent further developments that were meant to tackle those problems. These developments will be presented in our next articles discussing the evolution of statistical soccer predictions.

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This article summarizes the Poisson method for soccer prediction, its advantages and disadvantages.

Statistical soccer prediction methods mostly started appearing from the early 90s, but the first (and so far the most famous) method was published by Moroney in 1956. According to this method, soccer match scores can be successfully modeled as random observations drawn from the Poisson probability distribution. Let’s assume that x and y represent the number of goals scored by home and away teams respectively. Thus, according to the Poisson method x and y are random variables, each one coming from its own independent Poisson distribution. The Poisson distribution function differs for each team. The function has its own parameters (mean in the Poisson case), defining the expected number of goals scored by the opponents. Once the parameters of the distribution function are correctly estimated, the match outcome can be successfully predicted. It is clear that when estimated empirically, the parameters of any function include some error due to the limited number of observations. Thus, the predictions of soccer match are usually incorrect. This estimation error defines the confidence intervals assigned to the predicted number of goals.

The main advantage of the Poisson model is its ability to predict the expected number of goals. It holds for almost all soccer tournaments. Additionally, the estimation of mean for the Poisson distribution is usually based on all the historic matches played during a specific tournament, thus making the estimation reliable.

However, this method has many disadvantages. It predicts scores for each team independently, not taking into account the opponent’s team’ strength; It doesn’t distinguish between the attack and defense skills of the teams and doesn’t consider the time-dependent changes of these skills; In addition, it doesn’t refer to the influence of home ground advantage on the final score.

All those drawbacks resulted in further developments based on this method. The newer methods distinguish between attack and defense strengths of the teams, consider the strength of the opponent team and take into account home ground advantage. We will discuss these developments in our next articles discussing the evolution of statistical soccer predictions.

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The value bet calculation can be easily integrated into the well-known and proven Kelly’s strategy for money management. According to this strategy, a stake is calculated in a proportion to the starting wealth and the size of the expected profit. For example, if the probability of a win is 60% and the betting odds are equal to 2, then the betting stake which equals to 40%=60%-(1-60%)/2 of your wealth has to be placed. Given the betting tips, what would be the optimal value bet providing a maximum profit when using Kelly’s strategy?

This article summarizes a research intended to estimate an optimal value bet based on data from 10 top European Soccer Leagues that played during the 2008/2009 season: Austrian Bundesliga, English Premier, Dutch Eredivisie, French Ligue 1, German Bundesliga 1, Greek Ethniki Katigoria, Italian Serie A, Scottish Premier, Spanish Primera Division and Turkish Super Lig.

The assumption is that bookmakers provide the minimal betting odds for match favorites. Thus, these odds can be used to estimate the value bet for each match. The frequency of home wins, draws and away wins defines the probability of a win, and the value bet of a game is estimated by multiplying minimal average betting odds by the estimated probability of a win.

Summary

An optimal value bet is calculated in a way that maximizes the betting profits when using Kelly’s money management strategy. The average betting profit is calculated for the different value bets from 1.01 up to 2. The optimal value bet for the above top European Leagues was found to be 1.38. Thus, if your value bet is above 1.38, this is your opportunity to place a stake according to Kelly’s strategy.

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This article summarizes the methods and strategies of betting money management and provides a statistical comparison of their performance based on betting odds and match results of top European leagues.

The most common betting money management strategies in our days are: Martingale, Row of numbers and Kelly criterion. While the first two do not require any prior information, Kelly criterion requires the punter to know the probability of a win.

Definitions

Before presenting the performance analysis, a brief description of the above-mentioned strategies is necessary:

• Martingale strategy means doubling the stack after a loss and returning back to the starting stack after a win. This strategy is the most popular today and promises positive profits, but requires intensive money investments.
• Row of numbers means planning a series of constant profits. Given betting odds, the punter calculates each stake in a way that will allow him to make the planned profit. In case he loses, he should increase the next stack in such a way the profit will return both the money already lost and the planned profits for the lost games. This strategy is less aggressive than Martingale but still dangerous.
• Kelly criterion: mathematically proven to be the best strategy in the long run. However, it requires knowing the probability of a win. The stacks are calculated in proportion of the size of your funds and according to the relation between the probability of a win and the betting odds. When probability and odds are high, a high stack will be placed and vice versa.

Data and Methods

In order to evaluate the performance of each strategy, we analyzed the betting odds set by bookmakers for the top European leagues. Imagine that bookmakers are punters who place a stake on a favorite with minimal betting odds. One can easily estimate the probability of a win by dividing the average number of home/draw/away outcomes by the total number of games in a season.

The betting odds and results are taken from the four European top leagues playing in the 2008/2009 season: English Premier, French Ligue 1, German Bundesliga 1 and Spanish Primera Division.

Summary

• The results show that Kelly criterion is the best money management strategy of the three with an average profit of +5% compared to +1% (Row) and +1.2% (Martingale).
• The most profitable was the French Ligue 1 with a betting profit of +22% (Kelly), +9% (Row) and +10% (Martingale).
• The least profitable was the English Premier League with a betting loses of -10% (Kelly) ), -9% (Row) and -8% (Martingale).

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Captain Steven Gerrard and fellow attacking midfielder Yossi Benayoun also face spells on the sidelines after picking up injuries in the humiliating FA Cup third-round replay defeat by Championship (second division) Reading on Wednesday.

“Steven has a hamstring strain and will be out for a fortnight while Fernando has torn a cartilage in his right knee. The injury will require surgery and he is expected to be sidelined for six weeks,” Benitez told the club’s website (www.liverpoolfc.tv).

“Yossi Benayoun also suffered a fractured rib in the game and will be unavailable for between three and four weeks.”

The injured trio have scored more than 20 goals between them this season and their absence is another serious blow to Liverpool’s faltering campaign.

Liverpool begin their Europa League bid against Romanian side Unirea Urziceni on Feb. 18 having failed to progress beyond the Champions League group stages.

Benitez is likely to turn to Frenchman David Ngog as a replacement for Torres with new signing Maxi Rodriguez or young Spaniard Daniel Pacheco among his other options.

The Merseyside club lie seventh in the league table with 33 points from 20 games, 12 behind leaders Chelsea and five adrift of Manchester City in the coveted fourth spot.

The absence of key players might provide a golden opportunity for bettors to earn some extra money during the next match between Stoke City and Liverpool FC.

Source: Reuters

Mouscron, who are under administration due to debt, have not put out a team for their last two scheduled matches and told the league and FA that they would be unable to field a side on Wednesday.

The club’s elimination from the league means that all their results are void.

Mouscron, who will be relegated to Belgium’s third division, said in a short statement that its players would now be free agents.

Source: Reuters

There is no one million-dollar answer. Nevertheless, there are two ways that will allow you to beat the bookies. One way is to analyze non-measurable match information. Another way is to improve on statistical prediction models used by bookmakers.

The first method requires you to analyze data such as match type or priority, which is not used in statistical models. Among the most prominent factors that might influence the outcome of a soccer match are:

• Match type which can be an international/national league, a cup, or a friendly game. Especially profitable for you are the cup finals, where the media selects favorites and the better informed punter can profit from betting on the highly priced underdog teams.
• Match priority. Each team has to define its priority for the forthcoming matches, since team resources are limited. European national cups are good examples for the top teams of low priority games.
• Match time is important, since soccer predictions are usually inaccurate at the beginning and at the end of the season.
• Players’ injuries, illnesses and transfers especially in the cases of key players. Bookmakers’ odds are usually calculated before this information is available.
• European Leagues – predictable and unpredictable. The Italian, Norwegian, French and Spanish leagues are considered predictable. The unpredictable are the English and German leagues, especially at the beginning and the end of the season.
• Other factors are pitch conditions, team managers, match attendance, weather conditions and, of course, pure chance.

To analyze all that information for every match would be a complicated and time-consuming task. The alternative is to use advanced statistical prediction methods, which constitute an improvement on bookies’ prediction models.

Why can their models be further improved? First, when analyzing bookies’ predictions carefully, it is easy to notice that their models are based on average statistics. Low odds usually correspond to teams with high table positions and vice versa. It is clear that the accuracy of their models suffers when team skills change. Thus, by taking into account team skill dynamics, you can increase your profit by placing a bet on highly priced underdogs.

Second, the bookmakers’ models do not distinguish between the attacking and defensive strengths of soccer teams and don’t take into account that soccer teams choose different strategies when playing at home or away. Once you learn how to distinguish between attacking and defensive strengths, you can easily forecast the total number of goals and beat the bookies at under/over bets.

Statistical models that were developed over the past few years explain historical match results in terms of changing skills and strategy. Bookmakers don’t use such advanced models. Properly designed and optimized time-dependent models can predict as much as 70% of matches, outperforming the bookies’ predictions whose accuracy is much lower.

This article was written by a group of scientists, who developed a state-of-the-art method for soccer predictions. The predictions are based on time-varying skills of soccer teams. You may view charts that display attacking and defensive strengths of more than a thousand teams from around the world at www.scibet.com. This information is given free of charge and allows you to beat the bookies at their own game.