You should know however, that in this way the combination is necessary to have more resources because it is quite possible to not know enough meetings several days in a row. For example, if we play 6 Meetings of 4, 5 and 6 known and strive to 5 friends, and if the five characters go on the seventh day, we would bet Euros and will have revenue However, if the five characters come until the eighth day, will now have a loss.
Coefficients are 2. Here are a plus, and that column to come. The problem is that there are few cases that go more than one cross, and then we are at a loss. Therefore, most recommended version of me is as follows:. As crosses to go, there are a plus.
It is better that way - with safe return of the pledge, to await a few familiar characters than as in Tables 9 and Against the emergence of a third character - in this case pair, generally are powerless. We can do barbs and the third character, but will receive as much as would bet that renders this effort.
In Table 12, however, he first went Hicks, and then - the third place, we will not be profitable, but will return your money, which is the first task in the betting. I could recommend several ways to combine forecasts beyond that post.
One of them is as in Table 11, but here we select four meetings with the coefficient for the smallest sign around 1. Stake of 10 per column:. This game is proper for fans with less experience. Matches with relatively low coefficient for the smallest sign, which makes the release of more than one X, not to mention the third character, unlikely. These are usually matches of the big teams in European football. Fans with more practice can try the same scheme but with a slightly higher rate for the lowest coefficient - about 1, Revenue here is decent - more than four times the bet.
The probability of exit of the second X or third place - in this case pair is not large. Profits if hit the five units is seductive and practical in each of the contras to return the money. Here's another combination that not only play with gusto, but with success. The first three games choose from meetings of the European grandees with their victory factor about 1.
For each of the four slip these games are hard. Combine them with five games of the estimates give, at odds of lowest mark 2. The combination makes profit in less than a cross of the first three games and at least three known from five matches by a factor of 2. Here's another one of my favorite schemes to play. Pick three relatively controversial game, which are likely one team to come out victorious is more, but not off and tie.
Looking for a win ratio of preferred team would be around 1. Most importantly, the matches are on different days or at least at different times with sufficient time between the end of one and beginning of the next to be able to counter. Along with the main column of three units play in another sheet and a cross for the first counter.
If the first match out cross, we returned his money and completing their participation. If a unit, we counter with a cross at the second meeting with the higher stake than the first cross. If the result is equal, closing their participation, we pledged to return. If a second game unit, we counter with a cross at the third summit with a pledge of more than the second counter. If you cross out, we get their money back, if a unit, we win:.
This makes 10 columns. Once you have read my "bible", we can start new forecasts for I hope it to be successful! Accumulation of 2. Open navigation menu. Close suggestions Search Search. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Uploaded by Krasimir Georgiev. Date uploaded Nov 10, Did you find this document useful? Is this content inappropriate? Report this Document. Flag for inappropriate content.
Download now. Best Soccer Betting Strategy. Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. I apologize for the English language that is not my native. Dear fans of soccer betting Entry into the third year of our relationship.
Here the losses are even greater. Urge that the losses are significant. Even greater when we are tripling the bet. As you can see, do not give statistics on the average mark, since there are things worse Table 8 Opportunities doubling the biggest coefficient after the fifth time On what Single bet Number of Wager Coef. Here are some of the schemes, which combine many of my predictions site visitors: Full combine 5 of my estimates of 3, 4 and 5 characters.
Opportunities for profit are the following: Table 9 5 games to 3, 4 and 5 hit Number of hits Gain 3 ,48 4 ,18 5 ,44 Total wager When 3 friends are at a loss, but at 4 and 5 have hit a bad profit forecasts. Krasimir Georgiev. Related Interests Gambling Odds Business. Related searches Betting Soccer betting Betting strategy. Alex Popescu. Duarte Amorim Dos Santos. Majda Loofay. Harrison Okoyibo. Duca George. Maddie Grayhound. Dan Hagea. Panos Leo.
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Figure 1. Especially, sports betting has been male dominant, but event betting has gained a lot of female attention according to Paddy Power, the Irish bookmaker. Source: Svenska Spel Age distribution in Figure 1. The target group is the people between years of age. Sites currently operating under British jurisdiction, for example in Gibraltar, are held in high regard internationally because they operate to UK regulatory standards.
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Our main focus is in the English Premier League. In order to do this, we need to predict the outcomes with reasonable accuracy. We build the appropriate model for this purpose and examine its usage in the betting market. We also compare the model against other most commonly used prediction methods. We mainly consider the benefits of using the model in fixed odds betting. Also, its efficiency in more exotic handicap and spread betting is discussed in Chapter 6.
Chapter 2 covers the literature relating to the subject so far. Chapter 3 explains the model and makes comparisons against other most common prediction methods. In Chapter 6 we summarize the research and make a few suggestions for future work.
Even stronger opinion came from Hennessy who stated that only chance was involved. Hill argued that anyone who had ever watched a football match could reach the conclusion that the game was either all skill or all chance. He justified his opinion by calculating the correlation between the expert opinions and the final league tables, finding that even though chance was involved, there was also a significant amount of talent affecting to the final outcome of the match. Modelling football results has not gained too much attention in a scientific community.
Most of the models punters and operators tend to use are very ad hoc. They are not statistically justified, even though these might be useful in betting. Each of them has their own probability and the probabilities sum up to 1. Our task is to determine these probabilities as accurately as possible.
His article has been the basis of few others. Then he calculated the points awarded for each team and determined the proportions of times each team topped the table. Another important article written by Dixon and Coles investigated the inefficiencies in the UK betting market. Dixon and Coles emphasized in their article that in order to create a profitable betting strategy, one must consider several aspects of the game. Instead, we need to find the statistical way to incorporate these features.
English Premier league consists of 20 teams. The three lowest placed teams will be relegated to Division 1 and three top teams will be promoted to the league from Division 1 after each season. They also included cup matches in the analysis and thus obtained a measurement for the difference in relative strengths between divisions. We ignore cup matches in our study. Dixon and Coles had identifiable parameters, because of the number of divisions they dealt with.
In our basic model, we use only 41 parameters. Attack and defence parameter for each team, and a common home advantage parameter. One match is seen as a bivariate Poisson random variable where the goals are events, which occur during this minute time interval. The mean of the Poisson distribution has to be positive, so we say that the logarithm of the mean is a linear combination of its factors.
This is an example of a log-linear model, which is the special case of the generalized linear models. The theory of generalized linear models was obtained from the books by McCullach and Nelder , and by Dobson We can estimate the values of the parameters above by the method of maximum likelihood assuming independent Poisson distribution for Y.
For now on, we refer to this whole process as Poisson regression. They observed that the rate of scoring goals varies over the course of a match and concluded that inaccuracies exist in the spread betting market as well.
They applied Markov Chain Monte Carlo in order to estimate the skills of all teams simultaneously. In tennis, we are familiar with ATP rankings, which measure the level of each player based on their performances in the past. The betting line in American football is derived by handicappers, who use power ratings as their basic tool.
The basis of most of these rating schemes is the least squares-Gaussian approach. Harville and Stefani have published several articles on this subject. The main idea is to predict the win margin in a match between two teams based on these previously defined ratings. The Elo rating system calculates a numerical rating for every player based on performances in competitive chess.
A rating is a number normally between 0 and that changes over time depending on the outcomes of tournament matches. The more marked the difference in ratings, the greater the probability that the higher rated player will win according to Glickman and Jones These Elo ratings can be applied to football as well. The probabilities for home win, draw and away win are derived based on the difference in ratings.
These rating differences need to be stored over several years in order to examine how often the match ends to a home win, a draw and an away win with various rating differences. Initial ratings in Elo system are obtained by using a different set of formulas. They do not carry a great amount of confidence because they are based on a very small number of match outcomes. When a player has competed in fewer than 20 tournaments games, the post- tournament rating is calculated based on all previous games, not just the ones in a current tournament.
Glickman and Jones studied whether the winning expectancy formula could be used to predict game outcomes between pairs of established players. Their main conclusion was that there is a fair amount of variability in rating estimates. They also discuss similar topics that arise in football including the time variation and the problem of grouping. In the US college soccer, the team rankings are created by Bradley-Terry model Albyn Jones has an article about these on Internet.
It follows closely the Elo rating procedure. The Bradley-Terry model can be applied when the response variable is binomial. An article about ordered logit model by Forrest and Simmons was used as a reference in our model comparison in Chapter 3. Also, more theoretical articles by McCullach and Anderson were applied. Probit regression is an alternative log-linear approach in handling categorical dependent variables. The outcome of a match, Win 2 , Draw 1 or Loss 0 is considered as a categorization of a continuous variable Z.
Z is a normal random variable ordered probit. The cutpoints t1 and t2 are estimated by maximizing the likelihood. The home effect is absorbed into the estimates of t1 and t2. The probit version is thus very similar to the ratings, but parameters and cutpoints are chosen in a statistical manner by the method of maximum likelihood. In individual situations luck will play into the outcome of an event, which no amount of odds compiling can overcome, but in the long run a disciplined punter will win more of those lucky games than lose.
To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Kelly criterion has proven to work effectively in betting. It was named after an American economist John L. Kelly and originally designed for information transmission.
We will now show that Kelly betting will maximize the expected log utility for a game, which uses biased coins. Consider an even money bet that is placed on a biased coin which has a probability p of coming up heads and a probability 1 - p of coming up tails. If p is greater than 0. So, for a biased coin, one should bet a fraction of bankroll that is equal to the advantage in order to maximize this utility function.
Notice that absolute bankroll size is unimportant. One feature of sports betting which is of interest to Kelly users is the prospect of betting on several games at once. Again, one wants to find a betting strategy fA, fB, fC, fD which will maximize the expected utility, using log bankroll as a utility function. The overall utility OU function for this game is simply a weighted sum of the utility functions for each of the individual coins. Each coin contributes an amount to the overall utility, which is proportional to the probability of that coin being played.
The important thing to notice here is that the optimum bet size for fA does not depend on pA, so it does not matter how often coin A is played. So, when playing coin A, one simply should play as if that was the only coin in the game, and one should choose the correct bet size for that coin. Instead of maximizing the capital growth, strategies can be developed based on maximum security.
For instance, probability of ruin can be minimized subject to making a positive return, or confidence levels can be computed of increasing initial fortune to a given final wealth goal. To combine the goals of capital growth and security, an alternative is a fractional Kelly criterion, i. Thus security can be gained at the price of growth by reducing the investment fraction. How does Kelly criterion compare with other strategies over a time period?
The results are presented in Appendix C. The simulation provides support for Kelly system, even over a horizon as short as one racing season. Some punters may find the distributions of final wealth from other systems may be more appealing for this period, e. These include , , and seasons.
The data source was the website sunsite. This website records only dates, matches and results. A large amount of extra information of league football like goal scorers, times when the goals were scored, line-ups, attendances is available in other portals, but we are not using these in our study. In practice, it would be difficult to use more general information in a numerical format.
Later, we also make an extension to apply the odds data in our analysis. Due to the relegations and promotions, teams change from season to season. We used the data from the seasons to test the validity of Poisson and independence assumptions. Three seasons of data means full- time match scores. However, we can assess whether the assumption holds in an average sense. Below, we have summary statistics and histograms to demonstrate the distribution of home and away goals in the Premier League Histogram of away goals Actual Poisson 50 0 0 1 2 3 4 5 6 7 8 9 Number of goals Figure 3.
They made an adjustment in their likelihood function, where they included a coefficient allow for the departure from the independence assumption. We are not considering this slight departure from the independence any further in a proper statistical manner due to its complexity in calculations.
Instead we suggest an ad hoc approach later in this chapter. If we sum up all the cells our test statistic will be Therefore, we reject our null hypothesis and conclude that scores are not Poisson. Despite this, we adopt to use the Poisson assumption in our model. The big chi-square values for certain combination of scores , , affect the test statistic quite heavily. These departures probably arise from non-independence.
In a low-scoring match both teams normally will focus on defence in the latter stages of the match, and thus the probability of a result increases. Runaway victories , take place when the losing team gives up or the winning team has a psychological advantage.
Hence the probability of heavy defeats is higher than would be expected under the Poisson model. The closer comparison of empirical and model probabilities over three seasons of English Premier League is presented in Tables 3.
The reason for using Poisson regression is because we are modelling goals scored, which is discrete data. The S-Plus output of the regression is provided below. The data for this particular regression covers the whole season Error t value home 0. Arsenal 38 22 7 9 73 43 73 0. Leeds 38 21 6 11 58 43 69 Liverpool 38 19 10 9 51 30 67 Chelsea 38 18 11 9 53 34 65 Sunderland 38 16 10 12 57 56 58 Leicester 38 16 7 15 55 55 55 Tottenham 38 15 8 15 57 49 53 Newcastle 38 14 10 14 63 54 52 Middlesbrough 38 14 10 14 46 52 52 Everton 38 12 14 12 59 49 50 Coventry 38 12 8 18 47 54 44 Southampton 38 12 8 18 45 62 44 Derby 38 9 11 18 44 57 38 Bradford 38 9 9 20 38 68 36 Wimbledon 38 7 12 19 46 74 33 Watford 38 6 6 26 35 77 24 In a regular regression procedure variables with small t-values would be deleted.
When we observe the final league table and the attack and defence parameters, we notice that they are closely related. Among attack parameters, the larger value represents more effective attack. From Table 3. This statement is also supported by the amount of goals scored.
Manchester United scored 97 goals GF column , which is the best in the league. Among defensive parameters the smaller value means better defence. Liverpool has the best defence parameter value This agrees with the league table when we observe the goals allowed GA column. The correlation matrix in Table 3.
League points vs. Our interest was to model goals and therefore we need to see how well we were able to do that. If we sum up the lambdas derived using the model and compare that to actual number of goals both home and away, we get the estimates below: Home goals Away goals Model Actual This table was constructed for the full season dataset. It demonstrates that the Poisson model reasonably reflects some basic features of the data. In the fixed odds surroundings, we need to see how the outcome probabilities reflect the actual ones.
If we calculate the average of these model probabilities over three seasons we get the following numbers: Model Actual 1 X 2 1 X 2 In reality we do not have the whole season data available when placing the bet. We examine that problem in later sections. With the basic model we just want to prove the usefulness of the model. The model validation in regression is normally done by observing the fitted values and the residuals from the model.
The graphs indicate that response residuals are reasonable normally distributed with few outliers. This happens in a match where unusually many goals are scored. For instance, Sunderland achieved few heavy away victories on the first half of the season.
They beat Derby and Bradford Those victories weighted quite heavily also later in the season. They are not significant outliers though. We now consider alternative models in order to choose the best available model for our prediction process. The more comprehensive analysis on subject is found in the article by Clarke and Norman A common method to estimate home advantage is to divide the number of points accomplished at home by the total number of points received over the whole season.
The result of that is given in Table 3. Earlier in the English league, the teams who played on the artificial ground earned a significant home advantage. Nowadays, artificial fields are prohibited. In our study, we want to see whether the home advantage varies significantly from team to team.
Is there a need to include a separate home parameter for each team into our model? We observe that relatively high variability existed during the season This must be one of the worst records in the history of English football. Other than that, the home effect seems to be relatively constant. A Poisson regression with different home parameters was fitted with following home parameter values. The full regression output is in Table D.
Team Coefficient Ratio 1 manchester. We notice that the values form the model somewhat correspond to the ratio estimates. It indicates that Coventry received most of their points at home. Either they had a particularly good home advantage or they underperformed in away matches. We can observe this further by scatter plot. We leave the conclusion of including different home parameters to our model in Section 3. We tested this by considering a split season model. The interest is to find out whether the first half of the season is different from the second half.
Sunderland, for example, did noticeably worse on the second half than on the first half. Their attack parameter decreased from —0. This explains their change in position dropped heavily after Christmas. Home effect does not seem to change that much. Complete S-Plus reports are documented in Table D. Below we have the residual deviances and the corresponding degrees of freedom between different Poisson regression models.
The results are below: Model Diff. Deviance df p-value Basic vs. Different home parameters Separate halves The data source for odds is oddscomparison. Again, following the Section 2. E Score 0. We include this model in our comparison to find the best available Poisson model. We can incorporate the Poisson and dependence correction to our model in an ad hoc way by multiplying each cell by the ratio of the empirical and average model values from the above tables in the following way.
The week-by-week fitted time series charts show how the betas for particular teams vary over the season. It also shows how the home effect remains nearly constant. Attack 1. Home effect 0. These charts were constructed on a week-by-week updating scheme. Attack and defence charts were done for three teams in the Premiership season Aston Villa, Bradford and Chelsea. After approximately 10 weeks of the season, parameters start to stabilize, because more data is available.
The home effect behaves in a similar manner, but with less variation than attack and defence parameters. We conclude that the basic model in this format is useful after the 10th week of the season. In order to estimate the early weeks of the season, we could apply expert opinions, which are derived from odds data. That aspect is described later in this chapter. The definition of a weight function is discussed in the article published by Dixon and Coles, where they suggested the exponential weight function.
We suggest that half normal distribution could be better to emphasize the most recent results even more heavily. The weighted regression output run for the full season dataset is documented in Table D. The parameter estimation for our half normal distribution is not straightforward. In the next section, we make a comparison between the weighted regression and unweighted regression to see whether we get any improvement with weighting. Therefore, the basic model for the full season data gives the better results than in reality it would be possible.
We can only include the matches played up to the present date. If we calculate the average of these model probabilities over three seasons by updating the data on a week-by-week basis, we get the following numbers: 1 X 2 One weakness is that the probability of a draw is a little bit underestimated and the away win overestimated.
This is mainly due to the Poisson assumption. In order to adjust that, it is possible to use methods of Dixon and Coles or the Poisson Correction method described in Section 3. By running the regression on a week-by-week basis, we get approximately 40 different regression outputs. Thus, comparison of residual deviances to alternative models is not straightforward.
The graph below describes the Poisson models we chose for closer look. The probabilities were calculated based on English Premier League season November-February. Parameters are updated as described in Section 2. The parameters in Table 3. Sheffield Wednesday seemed to be a better team than their position in the league table indicates according to the Elo ratings. Elo ratings vs. Points 80 Points 60 40 20 0 0 Ratings Figure 3. The Figure 3.
We make a comparison between Elo and other approaches in Section 3. Points 90 80 70 60 Points 50 40 30 20 10 0 For the whole season data the probit parameters are very consistent with the league points as seen in the Figure 3. Team strenght 0. In the next section, we make a comparison between probit and other approaches. Elo ratings are updated week-by-week. Thus, we want to use the week-by-week Poisson and probit model in comparison.
Our point estimate for the comparison is the same as before, i. However, we use Poisson as it is much more versatile than probit. Probit fits well to fixed odds betting whereas Poisson can be applied to almost all kinds of betting.
That is the main reason why we establish a betting strategy based on Poisson. Also, the software for fitting the multinomial ordered probit model was not generally available. This is strictly mathematical approach to betting. You do not necessarily need to believe in the team you put your money on.
As long as the odds presented are better than the purely mathematical chance of winning the match, it is a value bet. Objects with good value are objects, which will give you a positive payoff over time. For example, if the odds for a single match are 1.
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