Creating a Profitable Betting Strategy for Football by Using Statistical Modelling Niko Marttinen M.Sc., September 2001 Department of Statistics Trinity College Dublin Supervisor: Kris Mosurski Abstract Our goal was to investigate the possibility of creating a profitable betting strategy for league football. We built the Poisson model for this purpose and examined its usefulness in the betting market. We also compared the Poisson model against other most commonly used prediction methods, such as Elo ratings and multinomial ordered probit model. In the thesis, we characterized most of the betting types but were mainly focused on fixed odds betting. The efficiency of using the model in more exotic forms of betting, such as Asian handicap and spread betting, was also briefly discussed. According to market research studies, sports betting will have an increasing entertainment value in the future with the penetration of new technology. When majority of government-licensed bookmakers are making their transition from online terminals into the Internet, the competition will increase and bring more emphasis on risk management. In this thesis, we investigated the benefits of using a statistically acceptable model as a support of one’s decisions both from bookmaker's and punter's point of views and concluded that it would have potential to improve their performance. The model proposed here was proven to be useful for football betting purposes. The validation indicated that it quite effectively captured many aspects of the game and finally enabled us to finish the season with positive return. i 1 Introduction.................................................................................................1 1.1 Structure of League Football................................................................2 1.2 Betting on Football...............................................................................3 1.2.1 Pari-mutuel Betting......................................................................3 1.2.2 Fixed Odds Betting.......................................................................4 1.2.3 Asian Handicap (Hang Cheng).....................................................5 1.2.4 Asian Handicap vs. Fixed Odds....................................................8 1.2.5 Spread Betting..............................................................................9 1.2.6 Person-to-person Betting............................................................10 1.3 Betting Issues.....................................................................................11 1.4 Return Percentage..............................................................................12 1.5 Internet Betting..................................................................................13 1.6 Taxation.............................................................................................18 1.7 Scope of the Thesis............................................................................19 2 Literature Review......................................................................................21 2.1 Maher-Poisson Approach...................................................................21 2.2 Alternative Prediction Schemes..........................................................26 2.2.1 Elo Ratings and Bradley-Terry Model........................................27 2.2.2 Multinomial Ordered Probit Model.............................................30 2.3 Betting Strategies...............................................................................31 2.3.1 Unconstrained Optimal Betting for Single Biased Coin..............32 2.3.2 Unconstrained Optimal Betting for Multiple Biased Coins..........34 2.3.3 More on Kelly Criterion.............................................................35 3 Data Description and Model Formulation...................................................37 3.1 Data Description................................................................................37 3.2 Poisson Regression Formulation.........................................................38 3.2.1 Assumptions...............................................................................38 3.2.2 Basic Model...............................................................................41 3.2.3 Separate Home Parameter Model................................................47 3.2.4 Split Season Model.....................................................................50 3.2.5 Comparison among Poisson Models with Full Season Data........50 3.2.6 Odds Data and E(Score) Model..................................................51 3.2.7 Poisson Correction Model..........................................................53 3.2.8 Weighted Model.........................................................................55 3.3 Comparison among Poisson Models Week-by-week..........................58 3.4 Elo Ratings ........................................................................................60 3.5 Multinomial Ordered Probit Model....................................................62 3.6 Comparison of Approaches................................................................64 4 Betting Strategy and Model Validation......................................................65 4.1 Value Betting.....................................................................................65 4.2 Betting Strategy.................................................................................66 4.3 Money Management...........................................................................66 4.4 Validation on Existing Data...............................................................67 5 Discussion.................................................................................................71 5.1 Implementation of the System............................................................71 5.2 Applications of the System.................................................................72 ii 5.2.1 Bookmaker’s Point of View........................................................73 5.2.2 Punter’s Point of View ...............................................................73 6 Summary and Future Work........................................................................75 6.1 Summary............................................................................................75 6.2 Future Work.......................................................................................75 6.2.1 Residual Correction....................................................................76 6.2.2 Other Types of Betting...............................................................76 6.2.3 Bayesian Framework..................................................................79 Appendices........................................................................................................80 Appendix A...................................................................................................80 Appendix B...................................................................................................81 Appendix C...................................................................................................82 Appendix D...................................................................................................83 References.........................................................................................................88 iii Chapter 1 1 Introduction Independent forecasters predict an explosive growth in global online betting. Ernst & Young (2000) claim in their market research paper that the driving force of Internet and digital technology will open up mass-market sports betting by delivering live entertainment, news and information to Internet linked PC’s, mobile phones and interactive television. More and more people have access to the Internet, which has evolved the sports betting business among other e- commerce businesses. It is inevitable that this change will bring new forms of betting into the picture. For example, so far the only live action betting has been spread betting. The spread betting firms accept the bets made “in running”, which means that the bets can also be placed while the event is going on. If the player notices that one has few bets going against him/her, those bets can be sold in order to minimize the losses. The only reason why spread betting has not fully taken off is its complexity. In order to attract casual punters, the game format needs to be quite simple. Balancing between simplicity and people’s interest requires a lot of creativity. Recently introduced person-to-person betting has effectively captured both these criteria. Punters can take each other on in several different topics and the gaming operator monitors and settles all the bets. Whether it is fixed odds, tote, spread or person-to-person betting, wagering will be much faster in the future and the requirements for the system operating this increase accordingly. Security, speed and pricing are the most crucial issues that will distinguish the profitable Internet sports books from the failing ones. Technology providers are responsible for the first two, but odds compilers mostly cover the pricing issues. 1 Currently, the odds compilers work in teams of three or four experts, with one head odds compiler making the final decision about what prices to release to punters. The alternative is to buy the odds from a consultant. Usually, odds compilers use several ad hoc techniques and their expert opinion in compiling final prices. In order to manage risks while competing with better prices in the market, a proper statistical tool should be developed for gaming operators. The purpose of this thesis is to create a model that is capable of predicting results of football matches with reasonable accuracy and to compare it to other forecasting techniques and the odds collected from a bookmaker. We investigate whether it is possible to create a profitable betting strategy by using statistical modelling. The pricing issues are thus examined both from the punter’s and the bookmaker’s point of views. In order to create a profitable betting strategy, one must be capable of estimating the probability of each outcome accurately enough. How accurately, depends on the level of the opposition. The opposition could be either a bookmaker or other punters. The goal of our study has been to establish a proper method for this estimation. The focus is in the football betting market. In this chapter, we first take a brief look at the structure of league football and the betting market. 1.1 Structure of League Football The reason for our focus on league football is because of its simplicity and data availability. Cup matches and international tournaments create problems due to the variability of participants and lack of consistent data. The most common format in the league football is a double round robin tournament, where each team plays against each other twice, once at home and once away. This way it is possible to eliminate the bias of a home advantage. Most of the major leagues in Europe are played in this format. Different variations are used in some countries, such as round robin and playoff combination or single/triple round robin, but we 2 restrict our attention solely to double round robin tournament because of its simplicity and popularity. A match outcome, in a round robin tournament, is converted to points that reflect the value attached to each outcome (3 points for a win, 1 for a draw and 0 for a loss). These points accumulate during a season and the team with the highest number of points wins the league. The teams’ ability changes over the course of a season due to things such as injuries, transfers, suspensions, motivation, etc. Therefore, determining the probabilities for each outcome in a particular match is not that straightforward. Lots of things need to be taken into consideration before the final conclusions can be made. Many of these things are hard to quantify and difficult to use in a numerical analysis. 1.2 Betting on Football Football is the most popular sport in the world, and also the most popular sport in betting. The most traditional bet is to place money on the outcome of a match. Whether the match will end to a home win, a draw, or an away win. Also, correct score, halftime/fulltime, handicap, total goals and future outright bets (f. ex. betting on the winner of the championship) are popular. In addition, there are nowadays numerous exotic variations of football betting, especially in spread betting where punters can bet on bookings, shirt numbers, corner kicks, etc. during a match. We take a look at the different types of betting in the following sections. 1.2.1 Pari-mutuel Betting In pari-mutuel betting the bookmakers take their money off the top, and the rest is distributed equally among the winners. A punter is competing against other punters in this type of betting. The more familiar name for this betting type is the 3 Tote. The odds are purely a function of betting volume’s reaction, so the bookmaker is playing safe in pari-mutuel betting. This is very common in horse racing, but also football pools work in this way. Out of certain number of matches the punter is required to pick one or more choices for each match. Very often, the home win is denoted as 1, the draw as X, and the away win as 2, and hence football pool is synonymous to 1X2-betting. On the coupon of twelve matches, the punter usually needs to predict ten or more outcomes correctly in order to receive any payoff. This is probably the most traditional football betting type. For a professional punter, though, it is not as exciting as other types listed below, because of the low return percentage. Some of the correct score and future outright bets are also based on pari-mutuel structure. 1.2.2 Fixed Odds Betting Fixed odds betting has increased its popularity very rapidly. There are more chances for profitable betting because the return percentage is greater than in football pools (sometimes even as high as 95 %). The bookmaker offers odds for each possible outcome in a match and the punter will determine which ones are worth betting on. For example, in a match Liverpool against Chelsea the bookmaker offers the following odds: Home team Away team Odds home Odds draw Odds away Liverpool Chelsea 2.00 2.60 3.00 If the punter has chosen to back Liverpool with £10 and Liverpool wins the match, the punter will get his/her stake multiplied by the odds for Liverpool’s victory. In this case the punter’s gross win would be £20 and the net win £10. If on the other hand the match had ended to a draw or Chelsea’s victory, the punter would have lost his/her stake. 4 In Great Britain and Ireland, the odds are the form x/y (say 1/2, where you need to bet 2 units to win 1 unit). On mainland Europe, the more common way to present odds is the inverse of a probability, called a dividend as in the example above. The traditional odds are converted to dividend odds by dividing x by y and adding one. Thus, 1/2 means 1.50 in European scale. The table of conversions is presented in Appendix A. Some bookmakers do not accept bets on a single match. Instead a punter needs to pick two, three or more matches on the same coupon. The matches are independent events, so this way the bookmaker decreases the return percentage to the punters. For example, if the bookmaker returns 80 % of the total money wagered and requires punters to pick at least three matches, the theoretical return percentage diminishes to 0.83 = 51.2 %. Fortunately from the punter’s point of view, increasing competition in the betting market forces bookmakers to offer better odds and ability to bet on single events or they go out of business. We take a closer look at the return percentage later on in this chapter. In fixed odds betting, the odds are generally published a few days before the event. Internet bookmakers can change their odds many times before the match takes place responding to the betting volume’s reactions. Their job is to keep the money flow in balance and thus guarantee the “fixed” revenue for the gaming operator. For the traditional High Street bookmaker altering odds on a coupon requires enormous reprinting efforts, whereas for the Internet bookmaker it happens just by clicking a mouse. Other popular fixed odds bets are correct score, first goal scorer, halftime/fulltime and future outright bets. 1.2.3 Asian Handicap (Hang Cheng) In Far East, handicap betting is more popular than traditional fixed odds betting. The approach, derived from the Las Vegas sports books, has expanded its 5 popularity to Europe as well. In Asian handicap, the bookmaker determines a predicted superiority (a difference between home goals and away goals). One team gets, let’s say, 1/2 goal ahead before the start of a match. Thus the draw is normally eliminated in Asian handicap and the odds are set for two outcomes. The fundamental idea is to create even odds in a match by means of a handicap. With Asian Handicap, there is a much better chance of profit, due to the fact that a punter may get his/her stake back (or at least parts of it, depending on the handicap). In fixed odds betting, one would lose money if wagered on something else than the correct outcome. You can bet on teams which you really do not believe will win the match, but due to the handicap, your team may still provide you a value opportunity. Asian Handicap betting also provides much more excitement, as one single goal in a match counts much more than in fixed odds betting. The worst thing in Asian Handicap, in our opinion, is a rather complex way of figuring out the return. You will also need an account with companies offering Asian Handicap, as not all bookmakers offer it. Below, we offer few examples of Asian handicap bets. Example 1: Milan-Juventus The handicap is: Home team Away team Odds home Handicap Odds away Milan Juventus 2.00 0 : ½ 1.85 Bet on Milan: • If Milan wins the match you will win stake x 2.00, otherwise you will lose Bet on Juventus: • If the match ends in a draw or Juventus wins you will win stake x 1.85 6