Change of course....

It's September already and I've realised that I've left this blog to die a slow and painful death. I'm pretty sure that everyone is wondering what happened to the system (and possibly myself) ... or maybe not! Anyway, work usually expands to fill available time, so there wasn't much time left to keep everything up-to-date.

The system resulted in significant losses (even though the yield was "only" -2.1%) as the following table shows:

I'm not going to post the remaining 200-or-so bets since the last update, but should anyone be interested enough, you can visit my thread at Punters' Lounge which also includes a small end-of-season analysis ...

What does the future hold? Well, I've been focusing on different modeling procedures, so I'll hopefully have some information on this in the not too distant future. Until then, take care!

Finding value

Following the posts on the football match prediction system. we have reached the point whereby a chosen model based on certain variables will provide estimates for the probability of a home win, a draw and an away win in any match. What is left, is the small step of translating these probabilities into odds and a deciding whether a bet would be profitable (in the long run) or not.

Assuming that according to a model, the probability of a home win in a given match is estimated at 40%. That would mean that the "fair" odds for this event occurring would be 1 / 40% = 2.50 in decimal form or 6/4 in fractional form. [I'll be using the decimal form from now on as it's easier in algebraic expressions]. If a bookmaker offers odds of 2.20 then according to the model, this betting opportunity does not represent "value" and therefore should be avoided. This does not mean that the match will definitely not end in a home win, however, if an identical match is priced by the model again and again (and again), in the long run, a punter betting on this event will be losing money since the odds offered do not reflect the probability (according to the punter) of that event happening. On the other hand, if a rival bookmaker offers odds of 2.62 for this event, then it should be profitable (in the long run) to bet on a home win since after a number of bets, the punter will be making money because of the value found in these prices.

Essentially, it all comes down to two things: the first is the estimated probability of something happening. The bookmaker and the punter try to price up a match. They both have their subjective probabilities for HDA which are then translated to odds. Time will tell who is pricing the matches correctly (and thus making money off the other).

The second factor to consider is an advantage to the bookmaker. The bookmaker does not need to offer odds which when translated to probabilities sum up to 1. This means that the odds offered are lower than what should have been offered if the bookmaker was fair. This difference is what is called as the overround, and it represents the bookmaker's profit margin. Therefore, a punter will not only need to find value in the bookmaker's odds, but also to overcome his profit margin before actually making money in the long run.

However, the punter can also act for himself. By shopping around, finding the best prices offered by different bookmakers, the punter can almost eliminate the overround, thus start from a level-playing field. He can also use the available booking exchanges to find more competitive prices. These exchanges, in effect, give him the opportunity to become a bookmaker by setting odds for others to bet on, thus creating a market for odds which may be better than the odds offered by online bookmakers.

So there you have it: the system picks will depend on the estimated probabilities of each event (HDA) occurring and the best available prices offered by several bookmakers. Time will tell how accurate our predictions were, and how profitable (or disastrous) the developed model actually is. Fingers crossed!

Predicting football matches

The background is out of the way, the tools have been selected, now it's the time to get our hands dirty with the small details. Whichever model we choose, it will need some input in terms of factors which may affect our predictions. These have to be chosen wisely otherwise we may replicate the old motto of "Garbage in, garbage out".

Our approach is based on the general football concept of "class" and "form". It is often suggested that form is temporary while class is permanent so we will pick variables to model these general ideas. To account for the class of each team, we start with the obvious choice of variable of ... the actual teams playing! This translates to the fact that when Man Utd are playing at home against Hull City, it is expected that the probability of a home win is much bigger than the probability of a home win when Man Utd are playing against Arsenal. In fact, past performance is a pretty good place to begin and it turns out that decent (but not necessarily profitable) models can be built using the "class" approach. As for how to rate each team, there are both ad-hoc methods and optimization techniques. This is not a statistics lecture, so I'll leave it for now...

The form of each team is something more transient. A lot of punters who are building football prediction systems use the recent matches to judge on a team's form. This has both advantages in the sense that if a team is going through a good patch, it's more likely to have a good game than not. On the other hand, something that is often overlooked is the standard of the opposition teams against which form is being evaluated, compared to the standard of the opposition team in the next match. Maybe, there is scope for improvement here.

A team manages to score a goal after it has created some chances. Sure, some teams are more lethal and take the few chances that come along, but usually, the more (and better) chances a team creates, the higher the number of goals it will score. Therefore, we decided to use variables which describe the attacking capability of each team and its propensity to create chances. Unfortunately, for now, we don't have a measure to classify chances as good or difficult, although this "problem" provides also room for potential improvement.

Again, the small print will be left out of the blog for now, but if anyone out there is reading this and has any comments or views, please feel free to post them and who knows, maybe a fruitful discussion will facilitate further information on this.

Choosing the right tools

Having now established two of the types of models that can be used for this project, we now turn our attention to choosing one of them. The fundamental difference between the two is that in the case of the logistic regression model of the match outcome, a 5-0 thrashing is considered (for modeling purposes) as the same as an ugly 1-0 win, while an entertaining 3-3 draw does not differ in any way with a boring 0-0 stalemate. Alternatively, modeling the whole probability distribution of match scores (i.e. assigning a probability estimate for each and every one of the scorelines) allows for these differences at the potential cost of higher estimation burden (possibly accompanied by an increased estimation error).

In effect we have a simple model, and a more complex one. We don't know much about their forecasting ability yet, although one could argue that sufficient backtesting should have clarified if one is significantly better than the other. However, one consideration that should be taken into account is the fact that modelling the whole distribution of goals (i.e. using the complex model) would also highlight cases where other types of betting (rather than 1X2 betting) could be profitable such as the "Number of Goals" market, Asian handicap, or even correct score betting.

As stated above, the chosen model tries to mimic the behaviour of two variables, namely the goals scored by the home team and the ones scored by the away team. In the univariate case, goals in a match can be seen to reflect events taking place at an unknown rate within a time-period (in the football scenario, 90 minutes), assumed to be constant throughout. This is called the "Poisson Process". The probability distribution of goals, that is the probability of the number of goals scored by the end of the match being 0, 1 2 , ... is entirely dependent on the unknown scoring rate. The bivariate case is simply an extension of this scenario, with the two teams having possibly differing scoring rates. But since they are playing each other, they interact, hence it's probable that their scoring rates are not independent, so under this scenario some sort of dependence structure is needed.

Anyone reading this blog will excuse me for not divulging further details for now. When adjustments are needed, more information on the type of model used may be given out but for now, allow me to keep some things to myself... Until then we shall be focusing on what may or may not be useful in predicting football scores.

The project

Today's post is somewhat different. It's the beginning of a long but hopefully successful journey. You see, one of the reasons of having a blog for me was to have a chance of combining a few of my interests, namely football, betting and statistics. Of course, I could do this without putting my thoughts on the blog, but having them here would put some sort of pressure on me to carry on, even if the going gets tough! And who knows, if it proves to be profitable, somebody else may benefit too!

As mentioned before this is simply the beginning, an introduction if I may. The idea was to develop a football match prediction model which would estimate the probability of a Home win, a Draw and an Away win (HDA from now on) of football matches as accurately as possible. These estimated probabilities would be used to decide whether the offered odds by a bookmaker provide value. But I am getting ahead of myself here. Let's take things from the beginning.

In strict statistical terms, modeling the outcome of a football match is a classic example of logistic regression. The "event" (that's the match) can take any of three "values" (H, D or A) with some unknown probability which we are trying to estimate. These probabilities will depend on factors such as the teams playing, home advantage, and possibly other variables such as the form of each team etc. It is our mission to find that model which mimics the real results as closely as possible.

One could also suggest that since the outcome of a match depends on the number of goals scored by each team, a better idea would be to model the match score itself. Such an analysis would provide probability estimates for every single possible result i.e. 0-0, 0-1, 1-0, 2-1, or even 3-5. By adding the appropriate probabilities one would be able to infer the estimated probability of H, D or A.

So to recap, on the one hand we have some sort of a logistic regression model of the match outcome, while on the other a (bivariate) probability distribution model of the match score. There are pros and cons in either case, which probably brings me to George Box's "All models are wrong, but some are useful". Only time will tell, whether the chosen approach is useful.