A support vectors regression model for prediction of the goal difference in football matches Mateus Ferreira, Eduardo Feitosa, Marco Cristo, Eulanda Santos ABSTRACT

Federal University of Amazonas, Manaus, BRAZIL {mateus, efeitosa, marco.cristo, emsantos}@icomp.ufam.edu.br 3) Noise 3. PROTOCOL OF EXPERIMENTS

Predict the difference of goals in football matches is a problem of great interest to the sports punters of the handicap mode. This . predictive capability is also important in preparing teams for the second round of a confrontation in knockout tournaments. Furthermore, it has been demonstrated that statistical information about the past performance of football teams correlate better with the goal difference than with the score. This paper employs a machine learning model to predict the goal difference in the outcome of football matches. It was attained a RMSE of 1.267822 using the support vector regression technique. For comparison with a reference model, it was also computed the quality of the predictions of the winners of matches. In this case, the obtained accuracy 60.53% was higher than the 55.26% accuracy achieved by the reference model.

1. INTRODUCTION

• The problem of prediction of goal difference was interpreted as a temporal regression task • We searched for a set of relevant historical attributes to indicate the qualification of teams and applied a mathematical regression method

3.1 METHOD

• The numerical regression (fractional number) allows the perception of closeness between the estimated value and a practical goal difference (integer number) • We used machine learning through a support vector regression method (Weka's SMOreg implementation)

2. CASE STUDY • Predict the goal difference in matches of the A Series of the Brazilian Football Championship held between the years 2002 and 2011 • The strategies employed use only data available prior to the matches • Data: "Chance de Gol" (score; teams' names; chances of victory, draw and defeat) "RSSSF Brasil" (participants in the Libertadores Cup, winner of the Brazil's Cup, teams from B Series and host city of all teams)

Libertadores Cup or won the Brazil's Cup and at the same time showed poor performance in the Brazilian Championship offered no benefits • Support vector methods suffer little influence of noise

3.3 PARAMETERS

• We used a grid search strategy to optimize the parameters. The process of successive refinement was repeated until the results did not show any improvement • We opted for an adaptation of cross-validation strategy • Distinct values were defined for each year studied Range of values tested:

3.2 ATTRIBUTES 1) Definition and production Basic characteristics:

4. RESULTS

Variants of numeric fields:

• Football, a world passion: 3% of the world trade and large representation in the betting market • In handicap betting type, larger gains are offered for the prediction of goal difference • In knockout type tournaments, predict the goal difference is nd helpful in preparing for the 2 round of clashes • There are studies to predict the exact score, but predictions of the goal difference are more accurate and have not been studied

• The removal of the records of teams that competed in

• Once the target attribute is the goal difference, the basic characteristics has been adapted to reflect the difference in performance between teams (e.g. difference of the average goal difference over the last 4 games between the home team and the visiting team) • Total: 81 selectable attributes 2) Selection • As the SVR demand a long run time, the selection of attributes was performed by linear regression •A greedy stepwise heuristic was used to search for the possible combinations of attributes •Attribute values were normalized to avoid distortions of importance

Two evaluation metrics were used: • RMSE: adequate to evaluate the floating point results expressed by the model, indicating the proximity between the expected goal difference and the real goal difference • Accuracy: used to compare the predictions of the winning team (or draw) with the results of the reference model • The test collection was built up raffling off 10 dates in which there were rounds of the Brazilian Football Championship. One date was selected for each year (2002-2011) 10 N Pi: goal difference predicted 1 2 E = 1 E ∑ E j= P −R CT j ∑ ( i i) 10 j=1 for a match "i" of the day "j" N i=1 Ri: the real value of this •Although developed to difference accomplish a more specific task, Ej: forecast error for the N our model has achieved a better matches of the day j result than the reference model: E : test collection error CT • ECT: 1.267822 • Accuracy: 60.53% (Ref. Model: 55.26%)

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5. CONCLUSION • The achieved result points to the feasibility of using machine learning techniques (especially support vector regression) for the prediction of goal difference in football matches