PARX model for football match predictions

• Date: 01 November 2017
• Author: Giovanni Angelini,Luca De Angelis
• DOI: http://doi.org/10.1002/for.2471
• Published date: 01 November 2017

Received: 30 August 2016 Revised: 2 March 2017 Accepted: 3 March 2017

DOI: 10.1002/for.2471

RESEARCH ARTICLE

PARX model for football match predictions

Giovanni Angelini Luca De Angelis

Department of Statistical Sciences and

School of Economics, Management and

Statistics, University of Bologna, Bologna,

Italy

Correspondence

Luca De Angelis, Department of Statistical

Sciences, University of Bologna, via Belle

Arti 41, 40126 Bologna, Italy.

Email: l.deangelis@unibo.it

Abstract

We propose an innovative approach to model and predict the outcome of football

matches based on the Poisson autoregression with exogenous covariates (PARX)

model recently proposed by Agosto, Cavaliere, Kristensen, and Rahbek (Journal

of Empirical Finance, 2016, 38(B), 640–663). We show that this methodology is

particularly suited to model the goal distribution of a football team and provides

a good forecast performance that can be exploited to develop a profitable betting

strategy. This paper improves the strand of literature on Poisson-based models, by

proposing a specification able to capture the main characteristics of goal distribution.

The betting strategy is based on the idea that the odds proposed by the market do

not reflect the true probability of the match because they may also incorporate the

betting volumes or strategic price settings in order to exploit betters’ biases. The

out-of-sample performance of the PARX model is better than the reference approach

by Dixon and Co les (Applied Statistics, 1997, 46(2), 265–280). Wealso evaluate our

approach in a simple betting strategy, which is applied to English football Premier

League data for the 2013–2014, 2014–2015, and 2015–2016 seasons. The results

show that the return from the betting strategy is larger than 30% in most of the cases

considered and may even exceed 100% if we consider an alternative strategy based

on a predetermined threshold, which makes it possible to exploit the inefficiency of

the betting market.

KEYWORDS

betting market, count data, density forecasts, Poisson autoregression, sports forecasting

1INTRODUCTION

Over the last fewyears, the football betting market has experi-

enced the fastest growth in gambling markets (Constantinou,

Fenton, and Neil, (2013)). Not surprisingly, many different

methodologies have been developed to construct a profitable

betting strategy that is able to capture the mispricing of odds.

Starting with the pioneering work of Maher (1982) and Dixon

and Coles (1997), many econometric methods have been

proposed to predict football match results.

The purpose of our paper is twofold: (i) to develop an

approach able to compute a set of probabilities associated with

each possible result; and (ii) to use these probabilities to profit

from the potential mispricing of the odds offered on the bet-

ting market. The odds proposed by the bookmakers may be

influenced by betting volumes and therefore mightnot always

reflect the true probability of the match outcomes. Indeed, one

of the aims of bookmakers is to encourage betters to subdivide

their wagers on each odd (Vlastakis, Dotsis, and Markellos,

2009). In doing so, they minimize the risk and gain from the

unfairness of the proposed odds. Moreover, bookmakers may

systematically set odds in order to take advantage of betters’

biases, such as the well-known preference for favorites and

local teams, in order to increase profits (Levitt, 2004). There-

fore, the comparison between true probabilities and odds can

be exploited to define a profitable betting strategy.

Journal of Forecasting.2017;36:795–807. wileyonlinelibrary.com/journal/for Copyright © 2017 John Wiley & Sons, Ltd. 795