منتفع شدن از بازار قمار فوتبال انجمن ناکارآمد: پیش بینی، ریسک و عدم قطعیت با استفاده از شبکه های بیزی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|29223||2013||27 صفحه PDF||سفارش دهید||11470 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Knowledge-Based Systems, Volume 50, September 2013, Pages 60–86
We present a Bayesian network (BN) model for forecasting Association Football match outcomes. Both objective and subjective information are considered for prediction, and we demonstrate how probabilities transform at each level of model component, whereby predictive distributions follow hierarchical levels of Bayesian inference. The model was used to generate forecasts for each match of the 2011/2012 English Premier League (EPL) season, and forecasts were published online prior to the start of each match. Profitability, risk and uncertainty are evaluated by considering various unit-based betting procedures against published market odds. Compared to a previously published successful BN model, the model presented in this paper is less complex and is able to generate even more profitable returns.
Association Football (hereafter referred to as simply football) is the most popular sport internationally ,  and , and attracts an increasing share of the multi-billion dollar gambling industry; particularly after its introduction online . This is one of the primary reasons why we currently observe extensive attention paid to football odds by both academic research groups and industrial organisations who look to profit from potential market inefficiencies. While numerous academic papers exist which focus on football match forecasts, only a few of them appear to consider profitability as an assessment tool for determining a model’s forecasting capability. Pope and Peel  evaluated a simulation of bets against published market odds in accordance with the recommendations of a panel of newspapers experts. They showed that even though there was no evidence of abnormal returns, there was some indication that the expert opinions were more valuable towards the end of the football season. Dixon and Coles  were the first to evaluate the strength of football teams for the purpose of generating profit against published market odds with the use of a time-dependent Poisson regression model based on Maher’s  model. They formed a simple betting strategy for which the model was profitable at sufficiently high levels of discrepancy between the model and the bookmakers’ probabilities. However, these high discrepancy levels returns were based on as low as 10 sample values; at lower discrepancy levels and with a larger sample size the model was unprofitable. The authors suggested that for a football forecast model to generate profit against bookmakers’ odds without eliminating the in-built profit margin, “it requires a determination of probabilities that is sufficiently more accurate from those obtained by published odds”. A similar paper by Dixon and Pope  was also published on the basis of 1993–1996 data and reported similar results. Rue and Salvesen  suggested a Bayesian dynamic generalised linear model to estimate the time-dependent skills of all the teams in the English Premier League (EPL) and English Division 1. They assessed the model against the odds provided by Intertops, a firm which is located in Antigua in the West Indies, and demonstrated profits of 39.6% after winning 15 bets out of a total of 48 for EPL matches, and 54% after winning 27 bets out of a total of 64 for Division 1 matches. In an attempt to exploit the favourite-longshot bias for profitable opportunities, Poisson and Negative Binomial models have been used to estimate the number of goals scored by a team . The conclusion was that even though the fixed odds offered against particular score outcomes did seem to offer profitable betting opportunities in some cases, these were few in number. Goddard and Asimakopoulos  proposed an ordered probit regression model to forecast EPL match results in an attempt to test the weak-form efficiency of prices in the fixed-odds betting market. To evaluate the model they considered seasons 1999 and 2000. Even though they reported a loss of −10.5% for overall performance, the model appeared to be profitable (on a pre-tax gross basis) at the start and at the end of every season.1 Using a benchmark statistical model with a large number of quantifiable variables relevant to match outcomes Forrest et al.  examined the effectiveness of forecasts based on published odds and forecasts generated. They considered five different bookmaking firms for five consecutive seasons (1998–2003) and demonstrated that the model generated negative returns ranging from −10% to −12% depending on the bookmaking firm, but the loss was reduced to −6.6% when using the best available odds by exploiting arbitrage between bookmaking firms.  attempted to investigate the rationality of bookmakers’ odds using an ordered probit model to generate predictions for EPL matches. By considering William Hill odds, they followed the betting strategy introduced in  and  and reported negative returns ranging from −2.5% to −15% for all discrepancy levels during seasons 2004–2006. In the absence of any consistently successful model against market odds, the authors claimed that “if it was successful, it would not have been published”.  considered the ELO rating system for football match prediction, although it was initially developed by  for assessing the strength of international chess players. Even though the ratings appeared to be useful in encoding the information of past results for measuring the strength of a team, resulting forecasts reported negative expected returns against numerous seasons of published odds using various betting strategies. However, Constantinou and Fenton  later developed a novel rating technique (called pi-rating) that outperformed considerably the two ELO rating variants of , in terms of profitability, over a period of five EPL season.  recently presented a Bayesian network model that was used to generate forecasts about the EPL matches during season 2010/2011, by considering both objective and subjective information for prediction. Forecasts were published online  prior to the start of each match, and this was the first academic study to demonstrate profitability that was consistent against published market odds over a sufficiently high number of betting trials without eliminating the bookmakers’ profit margin. In this paper we present a Bayesian network model for forecasting football outcomes that is based on the approach in , but with reduced complexity and higher forecasting capability (which we explain in detail in Sections 2, 3 and 4). The paper is organised as follows: Section 2 describes the model; Section 3 presents the various betting procedures along with a Bayesian network component for assessing the risks involved under each of the procedures; Section 4 discusses the results; Section 5 provides our concluding remarks.
نتیجه گیری انگلیسی
We have presented a Bayesian network (BN) model for forecasting football match outcomes that not only simplifies a previously publish BN model, but also provides improved forecasting capability. The model considers both objective and subjective information for prediction. The subjective information is important for prediction but is not captured in historical data. The model was used to generate the match forecasts for the EPL season 2011/2012, and forecasts were published online  prior to the start of each match. For assessing the forecast capability of our model, we have introduced an array of betting procedures. These are variants of a standard betting methodology previously considered for assessing profitability by relevant published football forecast studies. A unit-based profitability assessment over all betting procedures demonstrates that: (a) at level 2 (team form) the model component provided inferred match forecasts that were substantially superior to those generated at level 1 (which were solely based on historical performances); (b) at level 3 (team fatigue and motivation) the model component failed to provide inferred match forecasts that were superior to those generated at level 2. This resulted in concluding match forecasts with inferior profitability relative to that of level 2, but still superior relative to that of level 1; (c) a sub-component evaluation at level 3 revealed that we have overestimated the negative impact introduced by evidence of fatigue, and this should serve as a lesson-learned for relevant future models; (d) despite the consequences of (b), the concluding profitability of our model was even superior to that generated by the previous successful and profitable model under all of the betting procedures; (e) the predictive probability density distributions of unit-based returns showed that a bettor’s exposure to risk increases together with the substantial profitable returns that BP3, and BP4 provide over BP1 and BP2. However, we showed that one way a bettor may reduce his exposure to risk is by exploiting arbitrage opportunities which occur relatively frequently (70 out of the 380 match instances); (f) a team-based profitability assessment revealed further market inefficiencies (to the already extensive list) whereby published odds are consistently biased towards the trademark rather than the performance of a team. Evidently, the results of our study are critically dependent on the knowledge of the expert. Given that the subjective model inputs were provided by a member of the research team (who is a football fan but definitely not an expert of the EPL), it suggests that (a) subjective inputs can improve the forecasting capability of a model even if they are not submitted by a genuine expert who is a professional for the specified domain, and (b) if the model were to be used by genuine experts we would expect that the more informed expert inputs would lead to posterior beliefs that are even higher in both precision and confidence. The results of this paper have demonstrated a number of benefits of using Bayesian networks: in particular they enable us to incorporate crucial subjective information easily and enhance our understanding of uncertainty and our exposure to the relevant risks involved.