On determining probability forecasts from betting odds

We show that the probabilities determined from betting odds using Shin’s model are more accurate forecasts than those determined using basic normalization or regression models. We also provide empirical evidence that some bookmakers are significantly different sources of probabilities in terms of forecasting accuracy, and that betting exchange odds are not always the best source, especially in smaller markets. The advantage of using Shin probabilities and the differences between bookmakers decrease with an increasing market size.     

Efficiency of online football betting markets

This paper evaluates the efficiency of online betting markets for European (association) football leagues. The existing literature shows mixed empirical evidence regarding the degree to which betting markets are efficient. We propose a forecast-based approach for formally testing the efficiency of online betting markets. By considering the odds proposed by 41 bookmakers on 11 European major leagues over the last 11 years, we find evidence of differing degrees of efficiency among markets. We show that, if the best odds are selected across bookmakers, eight markets are efficient while three show inefficiencies that imply profit opportunities for bettors. In particular, our approach allows the estimation of the odds thresholds that could be used to set profitable betting strategies both ex post and ex ante.     

The value of statistical forecasts in the UK association football betting market

In this paper, we evaluate the economic significance of statistical forecasts of UK Association Football match outcomes in relation to betting market prices. We present a detailed comparison of odds set by different bookmakers in relation to forecast model predictions, and analyse the potential for arbitrage across firms. We also examine extreme odds biases. A detailed re-examination of match result odds and a new examination of correct score odds for the period 1993 to 1996 suggest that the market is inefficient.     

The behaviour of betting and currency markets on the night of the EU referendum

We study the behaviours of the Betfair betting market and the sterling/dollar exchange rate (futures price) during 24 June 2016, the night of the EU referendum. We investigate how the two markets responded to the announcement of the voting results by employing a Bayesian updating methodology to update prior opinion about the likelihood of the final outcome of the vote. We then relate the voting model to the real-time evolution of the market-determined prices as the results were announced. We find that, although both markets appear to be inefficient in absorbing the new information contained in the vote outcomes, the betting market seems less inefficient than the FX market. The different rates of convergence to the fundamental value between the two markets lead to highly profitable arbitrage opportunities.     

Forecasting football results and exploiting betting markets: The case of “both teams to score”

The continuous growth of available football data presents unprecedented research opportunities for a better understanding of football dynamics. While many research works focus on predicting which team will win a match, other interesting questions, such as whether both teams will score in a game, are still unexplored and have gained momentum with the rise of betting markets. With this in mind, we investigate the following research questions in this paper: “How difficult is the ‘both teams to score’ (BTTS) prediction problem?”, “Are machine learning classifiers capable of predicting BTTS better than bookmakers?”, and “Are machine learning classifiers useful for devising profitable betting strategies in the BTTS market?”. We collected historical football data, extracted groups of features to represent the teams’ strengths, and fed these to state-of-the-art classification models. We performed a comprehensive set of experiments and showed that, although hard to predict, in some scenarios it is possible to outperform bookmakers, which are robust baselines per se. More importantly, in some cases it is possible to beat the market and devise profitable strategies based on machine learning algorithms. The results are encouraging and, besides shedding light on the problem, may provide novel insights for all kinds of football stakeholders.     

A Markov chain model for forecasting results of mixed martial arts contests

In this paper, we present a new methodology for forecasting the results of mixed martial arts contests. Our approach utilises data scraped from freely available websites to estimate fighters’ skills in various key aspects of the sport. With these skill estimates, we simulate the contest as an actual fight using Markov chains, rather than predicting a binary outcome. We compare the model’s accuracy to that of the bookmakers using their historical odds and show that the model can be used as the basis of a successful betting strategy.     

Betting on a buzz: Mispricing and inefficiency in online sportsbooks

Bookmakers sell claims to bettors that depend on the outcomes of professional sports events. Like other financial assets, the wisdom of crowds could help sellers to price these claims more efficiently. We use the Wikipedia profile page views of professional tennis players involved in over 10,000 singles matches to construct a buzz factor. This measures the difference between players in their pre-match page views relative to the usual number of views they received over the previous year. The buzz factor significantly predicts mispricing by bookmakers. Using this fact to forecast match outcomes, we demonstrate that a strategy of betting on players who received more pre-match buzz than their opponents can generate substantial profits. These results imply that sportsbooks could price outcomes more efficiently by listening to the buzz.     

What Do Bettors Want? Determinants of Pari‐Mutuel Betting Preference

A bstract .   This paper is an analysis of the demand for thoroughbred racetrack wagers, examining evidence that would support the existence of two types of bettors: the risk-averse informed bettor versus the uninformed bettor. Looking at 12 major racetracks over the fall of 2002, we undertake an empirical examination of the determinants of bettors' preferences for particular wagers on specific races. The goal is to try to determine what individual aspects of a race (conditions, surface, participants, etc.) will encourage increased wagering dollars. With the advent of simulcasting, the competition for the wagering dollar is fierce, as the bettor can choose from more than 100 races daily, each race offering numerous betting options. We find for most wagers that higher quality participants, larger and more competitive fields, and turf races increase betting volume while higher pari-mutuel takeout, poor track conditions, and other races run concurrently reduce volume. However, more competitive fields reduce betting volume in the show and trifecta pools. Optimal field size is determined to be between 10 and 12 betting interests. Overall, we find support for the existence of a significant share of risk-averse informed bettors.     

Market efficiency in Scandinavian racetrack betting

This study analyzes Scandinavian racetrack betting markets. We discuss market efficiency and investor behavior in light of the fact that investors earn negative returns on average. Show bets on favorites in Norway yield a small positive return, while all the other betting markets are weak form efficient. We establish the favorite-longshot bias for quinella and exactor bettors, but not for win bettors. Our results can be explained by small pools and high track takes. Investors wagering at the racetrack have a different risk attitude than investors wagering off the track. We explain how our results should influence the design of betting products, especially with respect to the fraction of the pool returned to winners.     

Are betting returns a useful measure of accuracy in (sports) forecasting?

In an economic context, forecasting models are judged in terms not only of accuracy, but also of profitability. The present paper analyses the counterintuitive relationship between accuracy and profitability in probabilistic (sports) forecasts in relation to betting markets. By making use of theoretical considerations, a simulation model, and real-world datasets from three different sports, we demonstrate the possibility of systematically or randomly generating positive betting returns in the absence of a superior model accuracy. The results have methodological implications for sports forecasting and other domains related to betting markets. Betting returns should not be treated as a valid measure of model accuracy, even though they can be regarded as an adequate measure of profitability. Hence, an improved predictive performance might be achieved by carefully considering the roles of both accuracy and profitability when designing models, or, more specifically, when assessing the in-sample fit of data and evaluating out-of-sample forecasting performances.     

Additional evidence of heuristic-based inefficiency in season wins total betting markets: Major League Baseball

The large majority of sports betting papers have addressed questions of market efficiency based on the outcome of single game, such as spread (sides) or point totals wagers. This research examines the Major League Baseball (MLB) season wins total over/under betting market with respect to questions of market efficiency and profitability. Woodland and Woodland (2013, 2015) investigated the season wins total markets for the National Football League (NFL) and the National Basketball Association (NBA) and found significant inefficiencies. Betting rules tested in this paper parallel those proposed by Woodland and Woodland for the NFL and NBA. They aim to take advantage of the implications of the representativeness heuristic, that is, individuals expect results from a small number of games to generalize to the entire population. The MLB market is found to be inefficient, and provides opportunities for profitable wagering. We establish a tendency for bettors to overreact to a team’s performance in the previous season, particularly for teams with winning records. Results are consistent with the findings for the NFL and NBA season wins totals betting markets. This may be the consequence of monetary betting limits and a structure requiring the completion of a sport’s season before the bet outcome is determined, both of which could discourage some bettors from participating.     

Regional information and market efficiency: the case of spread betting in United States college football

Using game results over a seven year span (1999–2006), we find that United States college football teams in arid regions “win” against the spread in 56.64% of games in which they host a team from a humid region. This result provides statistically significant evidence for both weak and strong form inefficiency in the spread betting markets of such games. By examining other cases of intraregional and interregional competition within the sport, we conclude that this inefficiency does not arise from the effects of travel or home field advantage. Rather, the result indicates that climate aridity is an observed characteristic for which college football betting markets do not accurately control. It is quite rare to find strong form market inefficiency arise from a single variable rather than from an elaborate, multivariable betting strategy. Therefore, the effect of climate aridity upon college football spread betting market efficiency can be characterized as dramatic. It is conjectured that remote market participants may need to “experience” certain types of relevant regional information, such as climate, to act in a market efficient manner.     

The wisdom of large and small crowds: Evidence from repeated natural experiments in sports betting

Prediction markets have proved excellent tools for forecasting, outperforming experts and polls in many settings. But do larger markets, with a wider participation, perform better than smaller markets? This paper analyses a series of repeated natural experiments in sports betting. The Queen’s Club Tennis Championships are held every year, but every other year the Championships clash with a major soccer tournament. We find that tennis betting prices become significantly less informative when participation rates are affected adversely by the clashing soccer tournament. This suggests that measures which increase prediction market participation may lead to a greater forecast accuracy.     

Forecasting football match results in national league competitions using score-driven time series models

We develop a new dynamic multivariate model for the analysis and forecasting of football match results in national league competitions. The proposed dynamic model is based on the score of the predictive observation mass function for a high-dimensional panel of weekly match results. Our main interest is in forecasting whether the match result is a win, a loss or a draw for each team. The dynamic model for delivering such forecasts can be based on three different dependent variables: the pairwise count of the number of goals, the difference between the numbers of goals, or the category of the match result (win, loss, draw). The different dependent variables require different distributional assumptions. Furthermore, different dynamic model specifications can be considered for generating the forecasts. We investigate empirically which dependent variable and which dynamic model specification yield the best forecasting results. We validate the precision of the resulting forecasts and the success of the forecasts in a betting simulation in an extensive forecasting study for match results from six large European football competitions. Finally, we conclude that the dynamic model for pairwise counts delivers the most precise forecasts while the dynamic model for the difference between counts is most successful for betting, but that both outperform benchmark and other competing models.     

A profitable model for predicting the over/under market in football

The over/under 2.5 goals betting market allows gamblers to bet on whether the total number of goals in a football match will exceed 2.5. In this paper, a set of ratings, named ‘Generalised Attacking Performance’ (GAP) ratings, are defined which measure the attacking and defensive performance of each team in a league. GAP ratings are used to forecast matches in ten European football leagues and their profitability is tested in the over/under market using two value betting strategies. GAP ratings with match statistics such as shots and shots on target as inputs are shown to yield better predictive value than the number of goals. An average profit of around 0.8 percent per bet taken is demonstrated over twelve years when using only shots and corners (and not goals) as inputs. The betting strategy is shown to be robust by comparing it to a random betting strategy.     

Towards a theory of platform dynamics

I introduce a dynamic framework to analyze platforms. The (single) platform owner sets prices at the beginning of each period. Agents (buyers, sellers, readers, consumers, merchants, etc.) make platform membership decisions occasionally. I show that an optimal platform pricing addresses two externalities: across sides and across time periods. This results in optimal prices which depend on platform size in a nontrivial way. By means of numerical simulations, I examine the determinants of equilibrium platform size, showing that the stationary distribution of platform size may be bimodal, that is, with some probability the platform remains very low or takes very long to increase in size. I also contrast the dynamics of proprietary versus nonproprietary (i.e., zero‐priced) platforms, and consider the specific case of asymmetric platforms (one side cares about the other but not vice versa).     

Culture,participative decision making and job satisfaction

This study explores the impact of culture on participatory decision making (PDM) and job satisfaction (JS) using data obtained from the European Values Study (EVS). We parameterise two different cultural variables using principal components analysis: first a continuum based on survival versus self-expression values and second a continuum based on traditional versus secular-rational values. Application of ordered logistic regression to Likert scales of PDM and JS suggests that greater self-expression in the survival versus self-expression variable enhances both PDM and JS; and more traditional values in the traditional versus secular-rational continuum have the same effect.     

Stackelberg leadership with demand uncertainty

We consider a simple Stackelberg model with demand uncertainty only for the first mover in order to compare the advantages of leadership and flexibility, and use an example to provide some discussion about the endogenous order of moves in the presence of demand uncertainty. We find that only when the realized demand is in an intermediate zone does the first mover preserve its advantage; when the realized demand is far from its expected value, the second mover obtains higher profit than the leading firm, as the leadership advantage is dominated by the benefit of flexibility when demand fluctuation is significant. Even with this risk of losing flexibility under significant demand variation, for some parameter values in our model the first firm still has incentive to choose Stackelberg rather than Cournot competition. Copyright © 2005 John Wiley & Sons, Ltd.     

Testing the Wisdom of Crowds in the field: Transfermarkt valuations and international soccer results

This paper investigates the value of collective judgments which stem from settings that have not been designed explicitly to elicit the ‘Wisdom of Crowds’. In particular, I investigate information obtained from transfermarkt.de, an online platform where a crowd of registered users assess the value of professional soccer players. I show that forecasts of international soccer results based on the crowd’s valuations are more accurate than those based on standard predictors, such as the FIFA ranking and the ELO rating. When this improvement in forecasting performance is applied to betting strategies, it leads to sizable monetary gains. I further exploit information on the preferences of individual crowd members in order to investigate whether wishful thinking hampers the accuracy of crowd valuations, but fail to find evidence that such is the case.     

Sequential product positioning in the presence of an asymmetric network externality intensity

In this study, we analyze the sequential decisions on product positioning of two firms in the presence of network externalities. One commonly accepted phenomena in a market where a network externality arises is the first‐mover advantage, in which the first entrant into a market can earn a higher profit than later entrants. However, in some recent online services markets, we see that the second mover earns a higher profit than the first mover. This occurs because the second mover strengthens its variety of available functions and services markedly, thereby facilitating consumers' work and communication with its main product, which we call network externality intensity. Based on this observation, we analyze sequential positioning in Hotelling's framework by incorporating an asymmetric network externality intensity between firms. We show that unlike the results of previous related studies, both first‐ and second‐mover advantages can appear in the equilibrium depending on the relationship of the network externality intensity between firms; further, they do not change monotonically with the level of network externality intensity.