scholarly journals Efficiency Testing of Prediction Markets: Martingale Approach, Likelihood Ratio and Bayes Factor Analysis

Risks ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 31
Author(s):  
Mark Richard ◽  
Jan Vecer
Keyword(s):  
Likelihood Ratio ◽  
Bayes Factor ◽  
Efficient Market Hypothesis ◽  
Stopping Times ◽  
Prediction Markets ◽  
Martingale Approach ◽  
Optimal Trading ◽  
Betting Market ◽  
Football Betting ◽  
English Premier League

This paper studies efficient market hypothesis in prediction markets and the results are illustrated for the in-play football betting market using the quoted odds for the English Premier League. Our analysis is based on the martingale property, where the last quoted probability should be the best predictor of the outcome and all previous quotes should be statistically insignificant. We use regression analysis to test for the significance of the previous quotes in both the time setup and the spatial setup based on stopping times, when the quoted probabilities reach certain bounds. The main contribution of this paper is to show how a potentially different distributional opinion based on the violation of the market efficiency can be monetized by optimal trading, where the agent maximizes logarithmic utility function. In particular, the trader can realize a trading profit that corresponds to the likelihood ratio in the situation of one market maker and one market taker, or the Bayes factor in the situation of two or more market takers.

scholarly journals Investigating the efficiency of the Asian handicap football betting market with ratings and Bayesian networks

2021 ◽  
pp. 1-23
Author(s):  
Anthony C. Constantinou
Keyword(s):  
Bayesian Networks ◽  
Return On Investment ◽  
Relevant Literature ◽  
Rating Systems ◽  
Premier League ◽  
Betting Market ◽  
Traditional Market ◽  
Football Betting ◽  
English Premier League ◽  
Betting Decision

Despite the massive popularity of the Asian Handicap (AH) football (soccer) betting market, its efficiency has not been adequately studied by the relevant literature. This paper combines rating systems with Bayesian networks and presents the first published model specifically developed for prediction and assessment of the efficiency of the AH betting market. The results are based on 13 English Premier League seasons and are compared to the traditional market, where the bets are for win, lose or draw. Different betting situations have been examined including a) both average and maximum (best available) market odds, b) all possible betting decision thresholds between predicted and published odds, c) optimisations for both return-on-investment and profit, and d) simple stake adjustments to investigate how the variance of returns changes when targeting equivalent profit in both traditional and AH markets. While the AH market is found to share the inefficiencies of the traditional market, the findings reveal both interesting differences as well as similarities between the two.

scholarly journals Bayesian Inference and Testing Any Hypothesis You Can Specify

2018 ◽  
Vol 1 (2) ◽  
pp. 281-295 ◽  
Author(s):  
Alexander Etz ◽  
Julia M. Haaf ◽  
Jeffrey N. Rouder ◽  
Joachim Vandekerckhove
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Special Form ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Alternative Hypotheses ◽  
Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model-selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that the researcher specify exactly what is meant by a “null” hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, but in all cases the inferential procedure is based on the same underlying method of likelihood comparison. An associated app can be found at https://osf.io/mvp53/ . This article is the work of the authors and is reformatted from the original, which was published under a CC-By Attribution 4.0 International license and is available at https://psyarxiv.com/wmf3r/ .

Biases in the Football Betting Market

2017 ◽  
Author(s):  
Imant Daunhawer ◽  
David Schoch ◽  
Sven Kosub
Keyword(s):  
Betting Market ◽  
Football Betting

Using Prediction Market Prices to Differentiate Factors that Influence the Highest and Lowest Priced Tickets in Dynamic Pricing for Major League Baseball

2015 ◽  
Vol 9 (2) ◽  
pp. 43-63
Author(s):  
Rodney Paul ◽  
Andrew Weinbach
Keyword(s):  
Dynamic Pricing ◽  
Major League Baseball ◽  
Prediction Markets ◽  
Market Prices ◽  
Betting Market ◽  
Major League ◽  
Similarities And Differences ◽  
Using Data ◽  
Ticket Prices ◽  
Uncertainty Of Outcome

The use of prediction markets is extended to explain differences in preferences of fans that purchase different price levels of tickets under dynamic pricing for Major League Baseball.  Using data from eleven teams, this research investigates similarities and differences in variables that affect ticket prices for the highest-priced and lowest-priced tickets.  Key contrasts between the groups are found to stem from distinct preferences for uncertainty of outcome, measured by betting market odds, and team quality.  It is also shown that differences between the groups are attributable to sensitivity to factors such as key opponents, weekend games, opening day, and temperature.

APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES

2018 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Likelihood Ratio ◽  
Bayes Factor ◽  
Loss Functions ◽  
Posterior Distributions ◽  
Likelihood Ratio Order ◽  
Predictive Distributions ◽  
Sufficient Statistic ◽  
Bayesian Inferences ◽  
Bayesian Estimators ◽  
General Error

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

Team Travel Effects and the College Football Betting Market

2015 ◽  
Vol 18 (4) ◽  
pp. 388-425 ◽  
Author(s):  
B. Jay Coleman
Keyword(s):  
Market Efficiency ◽  
College Football ◽  
Temperature Elevation ◽  
Home Team ◽  
Late Season ◽  
Betting Market ◽  
Time Zones ◽  
Football Betting

This research examines whether the college football betting line and over/under accurately assimilate travel effects on visiting teams, including time zones traversed; direction and distance traveled; and temperature, elevation, and aridity changes. We investigate the market’s accuracy at predicting winners, point differentials, and points scored and examine its market efficiency, that is, whether travel affects the chance the home team covers the spread or the chance that an “over” bet wins. The betting market is found to be an inaccurate and inefficient processor of travel effects, most consistently for late-season games involving an underdog with a 1-hr time deficit versus its opponent.

scholarly journals Investigating inefficiencies of bookmaker odds in football using machine learning

2020 ◽  
Author(s):  
Benedikt Mangold ◽  
Johannes Stübinger
Keyword(s):  
Machine Learning ◽  
Simulation Study ◽  
Efficient Market Hypothesis ◽  
Learning Models ◽  
Efficient Market ◽  
Simple Machine ◽  
Football Betting ◽  
Available Information ◽  
Over Time ◽  
Machine Learning Models

The efficient-market hypothesis states that it is impossible to beat the market, as the price reflects all available information. Applied to bookmaker odds for football games, there should not be a systematic way of winning money on the long run.However, we show that by using simple machine learning models we can systematically outperform the markets belief manifested through the bookmakers odds. The effect of this inefficiency is diminishing over time, which indicates that the knowledge that has been derived from and the pure amount of the data is also reflected in the odds in recent times.We give some insights how this effect differs across major football leagues in Europe, which algorithms are performing best and statistics on the ROI using machine learning in football betting. Additionally, we share how the simulation study has been designed in more detail.

Embedding submartingales in wiener processes with drift, with applications to sequential analysis

1969 ◽  
Vol 6 (03) ◽  
pp. 612-632 ◽  
Author(s):  
W. J. Hall
Keyword(s):  
Lower Bound ◽  
Random Walks ◽  
Sample Size ◽  
Wiener Process ◽  
Likelihood Ratio ◽  
Sequential Analysis ◽  
Stopping Times ◽  
Wiener Processes ◽  
Size Function ◽  
Log Likelihood

Summary Skorokhod (1961) demonstrated how the study of martingale sequences (and zero-mean random walks) can be reduced to the study of the Wiener process (without drift) at a sequence of random stopping times. We show how the study of certain submartingale sequences, including certain random walks with drift and log likelihood ratio sequences, can be reduced to the study of the Wiener process with drift at a sequence of stopping times (Theorem 4.1). Applications to absorption problems are given. Specifically, we present new derivations of a number of the basic approximations and inequalities of classical sequential analysis, and some variations on them — including an improvement on Wald's lower bound for the expected sample size function (Corollary 7.5).

Never Tell Me the Odds: The Stingy Odds for Leicester City to Win the English Premier League

2018 ◽  
Vol 12 (1) ◽  
pp. 1-19
Author(s):  
Matthew Hood ◽  
William Chittenden ◽  
R. Todd Jewell
Keyword(s):  
Professional Sports ◽  
Expected Value ◽  
Expected Return ◽  
Premier League ◽  
Betting Market ◽  
History Of ◽  
English Premier League

The crowning of Leicester City FC as English Premier League champions in 2016 is arguably the biggest upset in the history of professional sports. The pre-season odds posted for LCFC to win the EPL were 5,000:1, worse than finding Elvis alive. In our model, they win just once per 70,000 simulations; thus, bettors could expect a return of just 0.071 of the stake when betting on Leicester City. This is similar to the expected return of betting on all of the long-shots in our simulations; however, the expected value of bets on favorites averages 0.864. We find that the betting market is segmented for favorites and long-shots; while the market for favorites resembles a normal betting market, the market for long-shots is like a lottery.

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