Betting Strategy Research Articles

MODELOS PREDITIVOS BASEADOS EM MACHINE LEARNING PARA OTIMIZAÇÃO DE ESTRATÉGIAS EM APOSTAS ESPORTIVAS NO FUTEBOL

This study presents an investigation into the application of predictive models based on Machine Learning to optimize sports betting strategies in football. The research was conducted using a combination of quantitative and qualitative methods, including the analysis of historical football match data and the implementation of machine learning algorithms. The results indicate that predictive models can be effective in forecasting football match outcomes, which can be useful for optimizing sports betting strategies. The practical application of these models can provide bettors with a competitive advantage, allowing them to make more informed decisions and potentially improve their financial outcomes. It is concluded that while predictive models offer a valuable tool for enhancing betting strategies, a careful approach and ongoing evaluation of the models are essential to maximize their effectiveness. The research suggests that future investigations could explore the integration of additional data and the improvement of algorithms to increase prediction accuracy.

Reality Cheque: Different Methods of Eliciting Fear-Related Beliefs Reveal Multiple Representations of Threat

Influential models of fears and phobias suggest that irrational threat beliefs underpin excessive fear. Yet, many fearful individuals recognize their fear is not justified. Drawing on memory competition/multiple representations theory, we developed a novel, fear-relevant procedure, which reveals conflicting representations of threat. In three experiments (Experiment 1, N = 49, Experiment 2, N = 47, Experiment 3, N = 75), fearful and non-fearful participants not only provided Probability Ratings for fear-related outcomes in a fear-relevant exposure task, but placed Bets, with payoffs depending on what happened in reality. Fearful participants displayed much higher Probability Ratings than Low fear participants. However, Bets revealed far less consistent group differences, even when proximal to threat (Experiments 1 and 2), and differences between High and Low fear participants’ Bets disappeared when they could not be anchored to previous Probability Ratings (Experiment 3). A Neutral Betting task also showed that general betting strategies were comparable between groups. We suggest that these findings may reflect the multi-representational nature of belief, in which both adaptive and maladaptive representations of a feared object may exist in parallel, with personal and contextual factors determining which form of representation is retrieved or expressed. This perspective can provide insights into the complex interplay of adaptive and maladaptive beliefs that is a central focus of currently dominant therapies.

On optimal betting strategies with multiple mutually exclusive outcomes

On optimal betting strategies with multiple mutually exclusive outcomes

Price of information in games of chance: A statistical physics approach.

Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded is an important and open problem in many settings. In this work we develop a statistical physics framework that allows one to determine analytically the fair price of information exchanged between players in a game of chance. For definiteness, we consider a game where N players bet on the binary outcome of a stochastic process and share the entry fees pot if successful. We assume that one player holds information about past outcomes of the game, which they may either use exclusively to improve their betting strategy or offer to sell to another player. We find a sharp transition as the number of players N is tuned across a critical value, between a phase where the transaction is always profitable for the seller and one where it may not be. In both phases, different regimes are possible, depending on the "quality" of information being put up for sale: we observe symbiotic regimes, where both parties collude effectively to rig the game in their favor, competitive regimes, where the transaction is unappealing to the data holder as it overly favors a competitor for scarce resources, and even prey-predator regimes, where an exploitative data holder could be giving away bad-quality data to undercut a competitor. Our analytical framework can be generalized to more complex settings and constitutes a flexible tool to address the rich and timely problem of pricing information in games of chance.

Inefficient Forecasts at the Sportsbook: An Analysis of Real-Time Betting Line Movement

This paper tests the efficiency of a set of sports betting markets using detailed betting line movement from opening until closing for four different sportsbooks for each of 3,681 Major League Baseball games. The reliability of the markets’ forecasts are assessed at several lead times. The forecasts are mostly reliable, but there are simple betting strategies that would have yielded significant profit. In addition, forecasts do not always improve monotonically as the games get closer, despite more information being available; forecasts at weekend day games’ start times are significantly worse than forecasts 90 minutes earlier. Furthermore, analysis of the sequences of forecasts within individual games reveals that these betting markets do not incorporate information optimally. There is sufficient evidence to reject weak form market efficiency; specifically, betting lines tend to overreact, exhibiting significant negatively autocorrelated changes that could be exploited by sophisticated bettors. This paper was accepted by Manel Baucells, behavioral economics and decision analysis. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.00456 .

Research and Application on Kelly's Formula

The subject of investment finance holds significant importance in contemporary society, with position management in investment serving as a critical factor in determining outcomes of success or failure. Acquiring knowledge in the realm of efficient asset allocation can significantly enhance individuals' ability to effectively oversee their financial resources. The Kelly formula, initially employed for determining the proportion of funds wagered on a particular game, has emerged as a prominent betting strategy within the realm of probability theory. This method aims to optimize the overall growth rate of the main amount throughout a series of independent bets, each of which is intended to yield positive net returns. This study will examine the historical context of the Kelly formula, its mathematical derivation, its utilization in the realms of gambling and investment, and its consequential implications for individuals' investment strategies.

This "Fail-Proof" Gambling Strategy Could Ruin You: The martingale betting strategy has ruined many gamblers--when the Kelly criterion could have brought them riches.

This "Fail-Proof" Gambling Strategy Could Ruin You: The martingale betting strategy has ruined many gamblers--when the Kelly criterion could have brought them riches.

Kelly Criterion and its Application

Kelly Criterion is a betting strategy that maximizes the long-term growth rate of principal in independent repeated bets. Kelly formula is beneficial to fund management and portfolio investment, and its application in investment is particularly prominent. In this paper, we take Kelly's criterion as the center, give the proof of Kelly's criterion with different methods and angles, and generalize it to a more general form. At the same time, this paper also illustrates the rationality of Kelly's criterion through examples and data simulation.

Weak Form Efficiency in Sports Betting Markets

Betting on sports is increasingly popular, and legal in the United States. Many states have moved to legalize sports betting both in-person and on-line. In this paper we evaluate the sports betting market and assess its efficiency in the financial sense. Using a large dataset of betting odds and outcomes across a wide range of sports over an extended period, we evaluate the weak-form efficiency of the sports betting market. While we find some minor technical inefficiencies, overall, the markets are generally efficient, and no odds-based betting strategy will yield statistically significant long-term profits. But some bets are better than others. Slight underdog bets in professional and collegiate football and the UFC have had positive returns over an extended time frame, though they do not clear a statistical significance test. On the other hand, we find some bets clearly under perform. Longshot bets in college basketball are among the worst bets and longshot biases can be shown to exist in collegiate football and basketball as well as baseball.

A subjective interpretation of Liu–Liu’s credibility measures and expectations

We consider credibility measures introduced by Liu and Liu and the corresponding credibility expectations, obtained through the Choquet integral. In analogy with de Finetti’s approach to probability, we show that also for credibility measures and expectations, a subjective interpretation can be given through suitable notions of coherence. In detail, coherence can be expressed equivalently in terms of consistency, through a fair betting scheme and through a penalty criterion. Such notions of coherence rest upon the concepts of partially resolving uncertainty due to Jaffray, the notion of consonance due to Shafer and the notion of pessimism-optimism indifference introduced in this paper.

Forecasting football match results using a player rating based model

The paper presents a model for forecasting the results of football matches, which takes into account the abilities of the players on each team. The advantage of this approach is that the dynamic nature of team strengths is incorporated into the model directly. We test our model against the bookmaker’s predictions and in a Kelly-type betting strategy applied to the pre-match win/draw/loss market. The new model results in significant positive returns to betting.

ALPHA: Audit that learns from previously hand-audited ballots

A risk-limiting election audit (RLA) offers a statistical guarantee: if the reported electoral outcome is incorrect, the audit has a known maximum chance (the risk limit) of not correcting it before it becomes final. BRAVO (Lindeman, Stark and Yates (In Proceedings of the 2011 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (EVT/WOTE’11) (2012) USENIX)), based on Wald’s sequential probability ratio test for the Bernoulli parameter, is the simplest and most widely tried method for RLAs, but it has limitations. It cannot accommodate sampling without replacement or stratified sampling which can improve efficiency and are sometimes required by law. It applies only to ballot-polling audits which are less efficient than comparison audits. It applies to plurality, majority, supermajority, proportional representation, and instant-runoff voting (IRV, using RAIRE (Blom, Stuckey and Teague (In Electronic Voting (2018) 17–34 Springer))) but not to other social choice functions for which there are RLA methods. And while BRAVO has the smallest expected sample size among sequentially valid ballot-polling-with-replacement methods when the reported vote shares are exactly correct, it can require arbitrarily large samples when the reported reported winner(s) really won but the reported vote shares are incorrect. ALPHA is a simple generalization of BRAVO that: (i) works for sampling with and without replacement, with and without weights, with and without stratification, and for Bernoulli sampling; (ii) works not only for ballot polling but also for ballot-level comparison, batch polling, and batch-level comparison audits; (iii) works for all social choice functions covered by SHANGRLA (Stark (In Financial Cryptography and Data Security (2020) Springer)), including approval voting, STAR-Voting, proportional representation schemes, such as D’Hondt and Hamilton, IRV, Borda count, and all scoring rules, and (iv) in situations where both ALPHA and BRAVO apply, requires smaller samples than BRAVO when the reported vote shares are wrong but the outcome is correct—five orders of magnitude in some examples. ALPHA includes the family of betting martingale tests in RiLACS (Waudby-Smith, Stark and Ramdas (In Electronic Voting. E-Vote-ID 2021 (2021) Springer)) with a different betting strategy parametrized as an estimator of the population mean and explicit flexibility to accommodate sampling weights and population bounds that change with each draw. A Python implementation is provided.

Close but no cigar: does winning the game moderate or amplify failing to cover the spread in future NFL games

ABSTRACT In this paper, I examine the joint role of the previous game’s outcome with and without the spread on wagers’ preferences and outcomes in the NFL gambling market. The results show that gamblers are more likely to wager on the home team if they covered the spread in their previous game, while they are less likely to bet on the home team if the visiting team won their last game (not considering the spread). Further results show that teams are more likely to cover the spread if they covered the spread but lost their previous game. Profitable betting strategies are then put forward based on this information.

Market Efficiency and Censoring Bias in College Football Gambling

The team totals and point spread betting lines jointly predict team scores in college football games. The gambling market’s score predictions are shown to be biased due to censoring at zero points. This presents arbitrage opportunities for gamblers who place wagers on the team totals line in cases for which expected bias is high. A naïve betting strategy that exploits this bias using only information contained within the two betting lines themselves yields a win percentage of over 55 percent over the past two decades. This significantly exceeds the typical transaction costs associated with wagers, indicating the market is semi-strong inefficient.

Kelly criterion and fractional Kelly strategy for non-mutually exclusive bets

Abstract This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. This type of situation is common in horse racing, where multiple types of bets are available for a single race. The paper begins by providing a theoretical overview of the Kelly betting strategy and then discusses how it can be extended to non-mutually exclusive bets. A new formulation of the fractional Kelly strategy, which involves betting a fixed fraction of the amount suggested by the Kelly criterion, is also presented for this type of scenario.

A Safe Hosmer-Lemeshow Test

This article proposes an alternative to the Hosmer-Lemeshow (HL) test for evaluating the calibration of probability forecasts for binary events. The approach is based on e-values, a new tool for hypothesis testing. An e-value is a random variable with expected value less or equal to one under a null hypothesis. Large e-values give evidence against the null hypothesis, and the multiplicative inverse of an e-value is a p-value. Our test uses online isotonic regression to estimate the calibration curve as a ‘betting strategy’ against the null hypothesis. We show that the test has power against essentially all alternatives, which makes it theoretically superior to the HL test and at the same time resolves the well-known instability problem of the latter. A simulation study shows that a feasible version of the proposed eHL test can detect slight miscalibrations in practically relevant sample sizes, but trades its universal validity and power guarantees against a reduced empirical power compared to the HL test in a classical simulation setup. We illustrate our test on recalibrated predictions for credit card defaults during the Taiwan credit card crisis, where the classical HL test delivers equivocal results.

EXPLOITING THE MAIN BIASES IN AMERICAN SOCCER BETTING MARKETS.

In this paper the author will discuss the main inefficiencies in the 4 American major leagues of football (Argentina, Brazil, Mexico and USA), proposing a betting scheme, which outperforms the market with consistency over the past 9 Seasons (from 2012/2013 up to 2020/2021). Analysing the available data it was discovered how “Home advantage bias” and “Championship favourite advantage bias” play a big role in these championships and, by betting only on events, in which they were predicted favourable betting odds, it was possible to obtain an average return of +6.87% over 567 matches, using average bookmakers coefficients available on the market. The results are particularly significant, since, at least to our knowledge, there were no similar strategies available, which could guarantee such a big positive outcome for the leagues presented.

When Fortune Doesn’t Favor the Bold: Perils of Volatility for Wealth Growth and Preservation

Successful entrepreneurs and executives often hold much of their wealth in a highly appreciated single stock and thereby face a difficult financial dilemma. On the one hand, the high idiosyncratic volatility of a concentrated single stock position can lead to significant risk of catastrophic losses; on the other hand, selling the stock can result in an immediate and punitive tax burden. This article develops an analytical framework for evaluating this choice and explains how it relates to classic betting strategies and economic theory. For many investors, a full and immediate liquidation of their appreciated single stock might be optimal from the perspective of long-run wealth growth and preservation. In fact, in the absence of diversification, most investors must expect catastrophic losses of wealth over reasonable investment horizons. For investors reluctant to incur an upfront tax burden, tax-efficient techniques for disposing of an appreciated single stock might strike the balance between the urgency to diversify concentrated risk and aversion to taxes. Whereas for median and mode cumulative wealth, the primary effect likely comes from diversification, be it tax efficient or not, for mean cumulative wealth, the tax efficiency of diversification can yield a tangible improvement.

Home advantage in professional soccer and betting market efficiency: The role of spectator crowds

AbstractFan support has often been considered to be a main driver of the home advantage in sports. Using the “natural exper‐ iment” of ghost games during the COVID‐19 pandemic in German professional soccer and a dataset of 6,120 matches ranging over the seasons 2011/2012 to 2020/2021, we test this claim. Indeed, applying a difference‐in‐differences setup, we identify a reduction in the home performance ‐ though with much heterogeneity across leagues and teams. We, moreover, observe the home advantage to recover over time. In analysing whether betting markets anticipated this drop in the home advantage and its recovery, we test the efficient market hypothesis. In the short‐run, betting odds do not properly reflect the effect of ghost games regarding changes in the home advantage but they suitably account for it in the long‐run. Also, league heterogeneity is efficiently captured in the odds. Based on these findings, we show how simple, short‐run betting strategies could have exploited the discussed phenomenon. Our findings also have implications for agents' behavior on financial markets in the presence of unforeseen and unfamiliar shocks.

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.