Bettors' reaction to match dynamics -- Evidence from in-game betting

It is still largely unclear to what extent bettors update their prior assumptions about the strength and form of competing teams considering the dynamics during the match. This is of interest not only from the psychological perspective, but also as the pricing of live odds ideally should be driven both by the (objective) outcome probabilities and also the bettors' behaviour. Using state-space models (SSMs) to account for the dynamically evolving latent sentiment of the betting market, we analyse a unique high-frequency data set on stakes placed during the match. We find that stakes in the live-betting market are driven both by perceived pre-game strength and by in-game strength, the latter as measured by the Valuing Actions by Estimating Probabilities (VAEP) approach. Both effects vary over the course of the match

Mechanical performance of cold-curing epoxy adhesives after different mixing and curing procedures

This paper presents strength, stiffness, and porosity characteristics of commercially available cold-curing epoxy adhesives for structural engineering applications in the field of externally bonded and/or near-surface mounted composite strip reinforcements. Depending on specific requirements, accelerated curing of the adhesive under high temperatures might be necessary. Experimental investigations aimed at assessing the possible differences in strength and stiffness between samples cured at elevated temperatures for a defined time span and the ones cured at room temperature. It could be demonstrated that for the same specimen age, nominal tensile strength and stiffness are lower after an initial accelerated curing process at elevated temperatures. Furthermore, it could be shown that the specimens after an accelerated curing at elevated temperatures exhibited an increased porosity. The development of a numerical code for image analysis allowed a detailed inspection of several fracture surfaces and subsequently to assess the level of decrease in available cross-section due to an increased overall porosity. Cross-section area losses in the range of 10–15% compared to the reference specimens could be deduced. The subsequent derivation of the actual tensile strength exhibits smaller differences between the room and high temperature exposed specimens while curing. Regardless of the short-term material strength, the observed porosity might be subject of important durability issues on a long-term and needs further investigation.FEDER funds through the Operational Program for Competitiveness Factors - COMPETE and National Funds through FCT - Portuguese Foundation for Science and Technology under the projects FRPreDur FCOMP- 01-0124-FEDER-028865 (FCT no. PTDC/ECM-EST/2424/2012)The authors want to express their gratitude to Max Heusser and Milos Dimic (Empa, CH) for their assistance in the experimental investigation. Marcel Rees, Iurii Burda and Andrea Battisti (Empa, CH) are kindly acknowledged for their assistance with the vacuum mixer and the sample preparation for porosity assessment. Eventually, Esther Strub (Empa, CH) is acknowledged for the instructions about the miscroscope utilization. Distributors S&P Clever Reinforcement AG (CH) and Sika (CH) are also acknowledged for their material provision. This work is also supported by FEDER funds through the Operational Program for Competitiveness Factors - COMPETE and National Funds through FCT - Portuguese Foundation for Science and Technology under the projects FRPreDur FCOMP- 01-0124-FEDER-028865 (FCT no. PTDC/ECM-EST/2424/2012)

Markov-switching decision trees

Adam T, Ötting M, Michels R. Markov-switching decision trees. AStA Advances in Statistical Analysis. 2024.**Abstract** Decision trees constitute a simple yet powerful and interpretable machine learning tool. While tree-based methods are designed only for cross-sectional data, we propose an approach that combines decision trees with time series modeling and thereby bridges the gap between machine learning and statistics. In particular, we combine decision trees with hidden Markov models where, for any time point, an underlying (hidden) Markov chain selects the tree that generates the corresponding observation. We propose an estimation approach that is based on the expectation-maximisation algorithm and assess its feasibility in simulation experiments. In our real-data application, we use eight seasons of National Football League (NFL) data to predict play calls conditional on covariates, such as the current quarter and the score, where the model’s states can be linked to the teams’ strategies. R code that implements the proposed method is available on GitHub

fHMM: fitting hidden Markov models to financial data (R package)

Oelschläger L, Adam T, Michels R. fHMM: fitting hidden Markov models to financial data (R package). CRAN; 2021

Bettors’ reaction to match dynamics: Evidence from in-game betting

Michels R, Ötting M, Langrock R. Bettors’ reaction to match dynamics: Evidence from in-game betting. European Journal of Operational Research. In Press.It is still largely unclear to what extent bettors update their prior assumptions about the strength and form of competing teams considering the dynamics during the match. This is of interest not only from the psychological perspective, but also as the pricing of live odds ideally should be driven both by the (objective) outcome probabilities and also the bettors’ behaviour. Using state-space models (SSMs) to account for the dynamically evolving latent sentiment of the betting market, we analyse a unique high-frequency data set on stakes placed during the match. We find that stakes in the live-betting market are driven both by perceived pre-game strength and by in-game strength, the latter as measured by the Valuing Actions by Estimating Probabilities (VAEP) approach. Both effects vary over the course of the match

fHMM: Hidden Markov Models for Financial Time Series in R

Oelschläger L, Adam T, Michels R. fHMM: Hidden Markov Models for Financial Time Series in R. Journal of Statistical Software . 2024;109(9):1-25.Hidden Markov models constitute a versatile class of statistical models for time series that are driven by hidden states. In financial applications, the hidden states can often be linked to market regimes such as bearish and bullish markets or recessions and periods of economics growth. To give an example, when the market is in a nervous state, corresponding stock returns often follow some distribution with relatively high variance, whereas calm periods are often characterized by a different distribution with relatively smaller variance. Hidden Markov models can be used to explicitly model the distribution of the observations conditional on the hidden states and the transitions between states, and thus help us to draw a comprehensive picture of market behavior. While various implementations of hidden Markov models are available, a comprehensive R package that is tailored to financial applications is still lacking. In this paper, we introduce the R package fHMM, which provides various tools for applying hidden Markov models to financial time series. It contains functions for fitting hidden Markov models to data, conducting simulation experiments, and decoding the hidden state sequence. Furthermore, functions for model checking, model selection, and state prediction are provided. In addition to basic hidden Markov models, hierarchical hidden Markov models are implemented, which can be used to jointly model multiple data streams that were observed at different temporal resolutions. The aim of the fHMM package is to give R users with an interest in financial applications access to hidden Markov models and their extensions

Demand for live betting: An analysis using state‐space models

Ötting M, Michels R, Langrock R, Deutscher C. Demand for live betting: An analysis using state‐space models. Applied Stochastic Models in Business and Industry. 2024.Sports betting markets have grown very rapidly recently, with the total European gambling market worth 98.6 billion euro in 2019. Considering a high‐resolution (1 Hz) data set provided by a large European bookmaker, we investigate the demand for bet placements during matches and in particular the effect of news. Accounting for the general market activity level within a state‐space modelling framework, we analyse the market's response to events such as goals (i.e., major news). Our results indicate that markets strongly react to news, but other factors, such as the day of the week and the uncertainty of outcome, also affect the stakes placed. We thus provide insights into the behaviour of bettors during matches, which can be relevant for bookmakers, for example to predict future revenues, but also for more specialised tasks such as fraud detection

Patterns of betting behavior for news in live betting markets

Deutscher C, Michels R, Ötting M, Langrock R. Patterns of betting behavior for news in live betting markets. In: Deutscher C, Wicker P, eds. 12th ESEA Conference on Sport Economics – Book of Abstracts. 2021: 33-35

State-switching decision trees

Adam T, Ötting M, Michels R. State-switching decision trees. In: Bergherr E, Groll A, Mayr A, eds. Proceedings of the 37th International Workshop on Statistical Modelling. Part II. Dortmund: TU Dortmund; 2023: 321-325

Quantitative Signal Intensity in Fluid-Attenuated Inversion Recovery and Treatment Effect in the WAKE-UP Trial

International audienceBackground and Purpose— Relative signal intensity of acute ischemic stroke lesions in fluid-attenuated inversion recovery (fluid-attenuated inversion recovery relative signal intensity [FLAIR-rSI]) magnetic resonance imaging is associated with time elapsed since stroke onset with higher intensities signifying longer time intervals. In the randomized controlled WAKE-UP trial (Efficacy and Safety of MRI-Based Thrombolysis in Wake-Up Stroke Trial), intravenous alteplase was effective in patients with unknown onset stroke selected by visual assessment of diffusion weighted imaging fluid-attenuated inversion recovery mismatch, that is, in those with no marked fluid-attenuated inversion recovery hyperintensity in the region of the acute diffusion weighted imaging lesion. In this post hoc analysis, we investigated whether quantitatively measured FLAIR-rSI modifies treatment effect of intravenous alteplase. Methods— FLAIR-rSI of stroke lesions was measured relative to signal intensity in a mirrored region in the contralesional hemisphere. The relationship between FLAIR-rSI and treatment effect on functional outcome assessed by the modified Rankin Scale (mRS) after 90 days was analyzed by binary logistic regression using different end points, that is, favorable outcome defined as mRS score of 0 to 1, independent outcome defined as mRS score of 0 to 2, ordinal analysis of mRS scores (shift analysis). All models were adjusted for National Institutes of Health Stroke Scale at symptom onset and stroke lesion volume. Results— FLAIR-rSI was successfully quantified in stroke lesions in 433 patients (86% of 503 patients included in WAKE-UP). Mean FLAIR-rSI was 1.06 (SD, 0.09). Interaction of FLAIR-rSI and treatment effect was not significant for mRS score of 0 to 1 ( P =0.169) and shift analysis ( P =0.086) but reached significance for mRS score of 0 to 2 ( P =0.004). We observed a smooth continuing trend of decreasing treatment effects in relation to clinical end points with increasing FLAIR-rSI. Conclusions— In patients in whom no marked parenchymal fluid-attenuated inversion recovery hyperintensity was detected by visual judgement in the WAKE-UP trial, higher FLAIR-rSI of diffusion weighted imaging lesions was associated with decreased treatment effects of intravenous thrombolysis. This parallels the known association of treatment effect and elapsing time of stroke onset