The implied volatility of a sports game

Polson, Nicholas G.

doi:10.1515/jqas-2014-0095

Cited by 6 publications

(11 citation statements)

References 14 publications

(14 reference statements)

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“…29 Sports analytics have become a serious adjunct to many sports, with international conferences and publications. [39][40][41] Although analytics hold considerable promise for performance prediction there have been few attempts to use training monitoring for prediction purposes. Most attempts at prediction have relied on competition information and data to use in trend analyses.…”

Section: Training and Competition Monitoring To Predict Future Performentioning

confidence: 99%

Modern Techniques and Technologies Applied to Training and Performance Monitoring

Sands¹,

Kavanaugh²,

Murray³

et al. 2017

International Journal of Sports Physiology and Performance

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Athlete preparation and performance continue to increase in complexity and costs. Modern coaches are shifting from reliance on personal memory, experience, and opinion to evidence from collected training-load data. Training-load monitoring may hold vital information for developing systems of monitoring that follow the training process with such precision that both performance prediction and day-to-day management of training become adjuncts to preparation and performance. Time-series data collection and analyses in sport are still in their infancy, with considerable efforts being applied in "big data" analytics, models of the appropriate variables to monitor, and methods for doing so. Training monitoring has already garnered important applications but lacks a theoretical framework from which to develop further. As such, we propose a framework involving the following: analyses of individuals, trend analyses, rules-based analysis, and statistical process control.Keywords: time-series analysis, dose-response, statistical process control Training is a process and a historical sequence of events. As with all processes, whether biochemical, manufacturing, raising children, or others, these processes require some type of regulation and oversight. 1 The level of oversight is related to the complexity of the process and the potential cost of losing process control. 2 Complex processes tend to have more opportunities for error resulting in a deviation from the most desired path. 3 For example, game sports are unique events that involve dynamic interactions between players, and as a result the observed behavior of an athlete or team is influenced by a situation or opponent. 4 The "unstable" nature of game sports creates a challenge to quantify performance indicators. Statistical process control is one method used to identify stable performance traits. 4 Statistical process control uses normative profiles or the averages of variables from several games, as well as tolerance limits expressed in confidence intervals based on a mean and variance estimates, to determine "reliable" or typical indicators of performance. 5 Mathematical modeling, such as probability analysis, also has been used for estimating the impact of a single player on team performance, predicting future behavior and identifying optimal decision-making strategies. 6 Processes can operate along a continuum from deterministically controlled to utterly chaotic 7-9 with both sharing a potential for unexpected problems and considerable expense in terms of money and threats to life and health. 2,10 Historically, more effort has been expended in assessing the athlete as a system. However, the preparation and performance of an athlete can also be addressed as a system. When viewed from the perspective of dynamic systems, athletes are described as "non-ergodic, out of equilibrium systems, exploring larger and larger regions of the state space but eventually getting trapped within some relatively small set of the whole state space by the constraints of their sport disci...

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Section: Training and Competition Monitoring To Predict Future Performentioning

confidence: 99%

Modern Techniques and Technologies Applied to Training and Performance Monitoring

Sands¹,

Kavanaugh²,

Murray³

et al. 2017

International Journal of Sports Physiology and Performance

View full text Add to dashboard Cite

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“…Since the probabilities are tiny, we set them equal to 0. The sum of the possible probabilities is still larger than 1 (see Dixon and Coles (1997) and Polson and Stern (2015)). This "excess" probability corresponds to a quantity known as the "market vig."…”

Section: Market Calibrationmentioning

confidence: 99%

“…There is considerable interest in developing probability models for the evolution of the score of sporting events. Stern (1994) and Polson and Stern (2015) propose a continuous time Brownian motion model for the difference in scores in a sporting event and show how to calculate the implied volatility of a game. We build on their approach by using a difference of Poisson processes (a.k.a.…”

Section: Connections With Existing Workmentioning

confidence: 99%

“…Here {λ A t , λ B t } re-veal the market expectation of scoring difference for both teams from time t to the end of the game as the game progresses. Similar to the martingale approach ofPolson and Stern (2015), {λ A t , λ B t } reveal the best prediction of the game result. From another point of view, this approach is the same as assuming homogeneous rates for the rest of the game.An alternative approach to time-varying {λ A t , λ B t } is to use a Skellam regression with conditioning information such as possession percentages, shots (on goal), corner kicks, yellow cards, red…”

mentioning

confidence: 99%

See 1 more Smart Citation

The market for English Premier League (EPL) odds

Feng¹,

Polson²,

Xu³

2016

Journal of Quantitative Analysis in Sports

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This paper employs a Skellam process to represent real-time betting odds for English Premier League (EPL) soccer games. Given a matrix of market odds on all possible score outcomes, we estimate the expected scoring rates for each team. The expected scoring rates then define the implied volatility of an EPL game. As events in the game evolve, we re-estimate the expected scoring rates and our implied volatility measure to provide a dynamic representation of the market's expectation of the game outcome. Using a dataset of 1520 EPL games from 2012-2016, we show how our model calibrates well to the game outcome. We illustrate our methodology on real-time market odds data for a game between Everton and West Ham in the 2015-2016 season.We show how the implied volatility for the outcome evolves as goals, red cards, and corner kicks occur. Finally, we conclude with directions for future research.

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“…Η επιλογή του κατάλληλου τύπου της εκ των προτέρων κατανομής είναι μία δύσκολη διαδικασία. Τυπικά αυτές οι κατανομές προσδιορίζονται βασιζόμενες στη πληροφορία που συσωρεύται από προηγούμενες μελέτες (Boulier & Stekler, 1999) ή γνώμες ειδικών (Polson & Stern, 2015).…”

Section: μπεϋζιανή στατιστικήunclassified

Ανάπτυξη Και Εφαρμογή Μοντέλου Έκβασης Αγωνιστικών Επεισοδίων Στην Πετοσφαίριση Ανδρών

Δρίκος¹

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Η Πετοσφαίριση είναι παιχνίδι μηδενικού αθροίσματος, η αγωνιστική επιτυχία του οποίου εξαρτάται από το αποτέλεσμα της εκτέλεσης των τεχνικών δεξιοτήτων και των τακτικών επιλογών. Οι σταθερές διαδοχές των αγωνιστικών ενεργειών στην Πετοσφαίριση, μπορούν να χαρακτηρισθούν ως καταστάσεις ομογενούς μαρκοβιανής αλυσίδας και να περιγραφούν με τη δημιουργία μαρκοβιανού πίνακα μετάβασης. Με στόχο τον υπολογισμό των πιθανοτήτων μετάβασης και τη δημιουργία της εκ των υστέρων κατανομής έγινε παραδοχή πολυωνυμικής πιθανοφάνειας. Χρησιμοποιήθηκε συζυγής Dirichlet κατανομή για τη δημιουργία της εκ των προτέρων κατανομής με γνώμη ειδικών του αθλήματος και με συντελεστή 0.1. Για την τελική εκτίμηση των τεχνικών δεξιοτήτων και των τακτικών επιλογών από την εκ των υστερών κατανομή υπολογίστηκαν τα δεδομένα με τη χρήση εκτιμητή Monte Carlo με 10.000 επαναλήψεις. Η ανάλυση βασίστηκε στον προτεινόμενο από τον Fellingham δείκτη σπουδαιότητας (Importance Index). Η εφαρμογή του μοντέλου έκβασης αγωνιστικών επεισοδίων έγινε με δεδομένα από την ανάλυση της αγωνιστικής απόδοσης, των πρωταθλητριών εθνικών ομάδων Ανδρών, Εφήβων, Παίδων στις πρόσφατες αντίστοιχες παγκόσμιες διοργανώσεις. Το μοντέλο περιέγραψε με ακρίβεια τις πιθανές μεταβάσεις μέχρι την έκβαση των αγωνιστικών επεισοδίων. Τα ευρήματα της έρευνας έδειξαν ότι η σπουδαιότητα των τεχνικών δεξιοτήτων και τακτικών επιλογών δε διαφοροποιείται στις ηλικιακές κατηγορίες της Πετοσφαίρισης Ανδρών. Προκειμένου να εντοπισθούν σημαντικές δεξιότητες με περιορισμένο μέγεθος δείγματος προτάθηκε ως συμπληρωματικός του δείκτη σπουδαιότητας ο δείκτης ασυμμετρίας, λόγος ημιδιαφοράς ποσοστημορίων (QMR).

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The implied volatility of a sports game

Cited by 6 publications

References 14 publications

Modern Techniques and Technologies Applied to Training and Performance Monitoring

Modern Techniques and Technologies Applied to Training and Performance Monitoring

The market for English Premier League (EPL) odds

Ανάπτυξη Και Εφαρμογή Μοντέλου Έκβασης Αγωνιστικών Επεισοδίων Στην Πετοσφαίριση Ανδρών

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