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Adversarial Risk Analysis for Decision-Making in Sports.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Adversarial Risk Analysis for Decision-Making in Sports./
作者:	Luxenberg, Samuel.
面頁冊數:	1 online resource (287 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-07, Section: A.
Contained By:	Dissertations Abstracts International84-07A.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29998492click for full text (PQDT)
ISBN:	9798368437521

Adversarial Risk Analysis for Decision-Making in Sports.
Luxenberg, Samuel.

Adversarial Risk Analysis for Decision-Making in Sports. - 1 online resource (287 pages)

Source: Dissertations Abstracts International, Volume: 84-07, Section: A.

Thesis (Ph.D.)--The George Washington University, 2023.

Includes bibliographical references

Decision-making in the presence of intelligent adversaries is all around us. Whether we are determining our optimal bid for a valuable auction item, devising a counter strategy for potential terrorist or cybersecurity threats, setting an optimal spending strategy for advertising in increasingly competitive markets, or optimizing coaching and playing strategy in sports, the decision makers in each scenario should account for the opponent's decision-making process. Traditionally, these kinds of strategic interactions are studied using techniques from game theory. However, game-theoretic models come with several disadvantages and have been criticized for a number of reasons (Rios Insua et al., 2009, Banks et al., 2016, 2022). To address many of these issues, Rios Insua et al. (2009) introduced a new decision framework called Bayesian adversarial risk analysis (ARA), a Bayesian alternative to game theory. Ultimately, ARA provides the decision maker with explicit methods for eliciting subjective probabilities over an opponent's actions. This collection of methods helps the decision maker to think about how her opponent makes decisions and to account for any relevant uncertainties she may have. In this dissertation, we develop the first applications of ARA to decision-making in sports.We focus on three distinct decision problems that occur in sports. First, we examine penalty kicks in soccer where a kicker and goalie simultaneously decide where to kick and dive, respectively. We compare both the decision process and the outputs of the traditionally-used game-theoretic model with various ARA models. We test our models on penalty kick data from Major League Soccer (MLS) during the 2018 and 2019 seasons. We find that while the game-theoretic solution is able to predict penalty kick decisions at the aggregate level with high accuracy, the ARA solutions are more practical for implementing, analyzing, and predicting decisions at the individual level. To determine which decision model is best against different types of opponents, we built a simulation for the different models of kickers and goalies to face off against each other for 500 penalty kicks. We found that game-theoretic decision makers typically perform the best only against other game-theoretic decision makers. Against other types of opponents, several of the ARA models tend to perform best. All of this seems to suggest that perhaps game theory should not be the go-to model for penalty kick decisions.Second, we study the optimal lineups problem in basketball in which two opposing coaches need to decide who to put in the game to make the most of the next possession. We consider both a simultaneous setup, where the two coaches make lineup decisions at the same time, and a sequential setup where one coach makes a decision, the second coach observes this decision, and then the second coach makes his own decision. We again compare game-theoretic and ARA solutions for this problem; however, here, we incorporate an extra layer of statistical learning. We input a Bayesian logistic regression directly into our decision frameworks to learn how well individual players are performing in the current matchup. We apply our models to a particular moment in a real National Basketball Association (NBA) game and find that while the game-theoretic and ARA solutions both output the same optimal lineup for the supported decision maker, the predictions of the opponent lineups are quite different. In fact, the game-theoretic predictions appear to be the most unrealistic of all.Finally, we propose a new set of decision problems that aim to find optimal team intensity or effort levels throughout a basketball matchup. In contrast to the previous two decision problems considered in this dissertation, this problem, known as a stochastic differential game, has a continuous-time setup. In such a game, opposing coaches compute their end-game expected utility subject to the evolution of quantities like the score differential throughout the match. Based on the ideas of Stern (1994), we model these quantities as an Ito process. Because stochastic differential games can be seen as an extension of stochastic optimal control theory, analytical solutions can be found only for a small selection of problems, typically using the so-called Verification Theorem. To keep our analysis as mathematically tractable as possible, the games we propose are simplistic in nature so that we can still find analytical solutions. To develop ARA solutions for such problems, we extend ARA methodology to incorporate the Verification Theorem while modeling a variety of uncertainties regarding the opponent's decision problem. We compute both game-theoretic and ARA solutions for each problem and then illustrate these solutions for two hypothetical NBA matchups. We hope that these differential games serve as a template or starting point for future and more realistic analyses in team sports using stochastic optimal control techniques.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798368437521Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Adversarial risk analysisIndex Terms--Genre/Form:

542853
Electronic books.

Adversarial Risk Analysis for Decision-Making in Sports.
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520 $a Decision-making in the presence of intelligent adversaries is all around us. Whether we are determining our optimal bid for a valuable auction item, devising a counter strategy for potential terrorist or cybersecurity threats, setting an optimal spending strategy for advertising in increasingly competitive markets, or optimizing coaching and playing strategy in sports, the decision makers in each scenario should account for the opponent's decision-making process. Traditionally, these kinds of strategic interactions are studied using techniques from game theory. However, game-theoretic models come with several disadvantages and have been criticized for a number of reasons (Rios Insua et al., 2009, Banks et al., 2016, 2022). To address many of these issues, Rios Insua et al. (2009) introduced a new decision framework called Bayesian adversarial risk analysis (ARA), a Bayesian alternative to game theory. Ultimately, ARA provides the decision maker with explicit methods for eliciting subjective probabilities over an opponent's actions. This collection of methods helps the decision maker to think about how her opponent makes decisions and to account for any relevant uncertainties she may have. In this dissertation, we develop the first applications of ARA to decision-making in sports.We focus on three distinct decision problems that occur in sports. First, we examine penalty kicks in soccer where a kicker and goalie simultaneously decide where to kick and dive, respectively. We compare both the decision process and the outputs of the traditionally-used game-theoretic model with various ARA models. We test our models on penalty kick data from Major League Soccer (MLS) during the 2018 and 2019 seasons. We find that while the game-theoretic solution is able to predict penalty kick decisions at the aggregate level with high accuracy, the ARA solutions are more practical for implementing, analyzing, and predicting decisions at the individual level. To determine which decision model is best against different types of opponents, we built a simulation for the different models of kickers and goalies to face off against each other for 500 penalty kicks. We found that game-theoretic decision makers typically perform the best only against other game-theoretic decision makers. Against other types of opponents, several of the ARA models tend to perform best. All of this seems to suggest that perhaps game theory should not be the go-to model for penalty kick decisions.Second, we study the optimal lineups problem in basketball in which two opposing coaches need to decide who to put in the game to make the most of the next possession. We consider both a simultaneous setup, where the two coaches make lineup decisions at the same time, and a sequential setup where one coach makes a decision, the second coach observes this decision, and then the second coach makes his own decision. We again compare game-theoretic and ARA solutions for this problem; however, here, we incorporate an extra layer of statistical learning. We input a Bayesian logistic regression directly into our decision frameworks to learn how well individual players are performing in the current matchup. We apply our models to a particular moment in a real National Basketball Association (NBA) game and find that while the game-theoretic and ARA solutions both output the same optimal lineup for the supported decision maker, the predictions of the opponent lineups are quite different. In fact, the game-theoretic predictions appear to be the most unrealistic of all.Finally, we propose a new set of decision problems that aim to find optimal team intensity or effort levels throughout a basketball matchup. In contrast to the previous two decision problems considered in this dissertation, this problem, known as a stochastic differential game, has a continuous-time setup. In such a game, opposing coaches compute their end-game expected utility subject to the evolution of quantities like the score differential throughout the match. Based on the ideas of Stern (1994), we model these quantities as an Ito process. Because stochastic differential games can be seen as an extension of stochastic optimal control theory, analytical solutions can be found only for a small selection of problems, typically using the so-called Verification Theorem. To keep our analysis as mathematically tractable as possible, the games we propose are simplistic in nature so that we can still find analytical solutions. To develop ARA solutions for such problems, we extend ARA methodology to incorporate the Verification Theorem while modeling a variety of uncertainties regarding the opponent's decision problem. We compute both game-theoretic and ARA solutions for each problem and then illustrate these solutions for two hypothetical NBA matchups. We hope that these differential games serve as a template or starting point for future and more realistic analyses in team sports using stochastic optimal control techniques.
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538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 517247
650 4 $a Sports management. $3 3423935
653 $a Adversarial risk analysis
653 $a Bayesian analysis
653 $a Differential games
653 $a Game theory
653 $a Optimal control theory
653 $a Sports analytics
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710 2 $a The George Washington University. $b Statistics. $3 1272926
773 0 $t Dissertations Abstracts International $g 84-07A.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29998492 $z click for full text (PQDT)