Probability Of Winning Research Articles

0174 Examining Circadian Disadvantages in the National Basketball Association’s Playoffs

Abstract Introduction Prior research on travel in the National Basketball Association’s (NBA) regular season has shown that teams journeying west relative to their home base face circadian disadvantages for evening games, while those traveling east have advantages. The current study extends previous research by examining these effects within the NBA playoffs. We hypothesized that teams would have a greater circadian advantage during eastward compared to westward travel. Methods In 2013, the NBA implemented a 7-game series playoff structure, in which teams play an alternating home/away 2-2-1-1-1 format. Data for all 499 postseason games played during the 2013–14 to 2018–2019 seasons were collected from Basketball-Reference and FiveThirtyEight. We investigated the impact of direction of travel based on home base city (same time zone, westward, eastward) and time zones traveled on game outcomes, Elo rating differences (i.e., a team quality metric based on wins and losses), win probability, and team scoring. Results Teams had lower win probabilities following 3-hour westward than same time zone and all eastward travel, while 3-hour eastward travel related to higher probabilities of winning compared to same time and all westward travel (p < .001, d > .95). Teams travelling westward with 2-hour time changes lost significantly more games than those experiencing 1-hour westward (p = .04, OR = 2.45), 1-hour eastward (p = .05, OR = 2.34), and 3-hour eastward changes (p = .02, OR = 4.68). Scoring was significantly higher following eastward travel compared to both westward (p = .001, d = 0.60) and same time zone travel (p = .003, d = 0.44). There were no differences in team quality based on direction of travel or number of time zones traveled, and game outcomes based on overall direction of travel (p > .05). Conclusion Direction and magnitude of travel were related to win probability, team scoring, and game outcomes, whereby teams travelling eastward and within the same time zone gained an advantage over those travelling westward. Adjustment to travel and time changes appear to influence in-game performances and outcomes in the NBA playoffs. Support None

A direct and conceptual replication of post-loss speeding when gambling.

To investigate the response to suboptimal outcomes, Verbuggen et al. (Verbruggen F, Chambers CD, Lawrence NS, McLaren IPL. 2017 Winning and losing: effects on impulsive action. J. Exp. Psychol.: Hum. Percept. Perform. 43, 147. (doi:10.1037/xhp0000284)) conducted a study in which participants chose between a gamble and a non-gamble option. The non-gamble option was a guaranteed amount of points, whereas the gamble option was associated with a higher amount but a lower probability of winning. The authors observed that participants initiated the next trial faster after a loss compared to wins or non-gambles. In the present study, we directly replicated these findings in the laboratory and online. We also designed another task controlling for the number of trials per outcome. In this task, participants guessed where a reward was hidden. They won points if they selected the correct location, but lost points if they selected the incorrect location. We included neutral trials as a baseline. Again, participants sped up after a loss relative to wins and neutral trials (but only with a response choice in neutral trials and a large sample size). These findings appear inconsistent with cognitive-control frameworks, which assume that suboptimal outcomes typically lead to slower responses; instead, they suggest that suboptimal outcomes can invigorate behaviour, consistent with accounts of frustrative non-reward and impulsive action.

Interface predictability changes betting behavior in computerized gambling

Recent development in human-computer interfaces (HCIs) including electronic gaming machines and online gambling has exposed novices to the risks of gambling-related harm. Interface characteristics not only reflect the structure of the game, they also shape users' sense of agency concerning their gambling. Although studies have indicated the importance of causal attribution in risky gambling, the roles of the sense of agency and its largest factor, predictability, remains unclear. Therefore, we assessed the impact of interface predictability on gambling tendencies. Participants played a computerized card-guessing game on two interfaces with distinct visual feedback predictability related to users' card choice operation (i.e., the consistency between the direction of mouse motion and cards). Between these interfaces, we compared participants’ subjective estimation of win probability and their wager history in each trial. Their subjective win probability did not differ between conditions. Intriguingly, participants only decreased their wagers following a loss when the interface was predictable, but not when it was unpredictable. Moreover, the effects of predictability of a “winning run” depended on individual difference in illusory control. This study provides evidence that feeling of agency mediates the impact of interface features on gambling. This may contribute to interface design for a healthy gambling experience.

How people vote in contests: new findings from Immortal Songs 2

Many important contests, such as job interviews and political debates, are presented in sequential order. Previous studies found serial position effects such that the later presenter has a higher probability of winning. However, no previous studies use both random assignments of contestants and a large number of contestants and judges. We use Immortal Songs 2, a popular TV program that satisfies both conditions, to confirm the findings of serial position effects. In addition, Immortal Songs 2 has round-by-round competition rules. The first round is a competition between the first and second contestants. Then, the winner of the first round is announced. The second round is a contest between the winner of the first round and the third contestant. As the rounds continue, in theory, the winner of the previous round should have a higher probability of winning; however, in fact, the second contestant’s probability of winning is always 0.5.

Virile crayfish escalate aggression according to body size instead of weapon size

Many crustaceans use their large claws to signal fighting ability during territorial contests. However, the size of a claw does not always reflect its strength or the bearer's ability to fight. If strength predicts the outcome of a fight, the mismatch between the size and strength of a claw creates dishonest signalling. Still, only a handful of species have been studied, leaving a gap in our knowledge of the taxonomic diversity and evolutionary history of dishonest signalling. To help fill this gap, we studied signalling and fighting between virile crayfish, Faxonius virilis. First, we measured the relationship between the size and strength of a claw in males and females. Then, we staged encounters between members of the same sex to determine how carapace length, claw size and claw strength influence the probability of fighting and the probability of winning. Both males and females possessed claws whose size poorly predicted their strength, especially at larger sizes. Unlike other species, which escalate aggression based on claw size, virile crayfish escalated aggression based on relative body size. When fighting occurred, however, both body size and claw strength determined the winner. Likely, virile crayfish ignore claw size because body size provides a more reliable signal of dominance. Our results stress the importance of observing behavioural dynamics in addition to functional relationships when studying the potential for dishonest signalling.

Weighted Games of Best Choice

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings is uniformly distributed. Given a statistic on the symmetric group, one can instead weight each permutation according to an exponential function in the statistic. We play the game of best choice on the Ewens and Mallows distributions that are obtained in this way from the number of left-to-right maxima and number of inversions in the permutation, respectively. For each of these, we give the optimal strategy and probability of winning. Moreover, we introduce a general class of permutation statistics that always produces games of best choice whose optimal strategies are positional, which simplifies their analysis considerably.

Win Probability for Volleyball estimated by service and points

Win Probability for Volleyball estimated by service and points

Revenue Management of a Professional Services Firm Under a Quality-Revelation Model

Professional service firms (PSFs) such as management consulting, law, accounting, investment banking, architecture, advertising and home-repair companies provide services for turnkey complicated projects. The operational tasks of such firms consists of first bidding for the project and, if successful in the bid, assigning employee resources to the project. In this paper we model this as a revenue management problem and develop a stochastic dynamic programming framework to aid the firm in their bidding and assignment process. We study this primarily under a quality-revelation model where the employees that would be assigned to the project are committed ex ante, as part of the bid. The win probability depends on the quoted price as well as the quality of the employees who would work on the project. We also consider a quality-reputation model where the bid’s win probability depends on past performance, say an average of the quality of past jobs. The problem is computationally challenging and we provide a series of bounds and solution methods to approximate the stochastic dynamic program. Based on our computational techniques we are able to address a number of interesting questions on utilization and the value of each employee type for a PSF. Our methodology provides management a toolkit for bidding on projects as well as to perform workforce analytics to determine optimal utilization levels and staffing decisions.

How the Republic of Venice chose its Doge: lot-based elections and supermajority rule

We study a family of voting rules inspired by the peculiar protocol used for over 500 years by the Republic of Venice to elect its Doge. Lot-based indirect elections have two main features: a pool of delegates is chosen by lot out of a general assembly, and then they vote in a single winner election with qualified majority. Under the assumption that the assembly is divided into two factions, we characterise the win probability of the minority and show that these features promote a more equitable allocation of political representation, striking a balance between protecting the minority and giving proper recognition to the majority. We then consider this family of voting procedures from a constitutional perspective: we analyse how the electoral result varies with the college size and the winning threshold in order to understand how these two parameters can be tuned when drawing up electoral law. We find that minorities are better off with larger majority thresholds. The role of the college size, on the other hand, is ambiguous: a smaller college size offers more protection to sparse minorities; for more sizeable ones, it depends instead on the qualified majority required for the election.

How the Republic of Venice Chose Its Doge: Lot-Based Elections and Supermajority Rule

We study a family of voting rules inspired by the peculiar protocol used for over 500 years by the Republic of Venice to elect its Doge. Such lot-based indirect elections have two main features: a pool of delegates is chosen by lot out of a general assembly, and then they vote in a single winner election with qualified majority. Under the assumption that the assembly is divided in two factions, we characterise the win probability of the minority and study how it varies with the electoral college size and the winning threshold. We argue that these features promoted a more equitable allocation of political representation and thus may have contributed to the political stability of the Republic of Venice.

Advanced Baseball Metrics Indicate Significant Decline in MLB Pitcher Value After Tommy John Surgery.

There are conflicting reports regarding the efficacy of Major League Baseball (MLB) pitchers following medial ulnar collateral ligament reconstruction (UCLR). As advanced baseball metrics have revolutionized the way general managers define pitchers' value, the authors believe that these should be used to measure clinical outcomes after UCLR. All MLB pitchers who underwent UCLR from April 1, 1991, through July 1, 2016, were compiled (N=253). Pitcher demographics and statistics were collected for up to 3 full seasons preceding and following surgery. Data for pitching controls (all MLB [AMLB] pitchers) were also collected (N=14,756). Prior to surgery, pitchers with UCLR were significantly better than the AMLB pitchers in nearly all advanced value-based statistics: higher wins above replacement (WAR; 0.93 vs 0.78; 95% confidence interval [CI], 0.80-1.06), lower fielding independent pitching (FIP; 4.23 vs 4.51; 95% CI, 4.12-4.34), lower expected fielding independent pitching (xFIP; 4.17 vs 4.38; 95% CI, 4.06-4.28), higher win probability added (WPA; 0.21 vs 0.05; 95% CI, 0.1-0.32), and higher leverage index (pLI; 1.03 vs 0.96; 95% CI, 0.99-1.06). Pitchers who returned to play after UCLR demonstrated significantly lower value with worse WAR, FIP, WPA, and pLI (P<.05). Conversely, after excluding pitchers who failed to achieve a sustained return to play of greater than 1 year, there were no significant decreases in value after surgery. The authors conclude that, prior to injury, pitchers who have UCLR are more valuable than average MLB pitchers. However, UCLR pitchers perform worse when compared with their presurgical values. This may be affected by players not being able to continue their careers for more than 1 year. [Orthopedics. 2019; 42(6):349-354.].

Offensive or defensive play in soccer: a game-theoretical approach

Abstract In many sports, such as soccer, a coach has to decide whether to adopt an “offensive” or a “defensive” approach to a match. This strategic decision depends on the strengths and weaknesses of his team with respect to the opponent, but also on the strategy chosen by the opponent’s coach. The fact that a draw also results in a point, which may be important for the ranking, further complicates this decision, as the coach must assess whether it is better to adopt a defensive team formation in order to obtain a draw, or to aim for victory despite the increased risk of defeat. We study this topic by means of a game-theoretical approach, and we develop an algorithm which allows to compute the optimal strategy. The algorithm tests the stability of the outcome with respect to uncertainty in the estimated win probabilities. Furthermore, our approach can handle in-game events, which may provoke changes in optimal strategy. Finally, our model also allows us to assess the effect of various point systems on the willingness of teams to opt for attacking play. Our method is applied to a case study, based on the match Italy – Costa Rica (World Cup 2014).

Do Tournaments With Superstars Encourage or Discourage Competition?

To test and replicate the superstar effect reported by Brown, we empirically study contests where a single entrant has an exogenously higher probability of winning. Unlike the previous literature, we test for the presence of the superstar effect in several new contexts. Ultimately, we collect and explore data from four sources: men’s and women’s professional golf, and men’s and women’s professional alpine skiing. Empirically, we find little robust evidence of the superstar effect in any of our data sets. In our replication exercise, we approximate the findings of Brown; however, we cannot reject the null that the presence of a superstar has no impact on high ranked competitors. In our new settings, we cannot reject the null that superstars have no influence on the performances of highly ranked competitors.

Dynamic Risk Profiling Using Serial Tumor Biomarkers for Personalized Outcome Prediction

Accurate prediction of long-term outcomes remains a challenge in the care of cancer patients. Due to the difficulty of serial tumor sampling, previous prediction tools have focused on pretreatment factors. However, emerging non-invasive diagnostics have increased opportunities for serial tumor assessments. We describe the Continuous Individualized Risk Index (CIRI), a method to dynamically determine outcome probabilities for individual patients utilizing risk predictors acquired over time. Similar to "win probability" models in other fields, CIRI provides a real-time probability by integrating risk assessments throughout a patient's course. Applying CIRI to patients with diffuse large B cell lymphoma, we demonstrate improved outcome prediction compared to conventional risk models. We demonstrate CIRI's broader utility in analogous models of chronic lymphocytic leukemia and breast adenocarcinoma and perform a proof-of-concept analysis demonstrating how CIRI could be used to develop predictive biomarkers for therapy selection. We envision thatdynamic risk assessment will facilitate personalized medicine and enable innovative therapeutic paradigms.

The impact of hypocrisy on opinion formation: A dynamic model.

Humans have a demonstrated tendency to copy or imitate the behavior and attitude of others and actively influence each other’s opinions. In plenty of empirical contexts, publicly revealed opinions are not necessarily in line with internal opinions, causing complex social influence dynamics. We study to what extent hypocrisy is sustained during opinion formation and how hidden opinions change the convergence to consensus in a group. We build and analyze a modified version of the voter model with hypocrisy in a complete graph with a neutral competition between two alternatives. We compare the process from various initial conditions, varying the proportions between the two opinions in the external (revealed) and internal (hidden) layer. According to our results, hypocrisy always prolongs the time needed for reaching a consensus. In a complete graph, this time span increases linearly with group size. We find that the group-level opinion emerges in two steps: (1) a fast and directional process, during which the number of the two kinds of hypocrites equalizes; and (2) a slower, random drift of opinions. During stage (2), the ratio of opinions in the external layer is approximately equal to the ratio in the internal layer; that is, the hidden opinions do not differ significantly from the revealed ones at the group level. We furthermore find that the initial abundances of opinions, but not the initial prevalence of hypocrisy, predicts the mean consensus time and determines the opinions’ probabilities of winning. These insights highlight the unimportance of hypocrisy in consensus formation under neutral conditions. Our results have important societal implications in relation to hidden voter preferences in polls and improve our understanding of opinion formation in a more realistic setting than that of conventional voter models.

Competitive balance with unbalanced schedules

Abstract Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.

Counting Your Chickens With Markov Chains

SummaryWe use Markov chains to analyze the cooperative children’s game, Count Your Chickens!. Similar to Chutes and Ladders or Monopoly, this game involves movement of a token on a game board in which the movement is determined by pure chance. We use Markov chains to determine the win probability for the game and the win probability for variants of the game in which we change the structure of the underlying game board.

Automatic Generation of Baseball Game Digest by Using Win Probability Added

Automatic Generation of Baseball Game Digest by Using Win Probability Added

Positional strategies in games of best choice

We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe the optimal positional strategies and develop formulas for the probability of winning.

NflWAR: a reproducible method for offensive player evaluation in football

AbstractExisting methods for player evaluation in American football rely heavily on proprietary data, are often not reproducible, lag behind those of other major sports, and are not interpretable in terms of game outcomes. We present four contributions to the study of football statistics to address these issues. First, we develop the R package nflscrapR to provide easy access to publicly available play-by-play data from the National Football League (NFL). Second, we introduce a novel multinomial logistic regression approach for estimating the expected points for each play. Third, we use the expected points as input into a generalized additive model for estimating the win probability for each play. Fourth, we introduce our nflWAR framework, using multilevel models to isolate the contributions of individual offensive skill players in terms of their wins above replacement (WAR). We assess the uncertainty in WAR through a resampling approach specifically designed for football, and we present results for the 2017 NFL season. We discuss how our reproducible WAR framework can be extended to estimate WAR for players at any position if researchers have data specifying the players on the field during each play. Finally, we discuss the potential implications of this work for NFL teams.