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This paper develops a simulator for matches in the National Hockey League with the intent of assessing strategies for pulling the goaltender. Aspects of the approach that are novel include breaking the game down into ner and more realistic situations, introducing the eect of penalties and including the home-ice advantage. Parameter estimates used i...
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... respect to scenario D (see Table 7), if we assume that Patrick Roy's intention was to pull his goalie not only during the 5-on-3 situation, but also for the 5-on-4 ensuing power-play, then his game plan corresponds to strategy 2. Indeed, it seems logical that if a coach decides to pull his goalie in power-play situations when trailing by 3 goals with 12 minutes left, then he is willing to do so with any lesser amount of time left. ...
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Citations
... The hope is to score a quick goal to get back in the game, but the risk is falling further behind. Beaudoin and Swartz (2010) show that NHL coaches do not always employ the optimal strategies, usually by waiting too long to pull their goalies. Skinner (2011) develops a general framework for these desperation strategies, which include the onside kick in American football, pulling the infield and/or outfield in baseball, and of course, the fabled Hack-a-Shaq strategy in basketball. ...
Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this paper, we connect four big ideas that are common across multiple sports: the expected value of a game state, win probability, measures of team strength, and the use of sports betting market data. For each, we explore both the shared similarities and individual idiosyncrasies of analytical approaches in each sport. While our focus is on the concepts underlying each type of analysis, any implementation necessarily involves statistical methodologies, computational tools, and data sources. Where appropriate, we outline how data, models, tools, and knowledge of the sport combine to generate actionable insights. We also describe opportunities to share analytical work, but omit an in-depth discussion of individual player evaluation as beyond our scope. This paper should serve as a useful overview for anyone becoming interested in the study of sports analytics.
... In water polo winners shot more time than losers when they have an extra man (Escalante et al., 2011); goals achieved by the winner teams in water polo were considerably more as compared to the ones of the loser team (Platanou, 2004) and a statistic significant difference between winners and losers was found in all the coefficient of performance in teams with an extra man (Argudo, Ruiz, & Abraldes, 2010). In ice hockey, winners have better performance than losers while being in power play (5x4 and 5x3) even pulling the goalie out (Beaudoin & Swartz, 2010). Gutierrez et al., (2010) in their study of European and World Handball Championship between 2002 and 2004 found out that during inferiority situations losers present worst performance than winners. ...
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... Advanced statistics and player valuation metrics are applicable to expansion draft optimization since they can serve as coefficients in the model representating the "value" of the players. While there has been much work on in-game decision making in hockey, such as the rich literature on pulling the goalie (e.g., Washburn (1991), Beaudoin and Swartz (2010)), there has been less focus on research related to team management decisions. ...
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... The study was more concerned with theories of criminology than the game itself. In contrast, Beaudoin and Swartz (2010) developed a simulator for NHL matches where their main focus was the timing involved in "pulling the goaltender". In a side comment (Remark #2), they noted that road teams are called for more penalties than home teams in a 11:10 ratio. ...
... x 1 = 0, x 2 = 0, x 3 = 30 and x 4 = 0), the probability that the next penalty is called on the home team isp = 0.47. This estimate agrees with Remark #2 from Beaudoin and Swartz (2010) which notes that penalties are called on the road team in a 11:10 ratio (i.e. ...
This paper investigates penalty calls in the National Hockey League (NHL). Our study shows that there are various situational effects that are associated with the next penalty call. These situational effects are related to the accumulated penalty calls, the goal differential, the stage of the match and the relative strengths of the two teams. We also investigate individual referee effects across the NHL. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016
... A defense independent rating of goalies is presented in Schuckers (2011) which uses data on the spatial locations of shots they faced. In Beaudoin and Swartz (2010) a simulator is developed which assesses strategies for pulling goalies in hockey games. ...
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... A summary of these research findings are provided in chapters 10 and 11 of the entertaining book by Moskowitz and Wertheim [4]. Some evidence of biased officiating in the National Hockey League (NHL) is given in Remark #2 of Beaudoin and Swartz [5]. ...
Although the home team advantage is known to exist in many sports, there are nuances of the advantage that are less well understood. In this paper, we investigate various aspects of the home team advantage including changes in the advantage over time, the relationship of the advantage to the overall scoring rate and differential advantages within leagues. The analysis is mainly based on descriptive statistics and is confined to the home team advantage pertaining to the National Hockey League and the National Basketball Association.
... Using in-game Poisson models, several authors examined the consequences and optimal timing of "pulling the goalie," a unique hockey strategy whereby an extra skater is substituted for the goaltender, typically employed by the trailing team towards the end of a game. These include Morrison (1976), Morrison and Wheat (1986), Erkut (1987), Nydick and Weiss (1989), Washburn (1991), Berry (2000), Zaman (2001), and Beaudoin and Swartz (2010), which develops a simulation program that considers various man-advantage situations and team-specific parameters. Collectively, these papers overwhelmingly suggest that teams wait too long to pull their goaltender. ...
... Stern (1994) develops similarlyspirited models for basketball based on Brownian motion that, while appropriate for basketball, are not well-suited for hockey where scoring is rare and the natural stochastic process is Poisson. Washburn (1991) did not consider the effect of penalties on goal scoring, but Buttrey, Washburn and Price (2011) and Beaudoin and Swartz (2010) did. In those papers, scoring rates were estimated for specific man-advantage situations (e.g. ...
... Note also from Table 2 that about 80% of all hockey is played at even strength, 19% is played with a one-man advantage, and 1% is played with a two man advantage. These rates are broadly consistent with those reported in Table 1 of Buttrey, Washburn and Price (2011) based on one NHL season that conditions on the actual number of skaters on ice (and not just their difference), though Buttrey, Washburn and Price do not distinguish scoring rates for home versus away; see also Beaudoin and Swartz (2010). ...
We extend the classic Poisson model of hockey based on score differential and time remaining in the game to include the effect of penalties, and derive the associated Markov win probability model given the goal/manpower differential state at any point in a hockey game. Given data from the 2008/9-2011/12 National Hockey League seasons (a total of 4,920 games) reporting second-by-second goal and manpower differentials (which results in roughly 17.7 million observations), we estimate the state dependent transition rates and win probabilities. The data reveal that even after controlling for the home edge afforded by visiting teams being penalized more frequently than home teams, the goal scoring rate for the home team is higher than for visiting teams at most equivalent manpower differential levels. We use the model to develop a new win probability added metric for evaluating individual players based on their incremental contribution to the probability of winning and illustrate its use and conservation properties.
... This directly incorporates the observed duration of the event as well as accounting for the relatively sparse number of goals. Simple Poisson models have been used for making strategic decisions in hockey (Morrison, 1976; Beaudoin and Swartz, 2010); these methods can be improved to account for heterogeneity in the scoring rate over time (Thomas, 2007). Moreover, the game can often be divided into a number of discrete states that give additional information about the game. ...
Evaluating the overall ability of players in the National Hockey League (NHL)
is a difficult task. Existing methods such as the famous "plus/minus" statistic
have many shortcomings. Standard linear regression methods work well when
player substitutions are relatively uncommon and scoring events are relatively
common, such as in basketball, but as neither of these conditions exists for
hockey, we use an approach that embraces the unique characteristics of the
sport. We model the scoring rate for each team as its own semi-Markov process,
with hazard functions for each process that depend on the players on the ice.
This method yields offensive and defensive player ability ratings which take
into account quality of teammates and opponents, the game situation, and other
desired factors, that themselves have a meaningful interpretation in terms of
game outcomes. Additionally, since the number of parameters in this model can
be quite large, we make use of two different shrinkage methods depending on the
question of interest: full Bayesian hierarchical models that partially pool
parameters according to player position, and penalized maximum likelihood
estimation to select a smaller number of parameters that stand out as being
substantially different from average. We apply the model to all five-on-five
(full-strength) situations for games in five NHL seasons.
The baton exchanges are undoubtedly the most critical parts of the 4 × 100 m relay race. Timing of the outgoing runner is critical. In this paper we analyze the race as a minimization problem under uncertainty. We formulate a stochastic model in which the outgoing runner at the baton exchange cannot perfectly assess the incoming runner's exact location relatively a checkmark position, and therefore potentially misjudges the right moment to start running. Also, the team members’ daily shape is subject to uncertainty. To understand the effect of these two random variables—incoming runners’ distance to checkmark and the daily shape of the running team—we conduct a simulation study to investigate the trade-off between the team's expected race time and their probability of being disqualified due to overrunning the takeover zone. Conditioning on a low disqualification probability, the difference in expected race time is shown to be substantial between teams with different variation in distance assessment and forecasting running performance, respectively.