Chellamuthu, Vinodh

Lovell, Joseph

Peterson, Craig

English

Digital Commons @ TRU Library (Thompson Rivers University)

 
Weighted Analytics –  
What Do the Numbers Suggest? 
 
Craig Peterson, Vinodh K. Chellamuthu, & Joseph Lovell 
Dixie State University 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Critical Commentary 
Journal of Emerging Sport Studies  
Volume 3, (2020): London, Ontario 
All Rights Reserved, 2019: ISSN – 2562-3184  
 
 
 
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Peterson et al.: Weighted Analytics – What Do the Numbers Suggest?
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2 Emerging Sport Studies   Volume 3 (2020) 
 
Introduction 
 
he growing popularity, as well as the profit-oriented business of sports, has recently led to an 
increased need to understand player and team performance. The expansion of statistical analysis for 
predicting individual and team success continues to be a need for sport organizations (Bedford & 
Baglin, 2009; Chan, Chow, & Novati, 2012). This has led to the introduction of various metrics that help 
teams be more successful by properly evaluating player performance. As analytical methods evolve because 
of the larger role they play in the success of sport performance, there is a strong push to improve the methods 
used for evaluating individual and team performance (Moskowitz & Wertheim, 2012). Hockey and 
basketball, particularly, have seen a surge of using analytics as a crucial component in designing winning 
strategies. Using various analytics provides coaches with better insight for practices and game preparations, 
as they highlight both the strengths and weaknesses of teams. This in turn gives fans better insight into 
potential game outcomes, thus increasing the popularity and profit of the sport. This critical commentary 
will discuss the use of analytics in sport and provide two possible models in the advancement of analytics in 
both basketball (modified effective field goal percentage) and hockey (modified Corsi) for effective 
evaluation of individual and team performance. 
 
 Statistics is a powerful tool used to understand and analyze dynamics in the sports world.  
Statistical analysis assists sport industry professionals in decision making to improve teams’ performance 
and recruitment. However, when it comes to statistics, there is an overabundance of information. Due to the 
vast amount of raw data available, it is easy to get lost. In order to understand statistical methods in sports, 
one must understand the basics of the Pythagorean Theorem, sometimes referred to as the Pythagorean 
expectation or Pythagorean value. While many might recall the application of this theorem for triangles, the 
statistic has been applied to various situations in sport. In the nineteen-eighties, Bill James developed a 
Pythagorean formula for baseball, focusing on the analysis of runs scored and runs allowed, as depicted in 
the formula:  𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠2
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 2+𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝐴𝐴𝑠𝑠𝑠𝑠2  . This formula will essentially indicate a team’s level 
of performance: the higher the percentage, the better the team is performing. Understanding the basic 
principles of this formula allows team managers and coaches to make changes in their lineup throughout the 
season. By doing so, management can increase their team’s Pythagorean value and increase the potential of 
T 
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Weighted Analytics – Peterson,   3 
 
success on the field, which is ultimately the goal. This statistic provides a relatively accessible understanding 
of sport analytics, for both executives and casual fans. 
 
 There are a number of ways to increase a team’s Pythagorean value, but the basic idea is to 
increase the runs scored. By increasing the number of runs scored, the Pythagorean value increases. Thus, 
the winning percentage increases. Another option is to lower their runs allowed.  Ideally, in an optimal 
situation, a team would increase the runs scored while decreasing their runs allowed. Though none of this 
information is new, it is important to understand this basic concept before expanding on the role of statistics 
in sports. Additionally, several studies have shown that the Pythagorean estimate also works in basketball, 
football, soccer, and hockey (Cochran & Blackstock, 2009; Horowitz, 1994; Hamilton, 2011; Kubatko et al., 
2007).  
 
Basketball Analytics 
 
Basketball has seen a significant increase in the use of analytics, which include offensive and 
defensive ratings, true shooting percentage, and individual efficiency, as well as many other analytical 
models. In particular, the Effective Field Goal (EFG) percentage is a model of great interest. The EFG is one 
of the major factors in Dean Oliver’s Four Factor Offense (Kubatko et al., 2007). EFG is calculated as 
𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠  𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴𝑅𝑅 𝑀𝑀𝐺𝐺𝑠𝑠𝑠𝑠+ .5(3 𝑃𝑃𝑠𝑠𝐹𝐹𝑅𝑅𝑡𝑡 𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠  𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴𝑅𝑅 𝑀𝑀𝐺𝐺𝑠𝑠𝑠𝑠)
𝐴𝐴𝐴𝐴𝐴𝐴  𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴𝑅𝑅 𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑠𝑠𝑠𝑠  This statistic is crucial, since it gives both 
teams and individuals’ weight, based on how they are performing (shooting). Weight is given to the three-
point field goal, as it is worth fifty percent more than the two-point field goal. However, the issue with this 
formula is that there is not an appropriate weight given to the individuals shooting the ball, since all players 
have their own unique attributes, behaviors, and effectiveness when playing the game. Hence, the authors 
designed a novel Weighted Effective Field Goal (WEFG) percentage formula that accounts for individuals’ 
attribute (shooting percentage) compared to EFG: WEFG  =   
 
𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑅𝑅𝑡𝑡𝐺𝐺𝑃𝑃𝑠𝑠 (𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴 𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑠𝑠𝑠𝑠)+3 𝑃𝑃𝑠𝑠𝐹𝐹𝑅𝑅𝑡𝑡 𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑅𝑅𝑡𝑡𝐺𝐺𝑃𝑃𝑠𝑠 ( 3 𝑃𝑃𝑠𝑠𝐹𝐹𝑅𝑅𝑡𝑡 𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴 𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑠𝑠𝑠𝑠)
𝐴𝐴𝐴𝐴𝐴𝐴 𝐹𝐹𝐹𝐹𝑠𝑠𝐴𝐴𝑠𝑠 𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴𝑅𝑅  𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑠𝑠𝑠𝑠  
  
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If a team were to have the majority of their shots taken from outside the arc (three-point shot), 
the team would need to ensure that they have a good three-point shooting percentage on both the individual 
level and the team average. If the team has a low three-point shooting percentage, having a coaching strategy 
to shoot more frequently from the outside would be counterproductive. For example, if a team were to have 
a slightly below average shooting percentage from inside the arc and an average three-point shooting 
percentage, the optimal strategy would be to work with the coaching staff to find a system where the team 
would be taking slightly more shots from the outside, rather than the inside. Furthermore, if a teams’ 
opponents have a low three-point percentage, the idea would be to lower the outside pressure and, in return, 
focus on the pass or rebound. Conversely, if a team had an excellent three-point percentage and an average 
two-point percentage, the focus would be to increase the outside pressure while minimizing the potential for 
passing options inside the arc.  
 
 The beauty of the WEFG is that it shows how successful the team can be, depending on the design 
of the team’s strategy. The authors achieved this versatility by giving both two-point and three-point field 
goals the appropriate weight for their respective shooting percentages.  In basketball, there are several 
situations similar to those mentioned above in which a team would greatly benefit from looking at the WEFG, 
as this value gives more detailed game information. In basketball, the team with the most points wins. 
However, if you break the game down further, it is comprised of a series of smaller games. Using statistical 
analyses, it can be determined how winning each one these games helps increase the teams’ chances of 
ultimately winning. Understanding the strengths and weaknesses of a team will allows a team to have the 
most effective strategy and to better prepare for games.  
 
Hockey Analytics 
 
Analytical models first used in hockey primarily focused on goal-based metrics, such as the plus-
minus analysis (Found, 2016). While the plus-minus analysis was first introduced in hockey, it has become 
a standard for most professional sports and has be altered as needed as better analysis required the process 
to evolve (Macdonald, 2012). The traditional plus/minus statistic is a simple point system. Players are 
awarded a positive-point if they are on the ice at the time their team scores a goal. Players receive a negative-
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point if they are on the ice at the time a goal was scored against their team. The advancement of various 
analytical models in hockey has led sport professionals to rely more and more on shot-based metrics. The 
Corsi value has become quite prominent in recent years. Corsi was named after Buffalo Sabres’ goalie coach, 
Jim Corsi.  The original idea behind the Corsi value was to track the workload for goalies, as the value looks 
at not only shots on goal, but attempted shots and blocked shots as well (Vollman, 2016). For each of these 
situations, the goalie would be anticipating the shot.  
 
The Corsi value has essentially become a glorified plus-minus statistic. Instead of having the 
focus on points, the focus is on attempted shots. The NHL has started to track individual Corsi values, but 
these values have been renamed as shot attempts (SAT). The NHL tracks SAT by taking the sum of the shots 
on the opposing goal (while that individual is on the ice), subtracted by the shots taken on their own net 
(while that individual is on the ice). As with the plus-minus statistic, anything above zero is a positive 
outcome and anything below zero is negative. Corsi value at the team-level is calculated 
by: 𝑆𝑆ℎ𝑠𝑠𝑡𝑡  𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑅𝑅 𝐹𝐹𝑠𝑠𝑠𝑠
𝑆𝑆ℎ𝑠𝑠𝑡𝑡 𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑅𝑅 𝐹𝐹𝑠𝑠𝑠𝑠+𝑆𝑆ℎ𝑠𝑠𝑡𝑡 𝐴𝐴𝑡𝑡𝑡𝑡𝑠𝑠𝐴𝐴𝐴𝐴𝑡𝑡𝑅𝑅 𝐴𝐴𝑃𝑃𝐺𝐺𝐹𝐹𝑅𝑅𝑅𝑅𝑡𝑡. For this value, fifty percent is where an 
average team falls. The higher the number, the better the team is performing, at least when it comes to 
attempted shots. A common criticism of the traditional Corsi measurement is that, when looking at the 
individual-level, players have the tendency to take shots from anywhere on the ice. The rationale behind this 
is that a player could intentionally increase their individual Corsi value, which would increase their value to 
their respective team. This can create quite a conflict for team management. Found (2016) examined this 
quandary and concluded that goal-based metrics (plus-minus) were better indicators of individual and team 
success than using Corsi because many of the shots taken were not effective enough to potentially result in 
goals. 
 
When evaluating individuals, it is important to take the veracity of their Corsi value into account; 
that is why Corsi needs to have weighting. While remembering that Corsi was developed to focus on the 
goalie, placing both the save-average and goals-against into the weighted Corsi value increases the accuracy 
of the value. The formula is relatively simple 𝑆𝑆ℎ𝑠𝑠𝑡𝑡𝑅𝑅 𝐹𝐹𝑠𝑠𝑠𝑠
𝑆𝑆ℎ𝑠𝑠𝑡𝑡𝑅𝑅 𝐹𝐹𝑠𝑠𝑠𝑠  +   ( 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝐴𝐴𝐴𝐴𝐺𝐺𝐴𝐴𝐴𝐴𝐺𝐺𝐴𝐴
1−𝑆𝑆𝐺𝐺𝑆𝑆𝑆𝑆 𝑃𝑃𝑆𝑆𝑃𝑃𝑃𝑃𝑆𝑆𝐴𝐴𝐴𝐴𝐺𝐺𝐴𝐴𝑆𝑆  )  the save 
  
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 percentage is calculated by   𝑆𝑆ℎ𝑠𝑠𝑡𝑡𝑅𝑅 𝐴𝐴𝑃𝑃𝐺𝐺𝐹𝐹𝑅𝑅𝑅𝑅𝑡𝑡−𝐺𝐺𝑠𝑠𝐺𝐺𝐴𝐴𝑅𝑅 𝐴𝐴𝑃𝑃𝐺𝐺𝐹𝐹𝑅𝑅𝑅𝑅𝑡𝑡
𝑆𝑆ℎ𝑠𝑠𝑡𝑡𝑅𝑅 𝐴𝐴𝑃𝑃𝐺𝐺𝐹𝐹𝑅𝑅𝑅𝑅𝑡𝑡  . The reason why goals-against and 
save-percentage are used in this equation is that they are not only key goaltending statistics, but they also 
include a value from the traditional Corsi value: shots-against.  
 
 The use of Modified Corsi is supported by the statistical analysis of data from ten recent NHL 
seasons, from 2008 to 2017. This includes every goaltender that has stepped onto the ice during that time. 
The mathematical backing is comprised of over 3,000 data points. In projecting the top sixteen teams in the 
NHL, without taking divisions into account, the traditional Corsi value was able to project, on average, eight 
of the sixteen teams. Conversely, the Modified Corsi was able to project, on average, twelve of the sixteen 
top teams. That results in a twenty-five percent increase when projecting the top 16 teams, as compared to 
the traditional Corsi value. When looking at the league, the Modified Corsi value was consistently able to 
project fourteen percent more accurately than the traditional Corsi value. The Modified Corsi value had an 
average of eighty percent accuracy in projecting the top teams over the past ten seasons. Figure 1 portrays 
the percentage of teams accurately projected to make the playoffs each year from 2008 to 2017, using both 
traditional and Modified Corsi. 
Figure 1. Corsi top 16 NHL teams compared to Modified Corsi top 16 NHL teams.  
0%
20%
40%
60%
80%
100%
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 AveragePe
rce
nta
ge 
of 
Ac
cur
acy
 Corsi vs Modified Corsi 
Corsi Top 16 M Corsi Top 16
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Weighted Analytics – Peterson,   7 
 
Using this Modified Corsi value can be extremely valuable to an organization.  Calculating the 
numbers on these modified Corsi values at the beginning of the season and projecting these numbers to the 
end of the season, organizations would be able to adjust a variety of areas, based on their initial results. 
Coaching staff and team management regularly need to find answers to the following questions: how is 
goaltending performing, is there enough blocking of shots, and is the offence or defense taking enough shots 
or preventing enough shots? With Modified Corsi, there are key factors that can significantly change its 
overall value. These factors come from every area of team performance, which is why this value has is such 
an accurate projection for the top teams in the league. 
 
Conclusion 
 
There is evidence to suggest that traditional analytic methods do not always obtain the most 
accurate results (Found, 2016; Macdonald, 2012). For this reason, the advancement of analytics continues 
to evolve as sport professionals strive to understand team performance and the value of individual players 
value to their teams. The models presented may be useful to analysts, coaches, teams and fans, as they 
continue to analyze the performance of individuals and teams. However, only focusing on the statistical 
analysis may cause a loss of direction for building an effective team. When these analytical methods are 
used, there may not be a symbiotic relationship between analysis, coaching staff, and management. 
Furthermore, while analytics is one tool that is gaining prominence in the sport industry, it should not be the 
only standard measured, as it is easy to get lost in copious data. There needs to be a firm understanding of 
the game and having a clear direction is the best way for an organization to achieve success.  The only way 
to accomplish this is to have an open line of communication from the top down. So long as all parties within 
the organization are on the same page, the results of these analytics can be more effectively applied. Utilizing 
the weighted formulas discussed in this paper provides additional tools that an organization can use to help 
determine the direction for their team.   
 
 
 
 
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Weighted Analytics – What Do the Numbers Suggest?

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Weighted Analytics – What Do the Numbers Suggest?

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