The document discusses how analytics can help high school basketball coaches make more informed decisions. It defines analytics as using data and analysis to increase knowledge and understanding to better predict outcomes and solve problems. While analytics are commonly used in professional sports, they have been less accessible to high school coaches due to limited resources. The document aims to explore how high school coaches can implement an analytics program through a case study with a high school basketball team in BC. It discusses frameworks for effective problem solving through bringing different perspectives together and viewing disagreements as a process of thinking rather than conflict.

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The Strengths and Limitations of Analytics for Basketball Coaches
By
Joshua Mullen
Bachelor of Education
Majors in Physical Education and Social Studies
A Project Submitted in Partial Fulfillment of the
Requirements for the Degree of
MASTER OF EDUCATION (COACHING STUDIES)
In the School of Exercise Science, Physical and Health Education
This project is accepted as conforming to the required standard
Dr John Meldrum, PhD
Supervisor
© Joshua Mullen, 2014
University of Victoria

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All rights reserved. This project may not be reproduced in whole, or in part,
by any means without the permission of the author

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To Eaks and G, without your commitment to collecting and organizing data this
work would not have been possible.

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Abstract
Through a case study, analytical tools that can be used by high school basketball coaches were
explored with a single A basketball team in British Columbia. By adopting and applying
analytical principles that are being used in the NBA, a framework was created that allowed for
more in depth analysis despite having limited resources in comparison to the pros. By coding the
games on paper and collecting statistics through an Ipad app, a rich data set was gained that lent
itself well to making more informed decisions as a basketball coach.

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Introduction
In our society and in sport we increasingly hear of organizations implementing and
investing more into their analytics programs (Alamar, 2013; Saxena, & Srinivasan, 2013;
Thomas & Cook, 2006). “Analytics” is a broad and complicated term whose meaning may not be
entirely clear. Houston Rockets General Manager Daryl Morey defines analytics as, “Increasing
knowledge (prediction power) using data and analysis” (Gordon, 2014). Former Seattle
Supersonics and Sacramento Kings analyst and author of “Basketball on Paper” Dean Oliver
defines analytics as “answering the same questions that fans, media, and sports professionals all
answer, but using a systematic approach with data” (Gordon, 2014). Neil Greenberg defines
analytics as “using all available resources (data, video, scouting, etc.) in concert to reduce the
gap between potential and reality in sports performance, at the team and individual level”
(Gordon, 2014). Ed Feng says “ analytics is using numbers as a tool to better understand
complex phenomena” (Gordon, 2014). Alamar (2013) defines analytics as ''the management of
structured historical data, the application of predictive analytic models that utilize that data, and
the use of information systems to inform decision makers and enable them to help their
organizations in gaining a competitive advantage'' (p. 27). Looking at definitions from various
experts it is clear that analytics refers to many different components of an organization. While
Feng’s definition is limited to looking strictly at numbers, most use broad terms such as “data”
which could include various types of information. The thing that comes through in all of these
definitions is that analytics is about collecting as much relevant information as possible,
synthesizing and organizing that information in order to increase your understanding of a
problem, which will in turn make you more adept at solving the problem. Dean Oliver (2004),

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often referred to as the godfather of basketball analytics, says that “predicting the future often
means understanding things well enough to be able to change the future” (p. 337). This is
precisely the purpose of this work; to give basketball coaches analytical tools to be able to better
understand their team in order to more effectively steer their group towards success.
The development of new analytical tools and frameworks are designed to inform decision
makers in many different facets of society (Alamar, 2013; Saxena, & Srinivasan, 2013; Thomas
& Cook, 2006). Whether it be in the venue of business, homeland security, or sport, analytical
tools can help inform the decision making process (Alamar, 2013; Saxena, & Srinivasan, 2013;
Thomas & Cook, 2006). By having experts in a given field interpret hard data, levels of
objectivity are brought to the decision making process (Alamar, 2013). In terms of the game of
basketball, analytical tools have traditionally failed to serve coaches as an effective resource to
help make decisions that lead to winning basketball games (Alamar, 2013; Goldsberry, 2012).
This has been the case because the traditional measurements have failed to reflect the complex
factors that contribute to on court success (Alamar, 2013; Goldsberry, 2012). This is largely due
to the fact that it is difficult to quantify things such as defensive effectiveness, spatial
components of the game, and relationships between given players (Alamar, 2013; Goldsberry,
2012; Hollinger,2005 ). However, with new technologies in place, such as cameras that record
spatial data, along with an increased emphasis on using analytical tools to inform coaching
decisions, we have seen large growth in this component of basketball (Alamar, 2013; Lowe,
2014 ; Pritchard, Zarren, Buford, & Gundy, 2013). With the increased availability of analytical
tools to basketball decision makers we have seen varied levels of resistance to the use of these
new tools (Alamar, 2013; Pritchard et al., 2013). On the other hand, we have seen many people

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embrace these tools who may not have traditionally been considered basketball “experts”
(Alamar, 2013; Pritchard et al., 2013). Furthermore, the embracing of new ideas and perspectives
from people with different backgrounds may present a superior way to solving problems than
having like minded thinkers tackle a problem (Heffernan, 2012).
In this work I will evaluate the impact of a more all­encompassing analytics program for
basketball coaches. While there is a great deal of literature that examines how analytical tools are
being used at the professional level, there is a lack of information on what analytics looks like in
more modest settings. Through a case study I will explore and examine how coaches at the high
school level can implement a more advanced analytics program to make more informed
decisions that will contribute to on court success.
Literature Review
A Framework for Problem Solving
Basketball coaches are presented with a fundamental problem: how do I win the game
given my players and my competition? This question presents a problem that is complex based
on the many variables at work. Margaret Heffernan (2012) provides us with an effective
framework for problem solving, where decision makers seek out people with different expertise
and backgrounds in looking at the same problem in order to find answers. This problem solving
framework very much mirrors the analytics movement in sport and more specifically basketball.
Heffernan (2012) provides us with the example of Dr. Alice Stewart, who found that
x­rays during pregnancy were one of the primary causes of childhood cancer. What made Alice
Stewart so effective at solving problems was her partner George Kneale (Heffernan, 2012). In

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Kneale, Stewart found someone who was her opposite as he looked to tackle the same problems
through a different lens (Heffernan, 2012). Kneale was much more data driven than Stewart, and
viewed his job as trying to show that Stewart’s theories were wrong (Heffernan, 2012). Stewart
would be reassured that her findings were correct if Kneale was unable to disprove her theory
(Heffernan, 2012). Stewart and Kneale viewed conflict as thinking, which allowed them to find
answers to difficult problems (Heffernan, 2012).
In order to establish this environment where you have beneficial conflict, you must first
find people who are different and who can look at the same problem through different lenses
(Heffernan, 2012). You must also have people who can recognize their biases and who are
willing to change their views based on convincing arguments (Heffernan, 2012). It is important
to have people who care enough about solving the problem, because as Heffernan (2012) points
out, having people with different perspectives who are looking to challenge other’s ideas in order
to reach a consensus, requires more energy and time. This framework for problem solving
requires people who embrace conflict and view it as thinking (Heffernan, 2012).
This idea of conflict as thinking is an idea that has clearly started to permeate sport
through the analytics movement. We see it in the “Money­Ball” example where the Oakland
Athletics General Manager Billy Beane hires Paul DePodesta as his assistant (Lewis, 2003). In
this example we see a former professional player teaming up with a Harvard Graduate who has a
degree in economics and views the game through numbers (Lewis, 2003). Together they are able
to make more informed personnel decisions to benefit the Oakland A’s (Lewis, 2003). In the
“Money­Ball” example we have two people who see the game through different lenses but view
their differences as thinking. If DePodesta makes an argument for a player and his perceived

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value, he is doing so with numbers (Lewis, 2003). Where Beane’s background is in looking at
technique, physique, and potential of a player (Lewis, 2003). The two view the game through
different lenses, but if they are able to come to the same conclusion based on discussion and
debate, it is more likely that they will be correct. The Boston Celtics provide a similar example
with General Manager Danny Ainge and Assistant General Manager Mike Zarren. Ainge, a
former professional basketball player, and Zarren, a University of Chicago and Harvard Law
Graduate, provide two very different skill sets. Ainge is seeking out the opinion of someone who
has a very different background than him to tackle the same complex problems. These are just
two of many examples of organizations using potential conflict as a tool to solve problems.
It is clear, through decisions on personnel, that some of the most successful
organizations in sport have adopted this model of thinking and problem solving, which is
centered around conflict. More decision makers have begun to recognize the value of different
viewpoints, backgrounds, and experiences. Analytics is an example of how coaches who lack a
background in math or statistics, can further progress their ability to solve the fundamental
problem of how to help their team win. This is done through challenging their ideas to gain a
more informed opinion.
Analytics Framework
Analytical tools are increasingly being used as a way to inform the decision making
process in a variety of facets of society (Alamar, 2013; Saxena, & Srinivasan, 2013; Thomas &
Cook, 2006). The purpose of analytics is to give the decision maker insight and more clarity on a
given issue (Alamar, 2013). The overall effectiveness of analytics is dictated by the framework
in place (Alamar, 2013). This framework is centered on: data management, analytic models,

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information systems, and how the decision maker interacts with the given data (see figure 1)
(Alamar, 2013). This is true for both a sport and business setting (Alamar, 2013; Saxena, &
Srinivasan, 2013).
Figure 1. (Alamar, 2013, p. 18)
Data management revolves around the collection of raw data and organizing it in a way
so it can feed the other systems (Alamar, 2013). The data you choose to collect will ultimately
dictate the information that can become available to you (Alamar, 2013). This makes it crucial
that you are collecting information that is relevant to what you are hoping to shed light on
(Alamar, 2013). This data can be used to feed the analytical models or be placed directly into the
information system (Alamar, 2013).

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The analytical models allow for you to gather more information from the data if the
proper questions are asked (Alamar, 2013). This is seen in the “Money­Ball” example where the
Oakland A’s assemble a team of undervalued players (Lewis, 2003). They are undervalued due
to traditional measurements failing to reflect a player’s true value (Lewis, 2003). One of the
questions asked by Oakland A’s management was not whether players were good hitters
(traditionally measured by batting average) but rather do the players get on base (Lewis, 2003)?
It seems quite intuitive that on base percentage would be measured rather than batting average as
the goal of an at bat is to get on base. So data on walks and times hit by a pitch were now being
placed into an analytical model that painted a clearer picture on a batter’s true effectiveness for
an at bat (Lewis, 2003). This information from the analytical model will be placed in the
information system and can also be given directly to the decision maker (Alamar, 2013).
The information system is where all relevant data to informing the decision making
process should end up (Alamar, 2013). The information that goes into the information system,
and an understanding of what the information is telling you, should be pre­determined (Alamar,
2013). This allows for everyone to first understand what the information is saying and secondly
determine what information is relevant to decision makers (Alamar, 2013). This information
should be presented in a way so that the decision maker(s) can interact with it while allowing
them to spend their time applying the information rather than interpreting it (Alamar, 2013).
This information might come in many different forms but its intention is simple, to give the
decision maker a more informed opinion on a given issue or decision (Alamar, 2013). The
information system should also be organized in such a way that it allows all decision makers to
have access to the available information (Alamar, 2013). This creates what Alamar (2013) calls,

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“one version of the truth” (p. 50). What Alamar means by this is that all decision makers within
an organization are operating with the same information (Alamar, 2013). When information is
isolated to particular individuals or groups, this is what Alamar (2013) refers to as a “data silo”
(p. 63). These data silos need to be avoided in order to ensure all decision makers are operating
with the same information or “version of the truth” (Alamar, 2013). By having an agreed upon
set of information that everyone has access to, an efficiency is created that would not be present
if information was segregated or if there was a lack of understanding on what the data is saying
(Alamar, 2013).
The final phase of the framework is the decision maker (Alamar, 2013). The purpose of
analytics is ultimately to inform the decision maker which in turn will create a competitive
advantage through an increased access to information (Alamar, 2013). However, the key to
establishing a strong analytical program is the decision maker (Alamar, 2013). In order for the
analytics program to serve the decision maker effectively, the decision maker(s) must display
strong communication and leadership skills (Alamar, 2013). It is imperative that decision makers
see analytics as a useful tool for gaining a competitive advantage (Alamar, 2013; Kerr, Stevens,
Gundy, Zarren, Lowe, Colangelo, 2014). If the information that is being presented is not being
applied, the purpose of analytics is lost (Alamar, 2013). This might seem obvious but many
analytic programs are limited by the unwillingness of decision makers to embrace the newly
available information (Alamar, 2013). It is also important that the analysts are measuring data or
designing metrics that are relevant to decision makers (Alamar, 2013). This can only happen
through effective communication (Alamar, 2013). For example, a business owner might be
interested in expanding his or her business into a new market. In order for the business owner to

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benefit from the use of analytics he or she must communicate to the analyst particular strategies
they intend to use and other relevant information to the expansion. The analyst will then be able
to shed light on the likelihood of the business succeeding in the given expansion due to the
increased availability of relevant information. When strong leadership is present in an analytics
program it gives the framework more direction and allows for everyone to have a stronger
understanding of where a competitive advantage can be gained (Alamar, 2013).
Analytics serves as a great tool to gain a competitive advantage when an effective system
is developed (Alamar, 2013). In order to develop an effective analytics program, an organization
must commit to strong: data management, analytic models, and information systems while
leadership must make a commitment to using analytics (Alamar, 2013). Whether it is in business
or sports, an increased access to information that address issues fundamental to success will cater
to more informed decision making for organizations (Alamar, 2013; Saxena, & Srinivasan,
2013).
Why Basketball is not Baseball
Baseball has served as the trailblazer for collecting data and using analytics to help
inform the decision making process (Alamar, 2013; Hollinger, 2005; Oliver, 2004). This has
inspired analysts in other sports (Alamar, 2013; Hollinger, 2005; Oliver, 2004). Analysts in other
sports, such as basketball, are still working to close the gap between baseball and their given
sport (Alamar, 2013; Hollinger, 2005; Oliver, 2004). The main reason basketball analytics still
fails to have the same influence on the game as it does in baseball, is due to the very different
structures of the games (Oliver, 2004).

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In baseball we see a game where analysts are more able to accurately quantify a player’s
value to a team (Oliver, 2004). Due to how compartmentalized and fragmented the game is,
along with the lack of interdependency between players, it is more simple to accurately
determine a player's contribution to the team (Oliver, 2004). In addition to this, baseball operates
at a slow pace, a built in measure exists for a players ability to work towards a run through the
bases, and the game has a well established system of collecting relevant quantitative data (Oliver,
2004). Basketball does not have these benefits due to the structure and history of the game
(Oliver, 2004).
As Oliver (2004) points out “the conceptual problem (of basketball) is that no player is a
team” (p. 60). As coaches we are seeking for a way to truly understand how much a player
contributes to winning, or losing basketball games (Oliver, 2004). The challenge of trying to
determine how much a player contributes is directly related to the team context (Oliver, 2004).
How much value does someone who is really good at rebounding have to a team that lacks other
strong rebounders? How much value does that same rebounder have on a team full of strong
rebounders? Furthermore, subtle spatial components of the game have traditionally been very
difficult to quantify to determine a player’s value (Oliver, 2004). What is the value of a cut that
opened up space for another player to eventually score a basket (Oliver, 2004)? What is the value
of a great shooter who opens up space on the floor due to the unwillingness of the defense to
help off that player and risk giving up an open shot (Lowe, July 2014)? Progress is being made
on the ability of analysts to quantify these spatial component of the game through new
technologies such as SportVU which produces data based on every player's movement in relation
to the ball and court (Alamar, 2013; March, 2013).

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Often coaches do not believe that analysts are capable of quantifying intangibles
(Alamar, 2013). While most coaches would agree that a player’s willingness to accept a given
role, their interaction with their teammates, and their overall demeanour contribute to the overall
effectiveness of the team, most coaches would view these skills as unquantifiable (Alamar, 2013;
Oliver, 2004). However, this may not actually be the case (Alamar, 2013; Oliver, 2004). One
example is Dean Oliver trying to quantify team chemistry (Alamar, 2013). In order to do this
Oliver had to get an understanding from coaches and other decision makers what was meant by
chemistry in order to be able to evaluate it (Alamar, 2013). Through his questioning he was able
to determine that chemistry was based on how different players’ skill sets blended and
complimented one another (Alamar, 2013). This questioning lead to Oliver being able to design a
framework that allowed him to quantify how well the players’ skill sets fit together in order to
measure the sum of the parts in creating the whole (Alamar, 2013). While Oliver’s framework
for quantifying chemistry still has to be developed in order to increase its accuracy, the example
shows the complexity of determining player value in a team context (Alamar, 2013; Oliver,
2004). The examples of team chemistry and spatial components of the game, also show that by
asking the right questions and through technology we are capable of bringing further clarity to
complex problems (Alamar, 2013; Lowe, February 2014).
Numbers Can Lie
When looking at the work and research of various analysts, one thing that becomes
apparent is that there is a recognition that all data has limitations (Alamar, 2013; Hollinger,
2005; Oliver, 2004). All too often we hear the idea that “numbers never lie”, when in fact
numbers can be extremely misleading or fail to represent what is actually occurring (Alamar,

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2013). Furthermore, people can shape and mould numbers to make them say things that reflect 1
their biases (Alamar, 2013 ; Gundy, Hollinger, Oliver, Zarren, 2012). It is extremely important
that we critically examine the data we collect in order to put the numbers in context (Alamar,
2013).
Quantitative data is data in which can be demonstrated in numbers. For example, the
number of points a player scored, rebound total, and blocks would all be considered quantitative
data. As Alamar (2013) explains “the problem, however, is that quantitative data are just data,
the lowest input into the analytic process, and without being transformed into information, they
are at best useless and can often be misleading” (p.55). For example a person might make the
assumption that because a player scores the most points, that they are the best scorer on their
team (Oliver, 2004). However this would be failing to put the numbers in context which would
be a mistake and could result in the data being misleading (Alamar, 2013). Perhaps the player
who scores the most points on their team also has the worst shooting percentage, and thus is
actually a detriment to their team’s success rather than an asset (Oliver, 2004). The player who
you thought was the most effective scorer due to the points per game measurement, is actually
shown to be a below average or poor scorer on the team when you measure efficiency (Oliver,
2004). We see in this simple example, how important context is to being able to use data in the
decision making process (Alamar, 2013). These complex interactions, and limitations of
statistics, are the reason people such as Bill Simmons (2009) can reasonably argue that Bill
Russell is a greater player than Wilt Chamberlain despite Chamberlain’s superior statistical
outputs.
1
For an example of how data can be misleading see: (2014). Previous page ­ Spurious Correlations.
Retrieved from: http://www.tylervigen.com/page?page=1.

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One way quantitative data can be put into context is through metrics (Alamar, 2013;
Hollinger, 2005). A metric is a measurement that allows for a comparison to take place. Useful
metrics will often offer comparison between two things that are different, for example in
basketball, players who play different positions (Hollinger, 2005). Even when quantitative data is
put into a context through metrics, further analysis is needed in order to gain a more clear
understanding of what the data is telling you (Alamar, 2013; Hollinger, 2005). In John
Hollinger’s (2005) Player Efficiency Rating (PER) metric where he has taken a range of 2
quantitative data and put it into context through assigning value to that data, he still explains the
importance of using other information to gain a more accurate picture. For example, a player
might be able to compile many steals and blocks through gambling on defense which would
strengthen their PER through increasing those numbers, but this strengthened PER rating would
fail to represent how their gambling hurts the player’s given team (Hollinger, 2005). The player
could be a net loss on the defensive end, but show up as a positive through their high statistical
total in blocks and steals (Hollinger, 2005). Furthermore, a player could play excellent defense
without compiling many steals or blocks which would fail to show up in the player’s PER
(Hollinger, 2005). This does not mean that the PER metric is not valuable to a decision maker,
but rather it needs to be paired with further quantitative and qualitative data in order to further
increase the context and usefulness of the metric to the decision making process (Hollinger,
2005).
We all too often look at numbers as facts (Alamar, 2013). It is important to realize when
viewing metrics and statistics that are presented, that they are designed to give coaches a more
2
PER will be examined more closely in the “Box­Score” section and in the case study.

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accurate understanding of performance and factors that will influence your ability to make
decisions to put your team in a position to have success (Alamar, 2013). While the various
quantitative measurements presented in this work will help provide clarity in informing the
decision making process, they cannot be used to get a definitive answer on the questions we face
as coaches (Alamar, 2013).
The Box­Score
In basketball, quantitative data on players and the team has traditionally been collected
through the box­score. The box score has evolved since the 1940’s to include new data to help
inform decision makers (Basketball­Reference, 2002). With the quantitative data that is currently
collected through a box­score, a great deal of information can be gleaned to help inform a
coaches decisions.
During the 1945­46 NBA season the amount of data that was included in the box score
was quite limited (Basketball­Reference, 2002). The number of baskets and free throws made by
the player were recorded to determine the player’s total points (Basketball­Reference, 2002)..
This data was then added to the team totals in order to show how each player's points contributed
to the team’s final score (Basketball­Reference, 2002). In 1946 it is impossible to determine a
player’s efficiency through the box score, without the documentation of attempts. There was also
no defensive measurements, which makes it impossible to judge a player’s defensive impact
through the box score (Basketball­Reference, 2002). Furthermore, there was no measure of a
player’s capacity to make their teammates better, or to gain possession. A coach in 1946 is going
to find limited value in the box score. 3
3
To view a box score from 1946 see:New York Knicks at Boston Celtics, December 7, 1946. Retrieved from:
http://www.basketball­reference.com/boxscores/194612070BOS.html )

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Today’s box­scores provide the opportunity for coaches and analysts to glean a lot more
information based on the quantitative data presented. With the inclusion of Field Goal Attempts
(FGA), Free Throw Attempts (FTA), and 3 Point Attempts (3PA) , an analyst is able to 4
determine a player’s scoring efficiency. On top of this we see the inclusion of a player’s capacity
to either secure or gain a possession through the Offensive Rebound (OR), Defensive Rebound
(DR), STeals (ST), or TurnOver (TO or TOV) statistics. In addition to the Steals measurement,
Blocks (BLK) are measured in order to help quantify a player’s defensive impact. There is also a
measurement to help weigh a player’s capacity to foster easy scoring opportunities for their
teammates through the Assist (A). Many basic box scores are also beginning to include a plus
minus measurement which is essentially a running score for when an individual is on the floor.
“PF” indicates the number of personal fouls that a player committed. An analyst is better able to
contextualize this data through gaining an understanding of the Minutes Played (MP). All of
these individual statistics are added up in order to determine the team totals for each
measurement (See Figure 2. for the Spurs box­score from game 5 of the 2014 NBA Finals)
MP FG FGA FG% 3P 3PA 3P% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS +/-
B. Diaw 38:03 2 7 0.286 1 3 0.333 0 0 1 8 9 6 1 0 2 1 5 14
T. Parker 36:06 7 18 0.389 0 1 0 2 2 1 0 1 1 2 0 0 0 2 16 1
K. Leonard33:59 7 10 0.7 3 4 0.75 5 60.833 2 8 10 2 1 1 3 6 22 15
T. Duncan 33:24 5 10 0.5 0 0 4 60.667 2 6 8 2 0 2 0 3 14 5
D. Green 19:07 0 5 0 0 3 0 0 0 0 2 2 2 2 0 1 0 0 -4
4
The 3 point line wasn’t introduced into the NBA until the 1979­1980 season.

20. 20
M.
Ginobili 28:26 6 11 0.545 3 6 0.5 4 5 0.8 0 4 4 4 0 0 2 3 19 21
P. Mills 17:40 6 10 0.6 5 8 0.625 0 0 0 1 1 2 0 0 0 2 17 15
T. Splitter 11:24 1 1 1 0 0 1 2 0.5 0 2 2 2 1 1 0 2 3 16
M.
Belinelli 8:37 2 3 0.667 0 0 0 0 0 2 2 1 0 0 0 1 4 2
M.Bonner 6:59 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 3
J. Ayres 2:12 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 0
C.Joseph 2:10 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -2
A.Baynes 1:53 0 0 0 0 2 2 1 1 0 1 0 0 0 0 0 2 -1
Team
Totals 240 37 78 0.474 12 26 0.462 18 230.783 6 34 40 25 5 4 8 21 104
Figure 2. (Basketball­Reference.com: Miami Heat at San Antonio Spurs Box Score, 2014). .
As coaches, it is extremely informative to understand what the outcomes of our team and
opponents possessions are (Hollinger, 2005; Oliver, 2004). A team’s ability to increase the
effectiveness of their possession while limiting the effectiveness of their opponent’s possession
will directly correlate with their ability to win the game (Kubatko, Oliver, Pelton, Rosenbaum,
2007; Oliver, 2004) This is the reason why the most informative quantitative measurements rely
on possessions (Hollinger, 2005; Kubatko et. al., 2007; Oliver, 2004). In order to use many of
these measurements we need to first figure out the number of possessions that have occurred in
the game, or over the unit of time we are measuring (Hollinger, 2005; Kubatko et. al. 2007;
Oliver, 2004). This can be done quite simply by using the formula: Team Possessions = Field

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Goal Attempts ­ Offensive Rebounds + Turnovers + (Free Throw Attempts X 0.44)
(Hollinger, 2005; Oliver, 2004). The only subjective number is .44 which accounts for the fact
that sometimes a player will shoot one free throw, two free throws, or three free throws,
dependent on the type of foul, so the number of .44 is used as an average (Hollinger, 2005). Once
we know the total number of possessions we can then determine the amount of points scored per
possession (ppp) for our team and our opponent by using the formula of Points Per Possession
= Points Scored/ Team Possessions (Kubatko, et. al. 2007). These three figures (total
possessions, opponent’s points per possession, and your team’s points per possession) are the
three figures that will give you the most insight into how your team is doing in the game
(Kubatko, et. al. 2007; Oliver, 2004). The points per possession measurement is often used to
determine a team’s offensive rating while the opponents point per possession is used to
determine a team’s defensive rating (Blott, 2009). These measurements are extremely
informative as they also allow for you to get a strong indicator of the pace in which the game is
being played at, and the effectiveness of both your offense and your defense (Hollinger, 2005;
Kubatko, et. al. 2007; Oliver, 2004). The reason pace is important is that the pace in which a
team plays at is often crucial to a team’s success (Oliver, 2004). For example, many underdogs
will try to limit the number of possessions in a game by seeking out the most effective shot in a
possession, while also hoping to limit the number of field goal attempts their opponent will get
by maintaining possession for most of the shot clock (Oliver, 2004). The reason underdogs often
want to reduce the amount of field goal attempts that occur in a game by playing at a slower pace
is because of the recognition that over a long enough timeline, the favorite is going to score more
points per possession (Oliver, 2004). By slowing the pace, and reducing field goal attempts that

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will occur in the game, you increase the likelihood for statistical anomalies to occur through the
reduced sample size (Oliver, 2004). North Carolina’s head coach Dean Smith placed a great deal
of value on these three possession based measurements to inform him on how effectively his
teams were operating (Oliver, 2004). By understanding the outcomes of possessions it gives you
a strong indicator into how your team is doing (Oliver, 2004). Furthermore, by being able to
figure out the number of possessions it allows for more in depth quantitative analysis to occur.
From the box score you are able to determine your team’s capacity to win the four
primary indicators of success in a basketball game (Oliver, 2004). These four indicators (in order
of importance) are: your ability to shoot a higher percentage than your opponent, your ability to
take care of the ball (through turnovers or steals), your ability to secure rebounds, and your
ability to get to the free throw line and make your free throws (Kubatko et. al, 2007 ;Oliver,
2004). Kubatko et. al. (2007) assign a value of 10 for shooting percentage, 6 for turnover
percentage, 3 for offensive rebounding percentage, and 3 for a team's capacity to hit free throws.
The ability to shoot a higher percentage than your opponent from the floor is represented through
Effective Field Goal Percentage which can be measured through the formula: Effective Field
Goal Percentage = Field Goals + 0.5 (3­Point Field Goals)) / Field Goal Attempts
(Basketball­Reference, 2002; Blott, 2009; Kubatko et. al., 2007). The effective field goal
percentage formula accounts for the fact that a three point field goal is worth more than a two
point field goal (Blott, 2009). While it may seem intuitive that this added value for a three point
shot be factored into the mathematical formula when determining the effectiveness of a shooter,
traditionally it has not been used. For determining your team’s and your opponent’s ability to
take care of the ball you can use the Turnovers Per Possession measurement by using the

23. 23
formula: Turnover Per Possession = Turnovers/Possessions (Kubatko et. al., 2007). For
determining Offensive Rebounding Percentage the following formula can be used: ORB% =
Offensive Rebounds / (Field Goal Attempts ­ Field Goals) (Blott, 2009). To determine your
ability to get to the free throw line and make your free throws, the Free Throw Rate formula can
be used: Free Throw Rate = Free Throws Made / Field Goal Attempts (Blott, 2009; Kubatko
et. al. 2007).
The reason shooting percentage is the primary indicator of whether or not a team will win
the game is because teams tend to finish with a similar amount of field goal attempts (Hollinger,
2005; Oliver, 2004). However, if your team is unlikely or unable to shoot a higher percentage
than your opponent, then you need to find a way to secure more shot attempts than your
opponent if you want a chance at winning the game (Oliver, 2004). This can be done through
reducing your turnovers and increasing your opponent’s turnovers, or grabbing more rebounds
than your opponent (Oliver, 2004). This is why underdogs often resort to strategies such as
pressing, or sending multiple players to try to secure an offensive rebound, despite the high risk
nature of these strategies (Oliver, 2004). This is due to the recognition that for an underdog to
beat a team who attains a higher level of value through each possession that ends with a shot,
they must find a way to gain additional field goal attempts (Oliver, 2004). A team that has a
lower effective field goal percentage will always lose when field goal attempts are the same or
less than their opponent, and an advantage has not been gained at the free throw line (Oliver,
2004).
While effective field goal percentage has been taken on by many as the best way to
determine who the most effective scorers are in the game, there is still room for improvement

24. 24
and debate (Smith, 2013). Again, the purpose of effective field goal percentage is to account for
the added value of a three point shot (three points rather than two points). However, as Smith
(2013) points out, the formula allows for players to shoot over 100 percent. When looking at the
formula: Effective Field Goal Percentage = Field Goals + 0.5 (3­Point Field Goals)) / Field
Goal Attempts, we see a flaw in that the denominator or the field goal attempts is not adjusted
to account for three pointers made (Smith, 2013). As Smith (2013) shows, this means that when
J.J. Redick went 4 for 4 from the field, and 5 for 6 from the three point line against the Pistons
his effective field goal percentage = 9 + 0.5 (5)/ 10 giving Redick an effective field goal
percentage of 115% for the night. For Smith (2013) this idea of shooting over 100 percent
represents a fundamental flaw with a framework where you can be better than perfect, especially
when you miss a shot. One drawback of effective field goal percentage is that it does not factor
in free throw shooting (Smith, 2013). This is where True Shooting Percentage tries to factor in
all elements of scoring through the formula: True Shooting Percentage = Points/ (2 (Field
Goal Attempts + 0.44 X FTA)) (Basketball­Reference, 2002; Hollinger, 2005; Smith, 2013). It
gives free throws a weight of .44 which is used to denote the amount of times a free throw results
in a possession (Smith, 2013). This .44 number might more accurately reflect possessions
gained, but it does not give a more accurate picture of a player’s scoring ability (Smith, 2013).
The formula also can have a player shoot over 100 percent as we see again in the same Redick
example; 26/ (2 ( 10 + 0.44 X 4) = 111% ( Smith, 2013). Smith (2013) offers up a formula he
refers to as Weighted Field Goal Percentage which he states is a superior alternative to both
measurements. The way the metric works is it gives free throws a weight of one, two point
attempts a weight of two, and three point attempts a weight of three (Smith, 2013). This system

25. 25
assigns intuitive value to each type of shot (Smith, 2013). The formula also factors in attempts
for each type of shot so that it is impossible to exceed 100 percent (Smith, 2013). The way the
formula looks is: Weighted Field Goal Percentage = (FT X (3/9)) + ((FG ­ 3ptFG) X (6/9)) +
(3ptFG) / (FTA X (3/9)) + ((FGA ­ 3ptFGA) X (6/9) + (3ptFGA) (Smith, 2013). With
Redick’s big night, after we plug in his numbers from the box score into the formula, he achieves
a Weighted Field Goal Percentage of 87 percent (Smith, 2013). We see a system that values three
point shots more than two point shots, while also factoring in free throws (Smith, 2013).
However, while the formula gives more weight to a three point make it also punishes a shooter
more for a three point miss (Smith, 2013). The reason for this is to make it impossible for the
shooter to shoot over 100 percent (Smith, 2013). However, is this an accurate reflection of a
game? While shooters are awarded more points for a made three, is a missed three anymore
harmful to a team than a missed two? In actuality a missed three is more beneficial than a missed
mid­range two point shot as it is more likely to result in an offensive rebound and thus the
maintenance of the possession (Goldsberry, July 2012). This results in the player being punished
more for a missed three in Weighted Field Goal Percentage, which fails to accurately reflect the
value of a missed shot. We have taken strides in our understanding of a player’s ability to score
the basketball through various mathematical formulas. However, each formula or metric has
limitations and drawbacks that fail to fully capture each player’s true scoring ability through the
various shots taken.
To most, the quantitative data presented in a box score is easy to understand. Most
coaches would understand that if Tim Duncan made 5 of 10 field goal attempts he would have
scored 10 points and shot 50 percent from the field. The exception is the inclusion of plus/minus

26. 26
in the box score, which is a relatively new measurement. The plus/minus system was designed
by Wayne Winston and Jeff Sagarin, who were looking for a way to more accurately
quantitatively determine a player’s value (Oliver, 2004). Plus/minus however, serves as a prime
example of the importance of context when viewing quantitative data (Oliver, 2004).
The plus/minus system serves to calculate the running score when a player is on the floor
(Kubatko et. al., 2007). For example, if Tim Duncan was on the floor for the first six minutes of
the game and the Spurs went up by 20 points before he checked out than he would have a
plus/minus of plus 20. His plus/minus would then be untouched, regardless of what happened in
the game, for as long as he was on the bench. When Duncan checks back into the game his
plus/minus starts at 20 and will then be effected by what happens in his upcoming minutes on the
floor. The positive of plus/minus is that it is an attempt to quantify how much an individual
player contributes or hurts their team by accounting for the value of of screens, spacing, team
defense, and all of the other factors that go into a player's impact on the game (Kubatko, et. al.
2007).
The problem with plus/minus as a player rating system is that it often does not pass what
Oliver (2004) or Alamar (2013) would refer to as the “laugh” or “eye” test. For example Andrei
Kirilenko accumulated a higher plus/minus rating than Shaquille O’Neal, while Kirilenko was a
rookie and Shaq was in his prime (Oliver, 2004). The system requires a great deal of context in
order to understand the numbers (Kubatko et. al. 2007; Oliver, 2004). If we examine the Spur’s
box score (Figure 2.) we can start to see some of the limitations of this measurement. Take the
example of Tony Parker who is arguably the best player on the Spurs yet he only managed to
accumulate a plus/minus rating of plus 1. This is one of the lowest ratings on the team, and even

27. 27
more alarming considering they defeated Miami by 17 points. If Popovich was to put a lot of
weight into Parker’s relatively low plus/minus he might opt to distribute some of Parker’s
minutes to Ginobili (plus 21 in the game). However this would be failing to put the numbers in
context by examining the reasons behind the numbers, a crucial component of analytics (Alamar,
2013 ; Kerr, et. al., 2014). Ginobili does not start, and he comes off the bench so he is likely
playing a majority of his minutes against weaker competition than Parker. On top of this, the
2013­2014 Spurs team had well documented depth which would foster an opportunity to build up
leads against the other teams bench players. Furthermore, due to Parker’s role of being a focal
point of the offense he is most likely being used to bolster lineups with lesser talent in order to
give the more valuable players on the team rest. In these instances of playing with lesser talent,
Parker would most likely have to up his usage which leads to a decrease in efficiency, and he
would have to operate with a defense that is more zeroed in on taking away quality opportunities
from him (Oliver, 2004; Lowe, March 2013). There are a host of other factors that could explain
why Ginobili was able to accumulate a higher plus/minus than Parker, but these various factors
help demonstrate the limitations of plus/minus in trying to determine a player’s value (Kubatko
et. al. 2007; Oliver, 2014).
A box score also provides enough quantitative data to begin a more in­depth analysis of a
game and individual players (Hollinger, 2005; Oliver, 2004). The first thing that a box score does
is to provide measurements for one game (Oliver, 2004). This provides an accurate picture of a
player and a team’s performance on that given night, while accounting for the natural ebbs and
flows of a basketball game (Oliver, 2004). The data from multiple box scores can then be used in

28. 28
order to increase the sample size which in turn increases the reliability of the chosen
measurements (Alamar, 2013).
One example of a more in depth analysis using quantitative data from a box score is
Memphis Grizzlies Vice President of Basketball Operations John Hollinger’s (2005) Player
Efficiency Rating (PER). The PER rating uses the data from a box score to better understand a
player’s true value (Hollinger, 2005). While the PER system has limitations, as all metrics do, it
aims to quantify a player’s overall value (Hollinger, 2005).
The first thing the PER metric does is it assigns a value to the quantitative data collected
through a box score (Hollinger, 2005). While the value attached to the data is subjective,
Hollinger (2005) provides a sound rationale for his assigned values. The assist is what Hollinger
(2005) notes as the most challenging piece of data to determine the value for. Part of the reason
for this is due to the fact that all other statistics presented in a box score are easy to recognize in
a game, where an assist has a measure of subjectivity (Hollinger, 2005). Furthermore, all assists 5
are not created equal (Hollinger, 2005). A pass that gives a player a high probability of making a
basket is more valuable than a pass that requires a player to make a difficult shot (Hollinger,
2005). This is different than data such as made baskets, where the value of a make or a miss is
always the same (Hollinger, 2005). The other issue with assists is that credit is not awarded for
passes that result in a player getting fouled (Hollinger, 2005). With all of these limitations
associated with the assist measurement, Hollinger (2005) assigns a value of 0.67 to all assists.
5
The NBA (2002) definition of an assist as: “a pass that directly leads to a basket. This can be a pass to the
low post that leads to a direct score, a long pass for a layup, a fast break pass to a teammate for a layup,
and/or a pass that results in an open perimeter shot for a teammate. In basketball, an assist is awarded only
if, in the judgement of the statistician, the last player's pass contributed directly to a made basket. An
assist can be awarded for a basket scored after the ball has been dribbled if the player's pass led to the field
goal being made.” There has been many accounts where people have questioned the statisticians decision
to award an assist. One example is Nick Van Excel’s 23 assist night in 1997.

29. 29
His logic behind doing this is that a made basket “consists of three actions: the pass, the shot, and
the act of getting open. The scorer does two of them so he gets two­thirds of the credit”
(Hollinger, 2005, p. 6). Hollinger’s (2005) decision to give all assists equal value has merit due
to the fact that someone who is able to put their teammates in a position where there is a high
probability of that player scoring is more likely to have their passes turn into assists.
Hollinger (2005) calculates the value of a field goal as: field goal value = field goals
made x {2­(team assists/team field goals x .586)}. A field goal is worth two points but he
accounts for the fact that some shots are assisted (Hollinger, 2005). He uses the player’s team
average for assists to determine the amount of assisted shots (Hollinger, 2005). In the 2004 ­
2005 NBA season the league average was 59.2 percent, and he applies that number to the
formula (Hollinger, 2005). Using a team average rather than having the numbers for individual’s
number of assisted shots is a limitation as it fails to account for individual differences in players
(Hollinger, 2005). We also see the shooter getting two­thirds of the value of a made field goal if
a shot is assisted, for the same reason that an assist is worth one­third the value of a made shot
(Hollinger, 2005). In the same way, the value of an assist accounts for the fact that players are
not awarded assists when they make a pass that results in a shooting foul, the value of a field
goal must do the same (Hollinger, 2005). Hollinger (2005) believes that fifty percent of free
throws were assisted in the 2004­2005 season. This results in Hollinger (2005) creating an assist
for 29.6 percent of every made field goal. In order for the values to add up, the 29.6 percent
needs to be subtracted from made field goals (Hollinger, 2005). During the 2004­2005 NBA
season for every made free throw there were 1.82 made field goals (Hollinger, 2005). With the
.296 assists that are awarded for a made free throw, it results in Hollinger (2005) having to

30. 30
subtract (0.296/3.64) or .081 assists for a made field goal. The end result is the assist factor for
this particular year is 0.586 instead of 0.667 (Hollinger, 2005). Using this formula, each field
goal has a value of roughly 1.65 points (Hollinger, 2005). Three pointers use the same formula
except one point is added, as the extra value of the shot is accrued through the shooter
(Hollinger, 2005).
While free throws are worth a point in the game, again Hollinger (2005) accounts for the
belief that half of free throws are assisted. Hollinger (2005) determines the value of a free throw
using the formula: free throw value = free throws made x .5 x {1 + (1­ team assists/team FG)
+ (team assists x 0.67/ team FG)}. This results in made free throws being worth roughly 0.9
points (Hollinger, 2005).
The value of a turnover is equal to the value of a possession (Hollinger, 2005). Since a
turnover is a lost possession, the expected value of the possession is subtracted from the total
(Hollinger, 2005). Hollinger’s (2005) formula is: Turnover value = ­(value of a possession x
turnovers). During the 2004­2005 NBA season the value of a possession was 1.04 points, thus
the turnover value would be ­1.04 points (Hollinger, 2005).
While a missed field goal is similar to a turnover, there is the possibility that the
offensive team can maintain possession (Hollinger, 2005; Kubatko et. al. 2007). This results in
both the value of a possession and defensive rebounding percentage having to be factored into
the formula (Hollinger, 2005). Hollinger’s (2005) formula is: Missed field goal value =
­(missed field goals x league value of possession x defensive rebounding percentage). During
the 2004­2005 season the league defensive rebounding percentage was 71 percent, thus the value
of a missed field goal was roughly negative 0.72 points during that season (Hollinger, 2005).

31. 31
A missed free throw is similar to a missed field goal, except there are a few additional
factors that need to be considered when determining their value (Hollinger, 2005). Since only 56
percent of free throws can be rebounded, due to first shot attempts and technical fouls, the effect
of a miss is reduced (Hollinger, 2005). Furthermore, free throws take up 0.44 possessions, a
much lower percentage than other shot attempts (Hollinger, 2005). The formula to determine the
value of a missed free throw is: Missed free throw value = ­ {Missed free throw x value of
possession x 0.44 x [0.44 + (0.56 x defensive rebounding percentage]} (Hollinger, 2005). The
result is a missed free throw was equal to ­0.38 during the 2004­2005 NBA season (Hollinger,
2005).
Since an offensive rebound erases the negative impact of a missed shot, the formula just
requires the negatives to be taken away from the missed field goal formula (Hollinger, 2005).
This equals: Offensive rebound value = Offensive rebounds x value of possession x defensive
rebounding percentage (Hollinger, 2005). The result is that an offensive rebound had a value of
roughly 0.72 points during the 2004­2005 season (Hollinger, 2005). This might not assign
enough value to an offensive rebound as shooting percentages increase on shots that occur
immediately after an offensive rebound (82 games, 2004). While this increased value will show
up as a field goal made, the ability to secure an offensive rebound correlates with a higher
probability of a team scoring on that possession and thus should be represented as more valuable
than a typical possession. Hollinger (2005) gives much more value to an offensive rebound than
a defensive rebound because of how much more challenging it is to gain an offensive rebound
versus a defensive rebound. However, he does not account for the higher probability of scoring
on a possession where an offensive rebound has occured (82 games, 2004).

32. 32
A defensive rebound concludes a successful defensive possession (Hollinger, 2005).
Hollinger (2005) argues that “a missed shot plus a defensive rebound should add up to the value
of one possession” (p. 7). The result is the following formula: Defensive rebound value =
defensive rebounds x value of a possession x (1­ defensive rebound percentage) (Hollinger,
2005).
The only two defensive measurements in the box score are steals and blocked shots.
Hollinger (2005) argues that a steal results in a turnover so it has the converse worth of a
turnover. This results in the PER formula for a steal being: Steal value = (steals x value of
possession) (Hollinger, 2005). Morris (2014) argues that this grossly underestimates the value of
a steal, which he proclaims to be the most “informative” statistic. Morris (2014) used an
empirical technique where he tested the differences between all of the players who played at
least 20 games in a season, the missing statistics or contributions for when an eligible (played 20
games) player missed a game, and what the impact was on the team’s capacity to win the game
for all seasons from 1986 to 2011. What Morris (2014) finds using this technique is that one
steal has the same value as 9.1 points scored. While some of the often cited reasons for the value
of a steal are that they take away a shot attempt from your opponent and lead to fast break
opportunities, Morris (2014) argues that a steal has a higher degree of “irreplaceability” not seen
in other statistics (Oliver, 2004). Morris (2014) argues that this is due to the fact that in an NBA
game there will be a certain amount of opportunity provided to score points, collect rebounds,
and accumulate assists regardless of who is on the floor, where a steal is something that is only
likely to occur if you have people who are skilled at getting steals. While in an NBA game this is
probably more true, due to the fact that everyone is fairly competent at scoring the ball, at lower

33. 33
levels there is probably a higher level of irreplaceability associated with statistics such as points
due to the possible increased variations in abilities. Furthermore, in NBA settings the level of
replaceability would have to be contextualized to the team’s system and the players on the given
team (Morris, 2014). However, Morris (2014) through his empirical tests presents an interesting
examination that assigns a much larger value to a steal than Hollinger’s PER.
A blocked shot, Hollinger (2005) argues, has the same effect as an opponent’s missed
shot. The formula that comes out of this logic is: Blocked shot value = (blocks x value of
possession x league defensive rebounding percentage) (Hollinger, 2005). The thing that does
not get factored into Hollinger’s formula is the fact that a blocked shot is more likely to result in
the offensive team maintaining possession than a defensive rebound (82 games, 2003). If
Hollinger could get the league averages or player averages for the likelihood of a team gaining
possession after a blocked shot, it would more accurately represent the value of a blocked shot.
Personal fouls are the final box score statistic used to determine a player’s PER
(Hollinger, 2005). The formula for personal foul value is: Personal foul value = ­{fouls x
[league average free throw makes per foul ­ (league free throw attempts per foul x 0.44 x
league value of possession)]} (Hollinger, 2005). The 0.44 is the value that was determined for a
free throw based on the 2004 ­ 2005 NBA season (Hollinger, 2005). Using this formula we see a
foul can have value to a team if there is a positive difference between the points scored as a
result of a foul and what a team would expect to score on the number of possessions those fouls
used (Hollinger, 2005).
In order to compare players who play different minutes, we must divide by the total
minutes played (Hollinger, 2005). This is done to account for the fact that a player who receives

34. 34
more playing time has an increased opportunity to accumulate positive or negative statistics
(Hollinger, 2005). If you are calculating PER for players on various teams then it requires you to
factor in a team’s pace in order to get a more accurate understanding of a player’s value
(Hollinger, 2005). This is due to the fact that teams who play at a faster pace have the
opportunity to accumulate more statistics in a game because of the increased number of
possessions (Hollinger, 2005). A team that uses the majority of the shot clock on each possession
versus a team that uses one third of the short clock on each possession will have fewer
possessions in a game and thus it would be an oversight not to account for this when comparing
players on different teams (Hollinger, 2005).
Hollinger’s (2005) final step is to “set the ratings to a league average of 15.00” (p.8).
Setting the rating provides an average in order to better understand a player’s value (Hollinger,
2005). This allows for more accurate comparisons to be made between players who played at
different times in the same league (Hollinger, 2005). For Hollinger (2005), who compares
players from different generations in the NBA, this is a useful tool, as pace of play and strategies
change over time. One example of this would be how teams use the three point line (Grantland,
2014).
Hollinger’s (2005) final PER formula is:
Player Efficiency Rating (PER) = (League Pace/Team Pace) x (15.00/ League average) x
(1/minutes played) x [3­pt. FG + (Assists x 0.67) + (FG made x {2 ­ [(team assists/team FG)
x 0.586] }) + (FT made x 0.5 x {1 + [1 ­ (team assists/team FG)] + [(team assists/team FG) x
0.67]}) ­ (Value of Possession x turnovers) ­ (Missed FG x VOP x league DRB%) ­ {Missed
FT x VOP x 0.44 x [0.44 + (0.56 x league DRB%)]} + [Def. rebounds x VOP x (1 ­ league
DRB%)] + (Off. rebounds x VOP x league DRB%) + (steals x VOP) + (blocks x VOP x
league DRB%) ­ {fouls x [league FT makes per foul ­ (league free throw attempts per foul x
0.44 x VOP)]}]

35. 35
In the PER metric we see a valuable tool that looks to quantify a player’s overall value.
What Hollinger (2005) and other analysts would argue is that PER should be used in conjunction
with other information inputted into the analytics framework, and is not to be used as a be all end
all (Alamar, 2013). While Hollinger (2005) provides a sound rationale for his assigned values for
certain statistics, it is important to remember that these values are the result of complex factors
and strong arguments can be made that he has improperly weighted certain statistics (Morris,
2014). What Hollinger (2005) outlines is that PER fails to measure individual defense outright,
and falls short in quantifying a player’s defensive impact. This is partially due to the lack of
defensive data provided through a box score (Goldsberry and Weiss, 2013; Hollinger, 2005). The
PER model is only one example of a “box­score­based player evaluation composite statistic”
(Myers, 2012). Other valuable composite statistics include Justin Kubatko’s “Win Shares”,
Dave Berri’s “Wins Produced”, and Daniel Myers “Advanced Statistical Plus/Minus” (Myers,
2012). Each one of these metrics has different rationales for their assigned values in looking to
determine a player’s overall value. Through such metrics we see how analysts look to quantify a
player’s overall value through the data provided in a box score.
Other Ways to Collect Data
While the box­score provides us with a lot of data to work with, decision makers and
analysts have sought out new data in order to strengthen their understanding of the game.
Specifically, the box­score fails to glean much light on a player's defensive impact as well as
spatial components of the game (Hollinger, 2005; Oliver, 2004; Lowe, 2013). This quest to
collect new data, and the evolution of how we interact with this data has only further enhanced

36. 36
our understanding of what leads to success on the basketball court in general and in specific
situations (Lowe, 2013, 2014).
Dean Oliver (2004) is the person who many people refer to as the “Godfather of
basketball analytics.” What Oliver (2004) did that was unique was he began collecting new
forms of data in the late 80’s through coding or using shorthand to record the actions of the game
on paper. Oliver’s (2004) basketball notes reflected actions that occurred with the ball and the
various players who interacted with the ball. An example of Oliver’s (2004) shorthand from
game 4 of the 1997 NBA Finals: “11 UTA 3RD / 12 14 32 12++R” (p. 12). In Oliver’s (2004)
code each possession is denoted a line that explains specific actions that occurred on that
possession. In this particular example we see that Utah has 11 points at this stage of the game,
denoted by the 11 and the UTA which is short for Utah (Oliver 2004). The ball was rebounded
by number 3 which we know through the “R” who then dribbles the ball, shown by the “D,”
across half court, which is shown by the “/” (Oliver, 2004). 3 then passes the ball to 12, who
passes to 14, who then passes to 32 (Oliver, 2004). We know the ball has been passed as the
number changes which represents the player in possession of the basketball (Oliver, 2004). 32,
otherwise known as Karl Malone, posts up which is shown by having his number underlined
(Oliver, 2004). Malone passes to number 12, or John Stockton, who scores a right handed layup
(Oliver, 2004). A “+” sign designates a made shot and a double “++” shows that shot was
assisted (Oliver, 2004). We know that Stockton finished with a right handed layup because at the
end of the “+” sign we see a small “R” (Oliver, 2004). Where if it had been a left­handed layup
we would have seen a small “L” (Oliver, 2004). If we look at another example of Oliver’s (2004)
recorded possessions we can see new symbols appear in the shorthand: “ 8 CHI 33 / 9D 23D­3

37. 37
13R­L 13F12(1) 23 91 33 9 23D­B” (p. 12). In this example we see that Chicago has 8 points
(Oliver, 2004). 33 passes the ball across halfcourt to 9, who dribbles and passes to 23 (Michael
Jordan) who then dribbles and shoots the ball from somewhere inside the three point line on the
right side of the floor and misses (Oliver, 2004). We know that Jordan misses the shot which is
indicated by the “­” and we know the location indicated by the “3” (Oliver, 2004). If you look at
Figure 3 you can see Oliver’s (2004) court areas in order for him to more accurately record
where shots are occurring. Jordan’s shot is then rebounded by number 13 who misses a left
handed layup and then after the rebound is fouled by 12 (Oliver, 2004).
Figure 3. (Oliver, 1991)
We know that 12 committed his first foul with the “F” representing the foul the “12” being the
player who committed the foul, and the “(1)” indicating the number of fouls that player has
acquired (Oliver, 2004). We know that it is a non­shooting foul as no foul shots are taken which
would be indicated by a “X” for a miss and a “*” for a make (Oliver, 2004). The ball is inbounded
to 23 who passes to 91, who passes to 33, who pases to 9, who passes it back to 23 who then

38. 38
dribbles and shoots from somewhere above the free throw line and inside the three point line
(Oliver, 2004).
While we see a lot of information through these two possessions, Oliver (2004) also
notes: bad passes, steals, time outs, blocks, and when the ball gets knocked out of bounds in his
notes for each game (Oliver, 2004). We can see through coding each possession on paper that we
can gain a larger data set to work with and new insights into a game that a box­score does not
provide. One area of the game that becomes very apparent in Oliver’s (2004) code is the value of
a possession. 6
Stats LLC has developed a SportVU camera data collection system that will most likely
revolutionize the way we look at the game of basketball through the opportunity to interact with
a very rich set of quantitative data (Goldsberry, 2014; Lowe, March 2013). While people like
Oliver (2004) and Hollinger (2005) have noted some of the limitations associated with using
box­score statistics, the data gained through SportVU will most likely address many of those
limitations. This is due to the fact that the traditional challenge for analysts has been collecting
valuable data (Goldsberry, 2014). We are now in a new place where we have this very rich and
valuable data set but we have only begun to understand ways the data can be turned into
worthwhile information (Goldsberry, 2014). Through these new data sets there is a great
opportunity to gain a competitive advantage and inform the decision making process for those
who ask the right questions (Alamar, 2013).
In basketball, the SportVU system uses six cameras installed in the rafters of every NBA
arena to collect data (NBA Stats ­ Player Tracking). The cameras capture each moving
6
For a more comprehensive look at Dean Oliver’s coding system see pages 8 to 27 in: Oliver, D. (2004).
Basketball on Paper. Washington, D.C.: Potomac Books, Inc.

39. 39
component on the court, including the players, the ball, and the referees, 25 times per second
(Alamar; 2013; NBA Stats ­ Player Tracking). This location based data, gives NBA analysts a
large amount of quantitative information to work with as they gain 72,000 observations on their
team alone during a game (Alamar, 2013). The cameras are capturing everything that is taking
place on the court: “how far and how fast a player runs during the game, how many dribbles he
takes when he has the ball, where he shoots from, the arc of his shot, whom he’s passing to,
whom he’s not passing to, the spots where he gets his rebounds, (and) the spots where others get
his rebounds” (Schwartz, 2013). 7
So these NBA analysts now have a large amount of quantitative data based on spatial
components of the game, but what do they do with it? Unfortunately for the public, the most
innovative ways this data is being used, is most likely occurring behind the closed doors of NBA
organizations (Schwartz, 2013). This makes sense, as the reason these NBA teams are interested
in analytics is to gain a competitive advantage over their opponents. However, these teams have
most likely only scratched the surface on ways to effectively use the data (Goldsberry, 2014 ;
Schwartz, 2013). People such as Oliver, now believe we have the quantitative information,
thanks to SportVU, to answer the tough questions about the game that we traditionally have not
been able to answer (Schwartz, 2013). It is going to require analysts to ask the right questions
and to contextualize the information appropriately, but there is now an opportunity to gain
insight into the game that previously was not possible (Alamar, 2013;Schwartz, 2013).
With that being said, through specific NBA organizations opening up their doors on ways
they use SportVU, Stats LLC presenting ways their data can be used, and analysts without ties to
7
To see SportVU cameras in action watch the following video: Stats LLC (January, 9 2014). SportVU NBA
[Video File]. Retrieved from: http://www.youtube.com/watch?v=jOQEl_tkEwE.

40. 40
NBA teams gaining access to the data, the public can gain greater insight into what contributes to
success on the court (Alamar, 2013; Lowe, March 2013). One example is the new statistics
provided through “stats.nba.com.” Examples of statistics provided on the website thanks to the
SportVU technology include: speed and distance, touches/possession, passing, defensive impact,
rebounding opportunities, drives, catch and shoot, pull up, and shooting efficiency (NBA Stats ­
Player Tracking). Touches/possession is an example of a measurement that shows where every
player is receiving the ball (very broad areas such as within 12 feet of the basket or more specific
areas such as elbow touches), and how many times the player gains possession of the ball (NBA
Stats ­ Player Tracking). From this data they are able to easily figure out how many points occur
per touch by dividing points per game by touches per game (NBA Stats ­ Player Tracking). If we
look at the statistic “rebounding opportunities” we see an attempt to better quantify a player’s
rebounding ability (NBA Stats ­ Player Tracking). A common critique of the rebounding statistic
is that many players will steal rebounds from teammates in the hopes of padding their
rebounding totals (The Lowe Post, 2014). One way the new measurement looks to delineate
between less valuable rebounds is by determining whether or not a rebound was contested (NBA
Stats ­ Player Tracking). A contested rebound is one where an opponent is within 3.5 feet of the
ball (NBA Stats ­ Player Tracking). So we can now look at this statistic to determine how
effective a player is at rebounding when there is a reasonable chance of their opponent gaining
possession of the ball. Furthermore, we can see how many uncontested rebounds a player is
collecting or how many of those rebounds a player is deferring to a teammate (NBA Stats ­
Player Tracking). This statistic also has value in that it factors in a player’s position or where
they play on the floor. A player who plays near the basket is more likely to have more

41. 41
opportunities to rebound the ball versus someone who plays away from the basket. Through the
rebounding opportunities measurement, we can now begin to quantitatively examine whether
someone who collects less rebounds than another player is better at rebounding based on the
number of available chances. While this statistic provides more insight into the complex issue of
rebounding, it still falls well short of measuring a player’s total contribution to this component of
the game. For example, it fails to take into consideration the player who properly boxes out their
check and thus frees their teammate to acquire the rebound. This player who boxed out may have
had the largest impact on gaining possession of the ball but in no way is this represented in the
measurement.
One example of a much more complexed and insightful use of the data is the “expected
point value” measurement (Cervone, D’Amour, Bornn, & Goldsberry, 2014). As Cervone et. al.
(2014) notes, an offensive basketball possession consists of many decisions that either increase
or decrease the likelihood of a team acquiring points. Decisions can be made well before the
eventual points are scored that dramatically increase the value of a possession, yet statistics such
as points and assists only account for those final moments of a possession failing to take into
consideration other actions that may have been more important to acquiring points (Cervone et.
al., 2014). That is the issue the “expected point value” model or “EPV” looks to address using
the data gleaned from the SportVU cameras (Cervone et. al., 2014). The EPV model takes into
consideration the skill set of every player on the floor, the positioning of the players, and which
player has the ball, to determine the expected amount of points that possession would yield
(Cervone et. al., 2014). Goldsberry (2014) explains, you are essentially pausing the game at any
moment to get a glimpse at how many points you could expect for that possession based on the

42. 42
positioning of the players and the ball at that time. Figure 8 is an example of a San Antonio
Spurs possession that has been paused and the expected point value at that time (Cervone et. al.,
2014).
Figure 4. (Cervone, D’Amour, Bornn, Goldsberry, 2014).
In order to determine the values, Cervone et. al. (2014) use a Markovian assumption to develop 8
what they call a possession model. The possession model calculates the likelihood of the player
with the ball making a certain decision and the EPV of the possession if that particular decision
is made (Cervone et. al., 2014). We see in figure 8 the probability of Leonard shooting or passing
8
The Markovian assumption calculates the probability of going from a current state to another state (Markov
Processes, 2012; Gauss­Markov, 2013). All possible states or outcomes must be considered in order to use
the Markovian assumption framework (Markov Processes, 2012; Gauss­Markov, 2013). For a more in depth
look at the math need to use a Markovian assumption see: Ben Lambert (May, 28 2013). Gauss­Markov
assumptions part 1 [Video File]. Retrieved from: http://www.youtube.com/watch?v=NjTpHS5xLP8. and Ben
Lambert (May, 28 2013). Gauss­Markov assumptions part 2 [Video File]. Retrieved from:
http://www.youtube.com/watch?v=ti9h­Au8LQw.

43. 43
and how it affects EPV. Also considered in the model is the probability of dribbling to another
area of the floor or towards the basket, a turnover, and the resulting impact on EPV (Cervone et.
al., 2014). Cervone et. al. (2014) explain the relevance of EPV through the opportunity to
examine “decision­making, opportunity creation and prevention, and optimal
responses that were not possible before” (p. 2). By examining how EPV changes over the course
of a possession we can gain insight into how a player’s, or players’, actions alter the expected
outcome of a possession (Cervone et. al., 2014). If we examine Figure 5 we can see how Tony
Parker’s ability to dribble into the paint increases the expected value of the possession (Cervone
et. al., 2014). With Parker in possession of the ball at the top of the three point line with 0.86
EPV, he is able to use Tim Duncan’s screen to get deep into the paint to increase the EPV to 1.36
Figure 5. (Cervone, D’Amour, Bornn, Goldsberry, 2014).
(Cervone et. al., 2014). Parker’s ability to draw the defense off their checks is accounted for
when he makes the pass to Leonard who is standing open for the corner three (the most valuable
shot in basketball) resulting in the EPV spiking at 1.75 (Cervone et. al., 2014). Leonard’s

44. 44
defender is able to close some of the distance which results in the EPV dropping to 1.58 at the
time of his shot (Cervone et. al., 2014). While Leonard hit the shot, we can see all of the value
that Parker added to the possession through dribble penetration deep into the painted area
(Cervone et. al., 2014). Cervone et. al. (2014) compares the continuous measurement of EPV to
the stock ticker. Through EPV we can gain insight into the value of an offense at any given time,
while a stock ticker allows for you to gain insight into how a company and investor actions
impact a business at any moment (Cervone et. al., 2014). Through EPV we can more effectively
evaluate how a player’s actions increase or decrease the value of an offense (Cervone et. al.,
2014). Furthermore, this value is accounted for regardless of the eventual outcome (Cervone et.
al., 2014). For example, in Figure 5 Parker dramatically increases the value of the possession
through his dribble penetration and his pass (Cervone et. al., 2014). This value is accounted for
regardless of whether or not Leonard hits the shot (Cervone et. al., 2014). If we were only using
traditional statistics, Parker would only receive credit for his actions in the form of an assist if
Leonard made the shot (Cervone et. al., 2014). The EPV framework opens up the opportunity to
more accurately measure the value that certain players, lineups, formations, and actions have on
a team’s offense (Cervone et. al., 2014).
Houston Rockets General Manager, Daryl Morey, points out that SportVU allows for
previously unmeasured areas of the game and contributions that coaches have valued to be
quantified and confirmed (Milton Lee, 2014). EPV through the measurement of decision making,
and actions that increase the likelihood of more points, but precede made baskets, is an example
of how SportVU is allowing us to measure the previously unmeasured. The Toronto Raptors
application of EPV to defensive positioning serves as another example of an area of the game

45. 45
coaches value but has not been effectively measured until now (Hollinger, 2005; Lowe, 2013;
Oliver, 2004). What the Raptors have done is designed a slightly more comprehensive EPV
model through a code that uses the X­Y data provided by SportVU that considers factors such as:
a player’s height, a player’s likelihood of scoring in particular situations such as a catch and
shoot, certain actions occurring on the floor such as a ball screen, the value of certain shots, team
tendencies, and the position of all these players on the floor at any given time (Lowe, 2013). The
code then factors in the Raptors defensive scheme to create “ghost” players that provide a visual
representation of where the coaching staff and analytics team believe the players should be
positioned based on the various factors that were stated (Lowe, 2013). These ghost players are
represented by transparent circles where the actual Toronto players are represented by solid
white circles (Lowe, 2013). This allows for the Raptors organization to assess a player’s 9
capacity to be in the right location (Lowe, 2013). One finding that the Raptors have found
through the use of their ghost system, is that almost every NBA team fails to provide what they
would determine to be the ideal amount of help defense (Lowe, 2013). The reason the Raptors
organization believe this to be the case is due to the players notion that they do not want their
check to score (Lowe, 2013). On top of this, it requires a high level of effort to provide so much
help to your teammates and then recover back to your check (Lowe, 2013). The ghost system is
using the EPV framework as the possession develops, in the same way as we saw with the Parker
example but applying it to where the defensive players should be (Lowe, 2013). With the EPV
measurement there is the opportunity for the Raptors analysts to explore what the perfect defense
would look like and not consider the Raptors coaches current defensive system (Lowe, 2013).
9
To view a possession of the Raptor’s ghost system see: Zach Lowe (March, 18 2013). NYKTOR [Video
File]. Retrieved from: http://www.youtube.com/watch?v=5Sq_Z6Um3UM.

46. 46
This however would require the decision makers, the Raptors coaches, to be open to such an
idea, which based on Lowe’s (2013) article does not appear to be a reality at the moment
(Alamar, 2013).
Related to this notion of the ideal defensive position being a representation of the threat
that particular players or actions represent to their team with expected value of a possession at
any given time, is the idea of “gravity.” As Zach Lowe (July 2014) notes, due to Kyle Korver’s
incredible shooting ability, teams and players are afraid of him getting his hands on the ball with
enough space to get a shot off. This fear is measured by a new measurement provided by Stats
LLC through the use of their SportVU cameras, called “gravity” (Lowe, July 2014; Pelton,
2014). A player’s gravity score is a measurement of how much attention a player receives when
they do not have the ball, through measuring the distance between the given player and their
check (Lowe, July 2014; Pelton, 2014). A player’s distraction score is the amount of attention a
player receives from the defense when they have the ball, by measuring how much the four
players off the ball are drawn off their check and towards the given player (Lowe, July 2014;
Pelton, 2014). This idea of gravity is something that coaches are extremely cognisant of
(Pelton, 2014). Coaches are trying to have players operate on the floor in areas where they have a
high amount of gravity (Pelton, 2014). The reason for this is simple, if a player is operating in an
area of the floor where they do not have a large amount of gravity, that frees their defender to
help on other players who are a larger threat to score. Furthermore, having players such as Kyle
Korver who have a large amount of gravity at the three point line opens up more space around
the basket, which has its own gravity, for teammates (Lowe, July 2014; Pelton, 2014). We hear
this principle of gravity being referred to constantly in the game of basketball when someone

47. 47
mentions a stretch four bringing rim protectors away from the basket, or a wing who is a poor
three point shooter who is clogging the paint for their teammates. With the gravity and
distraction measurement we now have a way to quantify a player’s ability to create space for
their teammates based on the attention they receive either with or without the ball (Lowe, July
2014; Pelton, 2014). This is extremely useful information for coaches who look to design
offenses that have good spacing which caters to a team’s ability to score the ball. Furthermore, it
helps to quantify someone like Tony Parker’s value, who attracts a considerable amount of
attention when he has the ball, due to his ability to get dribble penetration, making it so he can
put his teammates in a position to have success (Goldsberry, 2014). This new measurement
could be very informative for roster composition as coaches look to create the ideal amount of
space on the floor. For example, surrounding a player with a high distraction rating with players
with high gravity scores is going to result in defenders having to choose between being pulled in
towards the ball or staying out on shooters, a pick your poison scenario. While this idea of
gravity is probably quite intuitive for coaches, a more accurate understanding of the amount of
attention individual players receive may lead to better decision making.
Through these glimpses into a few ways NBA organizations and other analysts are using
the data provided by SportVU, we can see how spatial components of the game are becoming
quantified. These spatial components, such as a player’s gravity or positioning on defense, are
areas of the game that prominent analysts such as Hollinger (2005), and Oliver (2004) have
struggled to understand through numbers, mostly due to the lack of quality data available to
them. With these new data sets there is immense potential to further our understanding of what
contributes to success on the basketball court.

48. 48
Video
People often fail to consider video to be a part of the analytics framework (Alamar,
2013). When in fact video is qualitative data that is often needed to turn quantitative data into
useful information (Alamar, 2013). Through integrating structured qualitative and quantitative
data it results in increased clarity around the given issue or topic for the decision maker (Alamar,
2013).
In the same way that raw quantitative data is of little use to a decision maker, so too is
raw qualitative data (Alamar, 2013). For example ten recorded games of your opponent would be
considered raw qualitative data (Alamar, 2013). If you failed to process your video any further,
the usable information would be more time consuming to extract, making it more challenging to
turn video into a useful tool for a coach or other decision makers (Alamar, 2013).
In the past, video was typically processed through video coordinators observing the
games and tagging certain actions or areas of the game to later present to coaches or other
decision makers (Alamar, 2013). Now services such as “Synergy Sport Technology” code and
break the game up into play types for teams (Abbott, 2012). Synergy divides the offense into
certain types of plays, for example: pick and rolls, isolations, cuts, and dribble penetration
(Abbott, 2012). Synergy then calculates the points per possession that occur on each type of shot
for each individual and the league wide average in the NBA (Abbott, 2012). So quite quickly
someone like Abbott (2012) is able to look up the fact that isolation plays are the least efficient
play type in the NBA with 0.78ppp being the league average. Furthermore, Abbott (2012) is able
to quickly point to the fact that Kobe Bryant shoots below league average in isolation situations
in the last five minutes of the game with 0.5ppp per isolation play. Synergy also provides the