A New Framework to Estimate Return on Investment for Player

A New Framework to Estimate Return on Investment

for Player Salaries in the National Basketball

Association

Jackson P. Lautier

∗†

September 13, 2023

∗

Department of Mathematical Sciences, Bentley University

†

Corresponding to jlautier@bentley.edu.

arXiv:2309.05783v1 [q-fin.GN] 11 Sep 2023

Abstract

The National Basketball Association (NBA) imposes a player salary cap. It is therefore

useful to develop tools to measure the relative realized return of a player’s salary given

their on court performance. Very few such studies exist, however. We thus present the ﬁrst

known framework to estimate a return on investment (ROI) for NBA player contracts. The

framework operates in ﬁve parts. First, we decide on a measurement time horizon, such as

the standard 82-game NBA regular season. Second, we propose the novel game contribution

percentage (GCP) measure, which is a single game summary statistic that sums to unity for

each competing team and is comprised of traditional, playtype, hustle, box outs, defensive,

tracking, and rebounding per game NBA statistics. Next, we estimate the single game value

(SGV) of each regular season NBA game using a standard currency conversion calculation.

Fourth, we multiply the SGV by the vector of realized GCPs to obtain a series of realized per-

player single season cash ﬂows. Finally, we use the player salary as an initial investment to

perform the traditional ROI calculation. We illustrate our framework by compiling a novel,

sharable dataset of per game GCP statistics and salaries for the 2022-2023 NBA regular

season. Using only total GCP, we ﬁnd the top ﬁve performers to be Domantas Sabonis,

Nikola Joki´c, Joel Embiid, Luka Donˇci´c, and Bam Adebayo. With player salaries, however,

the top ﬁve ROI performers become Tre Jones, Kevon Harris, Nick Richards, Ayo Dosunmu,

and Max Strus. A scatter plot of ROI by salary for all players is presented. Notably, missed

games are treated as defaults because GCP is a per game metric. This allows for break-

even calculations between high-performing players with frequent missed games and average

performers with few missed games, which we demonstrate with a comparison of the 2023

NBA regular seasons of Anthony Davis and Brook Lopez. We conclude by suggesting uses

of our framework, discussing its ﬂexibility through customization, and outlining potential

future improvements.

Keywords: Load management, internal rate of return, IRR, most valuable player, NBA economics,

NBA ﬁnance, NBA proﬁtability, PVGCP

1 Introduction

On December 20, 2022, the Phoenix Suns of the National Basketball Association (NBA) in

combination with the Phoenix Mercury of the Women’s National Basketball Association were

purchased at a valuation price of $4 billion (Wojnarowski, 2022); the NBA is big business.

As in any ﬁnancial operation, it is of great interest to assess performance for the purposes of

allocating returns to investors or other parties with pecuniary interests. Among the many

ﬁnancial interests of NBA teams, such as ticket sales, television revenue, and merchandise

sales, there is the obvious consideration of compensating the players that make up each

team’s roster. This task is made complicated by a myriad of reasons, not the least of which

is that the NBA operates within a framework designed to restrict a free market. Indeed, a

crucial component of the competitive parameters of the NBA is a salary cap, which set a

minimum total salary of $111.290 million and a maximum total salary of $123.655 million

per team for the 2022-2023 NBA season (National Basketball Association, 2022), subject

to numerous additional restrictions (National Basketball Association, 2018). Thus, how to

eﬀectively allocate this ﬁxed total salary to on court personnel is a crucial component of a

team’s on court success.

It is natural, then, to suppose there exists a great number of studies that consider both

on court performance and salary simultaneously to arrive at methods to measure realized

return on investment (ROI) or the internal rate of return (IRR) of a player’s contract in view

of said player’s on court performance. A survey of related studies indicates that this is not

the case, however. Idson and Kahane (2000) attempt to derive the determinants of a player’s

salary in the National Hockey League with a model that incorporates the performance of

teammates. We consider the NBA, however, and our methodology diﬀers considerably (see

Section 2). Berri et al. (2005) identify the importance of height in the NBA and juxtaposes

it against population height distributions to explain competitive imbalances observed in

the NBA. Such imbalances are thought to negatively impact economic outcomes of sports

leagues (Berri et al., 2005). While ﬁnancial considerations enter into the analysis of Berri

et al. (2005), it does not concern the ROI of single players but rather professional leagues

overall. Tunaru et al. (2005) develop a claim contingent framework that is connected to an

option style valuation of an on ﬁeld performance index for football (i.e., soccer) players. Our

proposed method diﬀers materially, however, and we focus on basketball rather than football.

Berri and Krautmann (2006) ﬁnd mixed results to the question of whether or not signing

a long-term contract leads to shirking behavior from NBA players. The overall objective

of their study diﬀers meaningfully from that of our proposed realized ROI metric, however.

More recently, Simmons and Berri (2011) ﬁnd salary inequality is eﬀectively independent of

player and team performance in the NBA, a result that runs counter to the hypothesis of

fairness in traditional labor economics literature. In a related study, Halevy et al. (2012)

ﬁnd the hierarchical structure of pay in the NBA can enhance performance. Neither study

attempts to produce a contractual ROI, however. Kuehn (2017) assumes the ultimate goal of

each team is to maximize their expected number of wins to ﬁnd teammates have a signiﬁcant

impact on an individual player’s productivity. Kuehn (2017) subsequently reports that player

salaries are determined instead mainly by individual oﬀensive production, which can lead to

a misalignment of incentives between individual players and team objectives. Of note, the

salary ﬁndings of Kuehn (2017) correspond to those of Berri et al. (2007), a similar study.

Our forthcoming analysis diﬀers from all of these studies generally in that we do not attempt

to explain salary decisions and instead propose the ﬁrst known framework to measure the

realized return of a player’s contract in light of on court performance.

We do so by translating a player’s series of recorded regular season games in terms of on

court production (i.e., box score statistics, player tracking data, rebounding statistics, etc.;

see Table 1) into a series of realized cash ﬂows. This is done by our novel game contribution

percentage (GCP) player evaluation metric and a standard currency conversion calculation.

By treating the player’s salary as the initial time zero investment and using the converted

series of regular season games into realized cash ﬂows, we are able to calculate the realized

return using traditional ﬁnancial tools (e.g., Berk and Demarzo, 2007). We note that the

framework we propose considers all single game units separately, the importance of which is

well-known in canonical basketball treatments (e.g., Oliver, 2004, Chapter 16, pg. 192). In

other words, our approach treats any missed game as a zero cash ﬂow, which implicitly allows

us to quantify the cost of missing games (e.g., Figure 3). Furthermore, our GCP metric is

directly comparable between players, and it does not require standardization because it is a

per game metric (and thus already standardized). Finally, while we propose a contractual

ROI framework that is meant to be used directly, we also carefully note the ways the method

may be altered or enhanced to meet the needs of future analysts (e.g., the investment time

horizon need not be one regular season). That is, it is the framework we propose that is our

main contribution, and we take care to oﬀer suggestions for customization.

We proceed as follows. The bulk of the eﬀort is Section 2, in which we ﬁrst deﬁne and il-

lustrate the GCP method in Section 2.1, as well as contextualize its novelty within the current

landscape of basketball statistics. Next, we demonstrate how GCP may be used to complete

a ﬁnancial realized ROI calculation for each player in Section 2.2. Section 3 then performs

the realized calculations we propose for all players from the 2022-2023 NBA regular season.

We ﬁrst discuss the creation of a novel dataset that combines NBA player tracking data (Na-

tional Basketball Association, 2023d) with player salary information (HoopsHype, 2023). We

then present cumulative GCP results for the 2022-2023 NBA regular season, irrespective of

player salary, in comparison with other popular advanced NBA metrics to demonstrate the

utility of the novel GCP outside of the ROI framework. Section 3.3 then performs the real-

ized ROI calculations, and we report the top and bottom 50 performers, including a scatter

plot of ROI by salary. In support of reproducible research, the complete compiled data and

replication code may be found on a public github repository at https://github.com/jackson-

lautier/nba roi. Finally, the manuscript concludes with Section 4, which discusses how our

methodology may be utilized by NBA player personnel decision makers, NBA award voters,

and NBA governing bodies before closing with comments regarding a number of possibilities

to customize and improve upon our proposed ROI framework.

2 Methods

This is a lengthy two-part section. In Section 2.1, we introduce the GCP methodology. We

justify why a new metric is necessary despite a crowded landscape of on court statistical

evaluation methods, provide a formal deﬁnition and justiﬁcation of our approach, and close

with an illustrative calculation. In Section 2.2, we build on the work of Section 2.1 with

player salary data and standard currency conversation economic calculations to demonstrate

how the realized ROI may then be calculated using a ﬁnancial cash ﬂow framework.

2.1 Game Contribution Percentage

Recall the overall objective of our framework: converting a player’s series of recorded games

in terms of on court performance into a series of realized cash ﬂows. Because we may estimate

the dollar value of a single NBA game (see Section 2.2.1), i.e., a single game value (SGV),

it is left to allocate the SGV to each of the game’s active players. That is, a theoretically

ideal measure reports the true percentage contribution of each player per game (i.e., a game

contribution percentage). If we had such a measure, we could then imagine the counterfactual

of each team multiplying the SGV by the percentage contribution to ﬁnd the fair amount of

ﬁnancial compensation earned by each of the game’s participants, considering only on court

performance. Repeating this calculation for all recorded games over the chosen investment

horizon will therefore yield a series of CFs for all players, as desired. For ease of exposition,

we will assume the investment horizon to be the standard NBA regular season (i.e., we

desire to produce a series of 82 cash ﬂows for each player). This is for illustration only; the

measurement time horizon is a ﬂexible input into the framework.

Hence, we restrict all calculations to a contained single game unit. Indeed, the importance

of the single game unit is well-known (e.g., Oliver, 2004, Chapter 16, pg. 192), and it is thus

the most natural delineation of NBA performance units. Further, each game is treated as

a separate, contained entity by NBA league rules. In other words, margin of victory has

no bearing on regular season standings in the NBA as of this writing. This is a nuanced

point that warrants emphasis. We are interpreting a player contract as a debt instrument

of a single investment (i.e., the player salary) that obligates the player to produce 82 per

game payments. Because a player cannot contribute any more than the entire SGV within

a single game, missed games are treated as defaults or missed payments in our framework.

(This means that running season totals of GCP, such as those discussed in Section 3.2, allow

analysts to determine the exact inﬂection point of a dominant player that misses many games

versus a solid player that consistently plays; e.g., Figure 3.) In a further minor point, limiting

calculations to a single game and working in terms of percentages also helps somewhat oﬀset

issues from garbage time (e.g., Oliver, 2004, pg. 138), which may result in players inﬂating

their statistics, or the need for per possession standardization (e.g., Oliver, 2004, pg. 25).

Is a new metric necessary? Given what is available at present, we believe the answer is

aﬃrmative. Classical regression treatments, such as Berri (1999), do not perform calculations

on a game-by-game basis and have become dated in light of the advancements in data

availability (National Basketball Association, 2023d). Data advancements also rule out Page

et al. (2007), who ﬁt a hierarchical Bayesian model to 1996-1997 NBA box score data to

measure the relative importance of a position to winning basketball games. The same is true

for Fearnhead and Taylor (2011), who, in another Bayesian study, propose an NBA player

ability assessment model that is calibrated to the relative strength of opponents on the court

(via various forms of prior season data; Fearnhead and Taylor (2011) provide results for

the 2008-2009 NBA regular season). The work of Casals and Mart´ınez (2013), who ﬁt an

ordinary least squares (OLS) model to 2006-2007 NBA regular season data in an attempt

to measure the game-to-game variability of a player’s contribution to points and win score

(Berri and Bradbury, 2010), is closer in spirit but does not provide the level of box score

detail we require. In a promising study, Lackritz and Horowitz (2021) create a model to

assign fractional credit to scoring statistics for players in the NBA. Unfortunately, Lackritz

and Horowitz (2021) consider only oﬀensive statistics. Finally, the aforementioned Idson and

Kahane (2000) and Tunaru et al. (2005) do not consider basketball.

It also worth considering popular basketball metrics, such as NBA Win Shares (Sports

Reference LLC, 2022) based on Oliver (2004) or those summarized in Table 4 from Sports

Reference LLC (2023a). Despite the fair criticism of Berri and Bradbury (2010), these

metrics deserve consideration given their popularity. In particular, Game Score (Sports

Reference LLC, 2023b) appears to exactly meet our needs. Upon review, however, Game

Score does not utilize any of the NBA data advancements of Table 1 and also utilizes hard-

coded coeﬃcients, which are diﬃcult to interpret generally. Further, the popular metrics

included in Table 4 are calculated as a running total of cumulative statistics and thus do not

adequately meet our game-by-game needs. Hence, we believe adding GCP to the growing

pile of basketball statistics is justiﬁed.

There is an admitted level of subjectivity to assigning credit to players in a basketball

game. Oliver (2004, Chapter 13) provides a nice introduction to this problem, though our

approach diﬀers materially from his Diﬃculty Theory. Indeed, we make no attempt to

claim that the GCP metric we propose is perfect and would even go so far as to concede

we have intentionally erred on the side of simplicity so as not lose sight of the overall ROI

framework design. Nonetheless, we do anticipate a close read of our reasoning behind the

principles of the GCP will alleviate concerns it is too artiﬁcial. To reiterate: the purpose

of GCP is to illustrate the percentage credit calculation necessary to perform our realized

contractual ROI calculation for NBA players. Thus, the GCP method may be tweaked,

updated, or overhauled by future analysts without materially changing the framework herein,

as long as any future contribution percentage measure sums to unity. In short, customization

is possible, and we will elaborate on this point in Section 4. As a ﬁnal comment before

proceeding to formally introduce GCP, Terner and Franks (2021) provide a comprehensive

review of the current landscape of basketball statistics. Hence, one may review Terner and

Franks (2021) to see that the GCP concept, especially for the combination of statistics we

propose in Table 1, is itself a contribution to the basketball analysis literature.

2.1.1 Deﬁnition

In attempting to measure a nebulous theoretical construct, such as a basketball player’s

GCP, it is unavoidable to ﬁrst establish a set of fundamental principles or axioms. In light

of the objective of this manuscript, which is to establish a working framework to estimate a

player’s realized ROI and simultaneously provide a benchmark calculation, we make a good

faith attempt at instituting the following six principles: value all activity, process over results,

no double counting, venerate the ﬁfty-ﬁfty ball, sign and aﬀect agnostic, and retrospective

over prospective. We now discuss each in turn.

Value All Activity. We desire to recognize any form of on court activity. This is in

deference to the truism that it is possible to impact a basketball game without recording

traditional box score statistics. A classical example is a defensive player that contests a

shot to the point it results in an altered, inaccurate ﬁeld goal attempt, but the defender

does not tip the ball. In this case, the defender’s contest had an impact but a traditional

block would not be recorded. Therefore, in addition to the traditional statistical categories,

such as two-point ﬁeld goals made, turnovers, and blocks, we also utilize more recent player

tracking and hustle statistics, such as distance traveled, box outs, and touches. This principle

is also why we calculate a GCP for both the winning and losing team. Quite simply, the

zero-sum nature of wins and losses in an NBA regular season suggests that approximately

50% of all player compensation is for losses. Thus, we desire to recognize losses in our novel

ROI framework. Notably, this diﬀers signiﬁcantly from a wins-focused analysis (e.g., Sports

Reference LLC, 2022) and also eliminates the Factors Determining Production of Mart´ınez

(2012), which is a model based on non-scoring box score statistics and is ﬁtted via OLS

against the diﬀerence in ﬁnal score.

Process Over Results. We desire to recognize the virtue of a single player’s individual

process over the resulting outcome. This is admittedly a controversial position, even without

wading into the now infamous period in the history of the Philadelphia 76ers (Rappaport,

2023). Our reasoning stems from a preference for virtue-based (or character) ethics over

outcome-based or duty- and rule-based ethics. In other words, under this principle, a good

outcome, like a made basket, does not absolve a potentially poor decision, like shooting

against a triple-team and ignoring open teammates. For an excellent introduction to such

ideas within the context of economics, see Wight (2015). Within a basketball game, a

classical example would be a player that makes an excellent pass to a teammate for a high-

percentage look at the basket (good process), but the recipient of the pass misses the shot

(bad outcome). In this example, the traditional assist statistic would not be recorded because

there was not a made basket. In addition, the passing player, aside from delivering a quality

pass, has no control on the receiving player’s ability to make the basket. Hence, we prefer

the statistic potential assists to the traditional assists. Similarly, we prefer an adjusted form

of rebound chances to the traditional rebounds, and we track both ﬁeld goals made and ﬁeld

goals missed. In some instances, we are unfortunately constrained by data availability. For

example, it is preferable to track screens set instead of screen assists, but detailed data for

screens set by game is not readily available as of this writing.

No Double Counting. We desire to avoid the classical economics problem of double count-

ing, which is undesirable in the measurement of macroeconomic calculations like gross do-

mestic product (e.g., Mankiw, 2003, Chapter 10). In essence, our objective is to avoid giving

a player double credit in the GCP calculation. In some cases, the adjustments are straightfor-

ward. For example, we create statistics such as three-point ﬁeld goals missed rather than use

both three-point ﬁeld goals made and three-point ﬁeld goal attempts, and we track potential

assists but do not also include the traditional assists (see the discussion in the principle Pro-

cess Over Results to see why we do not diﬀerentiate between assists and potential assists).

Similarly, we track two-point ﬁeld goals made, three-point ﬁeld goals made, and free throws

made but do not also track total points scored. In other instances, we make some subjective

adjustments. For example, we subtract contested rebounds from rebound chances, and we

subtract blocks from contested two-point shots. For the latter, it is possible a three-point

shot was blocked, but we make the assumption most blocked ﬁeld goal attempts are two-

point shots. Lastly, we subtract both potential assists and secondary assists from passes

made. In other instances, it is more diﬃcult to parse out possible double counting. For ex-

ample, we track both minutes played and possessions played. Conceptually, these categories

track similar metrics and must overlap or double count in some form. An adjustment is not

straightforward, however, and so we elect to track both at present.

Venerate the Fifty-ﬁfty Ball. Given the importance of each possession in a basketball

game, we make an eﬀort to recognize moments when possession of the ball is uncertain.

This is clear in our use of loose balls recovered within the GCP calculation. More subtle

perhaps, is our preference to track contested rebounds over rebounds. In the moment a

ﬁeld attempt is missed, future possession is uncertain. Hence, we ﬁnd it is of more value to

record a rebound when it is contested then when the oﬀensive team does not elect to pursue

the ball. Indeed, the value of such rebounds and possession in general is well understood

within the context of valuing a basketball player’s contribution (e.g., Oliver, 2004, Chapter

2, 6), and so we omit additional explanation. We further acknowledge our preference to

diﬀerentiate between rebounds and contested rebounds borrowers from the aforementioned

Diﬃculty Theory (Oliver, 2004, Chapter 13).

Sign and Aﬀect Agnostic. This principle perhaps diﬀers the most from traditional bas-

ketball player evaluation metrics, such as win shares (Oliver, 2004; Sports Reference LLC,

2022) or game score (Sports Reference LLC, 2023b). In short, we do not distinguish between

a positive and negative contribution, and we do not attempt to measure the relative value

or impact of one statistical category versus another. While such a principle does contribute

towards a ﬁnal metric that is easy to interpret and easily tweaked to meet the speciﬁcations

of diﬀerent analysts, i.e., suitable to establish a framework, we do also feel justiﬁcation is pos-

sible. Consider ﬁrst the traditional statistic turnovers. It is nearly unanimous to basketball

analysts that loosing possession of the basketball is a negative outcome. Our GCP metric

does not attempt to measure a player’s contribution to winning, however. Instead, it is more

akin to usage percentage (National Basketball Association, 2023a) in that we attempt to

measure a player’s overall contribution to a game’s outcome. From this point-of-view, it is

not unreasonable to suggest that a player with many turnovers in a single game likely had

a large contribution on the outcome, albeit negative. In terms of relative impact, diﬃculties

quickly arise in attempting to assign relative value. For example, it appears straightforward

that a made three-point ﬁeld goal should be worth 50% more than a made two-point ﬁeld

goal. Basketball is more nuanced, however. If a player has the ability to easily score two-

point ﬁeld goals near the basket, then the defense must adjust their approach with double

teams. This in turn will leave other players open, which may lead to valuable open ﬁeld

goal attempts. We thus elect to use an equal weighting system as both a logical starting

point and for ease of interpretation. This principle rules out many current basketball player

contribution statistics already discussed. One not yet mentioned and also not suitable for

our needs, however, is Niemi (2010), who oﬀers a hierarchical model to derive underlying

distributions for player contributions and considers play-by-play data from the 2009-2010

NBA regular season.

Retrospective Over Prospective. Finally, we remain aligned with the principles of ﬁnancial

accounting in that we consider only what was actually received on the ledger. In other words,

we do not adjust for potential randomness. For statistically minded readers, this may appear

troubling. Indeed, for the purposes of designing an oﬀense, for example, it is more valuable

to know the long-term average ﬁeld goal percentage of a shot location than if a player

happened to make or miss one single ﬁeld goal attempt. This diﬀers from our objective,

however, and we illustrate with an example from consumer ﬁnance. If a borrower misses a

monthly mortgage payment, it does little for the lender to hear an explanation that similar

borrowers made last month’s payment with a high percentage on average. From the lender’s

perspective, it only matters that the payment was missed. Hence, as a form of retrospective

accounting, we attempt to track only what actually occurred within a single game. Phrased

diﬀerently, after the season, we can use the GCP to look backwards and see how a player

performed (just as ﬁnancial analysts look backwards on historical quarterly earnings to see

Field Description nba.com Statistic nba.com Type

MIN Minutes Played MIN Traditional

FG2O 2 Point Field Goals Made FGM - FG3M Traditional

FG2X 2 Point Field Goals Missed (FGA - FG3A) - FG2O Traditional

FG3O 3 Point Field Goals Made FG3M Traditional

FG3X 3 Point Field Goals Missed FG3A - FG3M Traditional

FTO Free Throws Made FTM Traditional

FTX Free Throws Missed FTA - FTM Traditional

PF Personal Fouls PF Traditional

STL Steals STL Traditional

BLK Blocks BLK Traditional

TOV Turnovers TOV Traditional

BLKA Blocks Against BLKA Traditional

PFD Personal Fouls Drawn PFD Traditional

POSS Possessions Played Poss Playtype

SAST Screen Assists SAST Hustle

DEFL Deﬂections Deflections Hustle

CHGD Charges Drawn Charges Drawn Hustle

AC2P Adj. Contested 2PT Shots Defensive Contested 2PT Shots - BLK Hustle

C3PT Contested 3PT Shots Defensive Contested 3PT Shots Hustle

OBOX Oﬀensive Box Outs OFF BOX OUTS Box Outs

DBOX Defensive Box Outs DEF BOX OUTS Box Outs

OLBR Oﬀensive Loose Balls Recovered Off Loose Balls Recovered Hustle

DLBR Defensive Loose Balls Recovered Def Loose Balls Recovered Hustle

DFGO Defended Field Goals Made DFGM Defensive

DFGX Defended Field Goals Missed DFGA - DFGM Defensive

DRV Drives Drives Tracking

ODIS Distance Miles Oﬀense Dist. Miles Off Tracking

DDIS Distance Miles Defense Dist. Miles Def Tracking

TCH Touches Touches Tracking

APM Passes Made Passes Made - 2AST - PAST Tracking

PASR Passes Received Passes Received Tracking

AST2 Secondary Assist Secondary Assist Tracking

PAST Potential Assists Potential Assists Tracking

OCRB Contested Oﬀensive Rebounds Contested OREB Rebounding

AORC Adj. Oﬀensive Rebound Chances OREB Chances - ORCO Rebounding

DCRB Contested Defensive Rebounds Contested DREB Rebounding

ADRC Adj. Defensive Rebound Chances DREB Chances - DRCO Rebounding

Table 1: Complete list of statistics used to compute game contribution percentage. The

statistical categories used to compute the GCP are listed in the Field column. The Description

column provides a brief description of the statistic in words. The statistics in the nba.com Statistic

column are the source statistics from the National Basketball Association (2023d), with formulas

as appropriate. The column nba.com Type lists the type of statistic used in terms of the nba.com

statistical categories. For complete deﬁnitions and categories of nba.com statistics, please see

National Basketball Association (2023a).

how a company performed).

The complete set of ﬁelds, F, used in the GCP may be found in Table 1, along with

descriptions, adjustment formulas, and references to nba.com statistics (National Basket-

ball Association, 2023d). The ﬁelds in Table 1 are meant to align with the principles just

outlined. Nonetheless, we certainly concede alternative choices may be preferable to other

analysts. Indeed, it may be a collaborative eﬀort between coaches, scouts, and quantitative

departments to determine F. For our purposes, we proceed with the 37 ﬁelds deﬁned in

Table 1. For a discussion of potential future customization of the GCP, see Section 4.

Once F has been determined, the GCP calculation proceeds as follows. Let g ∈ G ≡

{1, . . . , 1230} be one of the 1,230 games played in a standard 82-game NBA regular season

(recall we assume an investment horizon of the regular season as an illustration; this may

be changed without materially changing our framework). Each game, g, will consist of two

teams, t

, t

∈ T , where t

̸= t

and T ≡ {ATL, . . . , WAS} is the set of 30 NBA teams. Each

, i = 1, 2, will consist of a set of the game’s active players, P

. We desire to calculate a

GCP per player, per team. Formally, for g ∈ G, t

∈ T , and p ∈ P

GCP

= ω

f∈F

, (1)

where f

is the game value of ﬁeld f ∈ F

for player p ∈ P

, f

is team t

’s game total for

ﬁeld f ∈ F

p∈P

, (2)

is the set of ﬁelds such that the game totals f

> 0, i.e., F

= {f ∈ F : f

> 0}, and

card{F

}

. (3)

Restricting the calculation of ω

to only those ﬁelds with a positive team value explicitly

ignores any missed categories in the GCP calculation. In this way, (1) is dynamic and depen-

dent on a team’s performance. We acknowledge alternative approaches may be preferable.

For example, it may be desirable to keep the ﬁelds and weights ﬁxed, which would imply that

a team recording no instances of a particular ﬁeld would be a loss of credit for all players.

We expand on the important choice of weights and possible future iterations in Section 4.

The calculation in (1) is calculated for each team, i.e., for i = 1, 2.

There are some instructive properties of GCP

, which we now review. First, for all

g ∈ G, i = 1, 2.

p∈P

GCP

= ω

p∈P

f∈F

= ω

f∈F

p∈P

= 1, (4)

by (2) and (3). Thus, the sum total of each player’s GCP for each team will be unity for

every game. This makes direct comparisons possible, and it does not require standardization,

such as a need to report metrics per 100 possessions (Sports Reference LLC, 2023a). Second,

because of NBA forfeit rules and the statistical categories minutes and possessions played

may be recorded by a player without touching the ball or even moving, the upper bound of

GCP is less than unity for a single player, p,

0 ≤ GCP

≤ 1 − ω



MIN

− MIN

MIN

POSS

− POSS

POSS



, for all g ∈ G, i = 1, 2.

Finally, we emphasize (4) holds for both the winning and losing team. We refer again to the

principles value all activity and sign and aﬀect agnostic as justiﬁcation for why each team

summing to unity regardless of the team’s win-loss outcome is a desirable property.

2.1.2 Illustrative Calculation

For the purposes of illustration, we will consider the April 4, 2023 game between the

Philadelphia 76ers and the Boston Celtics. The 76ers won the game 103-101. It

was a notable game because Joel Embiid scored 52 points for the 76ers, and the game was

televised nationally in the United States on TNT (National Basketball Association, 2023b).

The game statistics corresponding to the ﬁelds in Table 1, and GCP calculations for Boston

and Philadelphia may be found in Tables 2 and 3, respectively.

The high player for Boston was Jayson Tatum, with a GCP of 20.64%. If we consider that

Tatum’s 37.8 minutes represent only 15.75% of the total 240 minutes, we can see that Tatum

has an out-sized impact on the game in comparison to a basic minutes played percentage

calculation. The next two players for Boston are Derrick White and Marcus Smart, with

GCPs of 14.25% and 14.02%, respectively. Not close behind are Al Horford and Malcolm

Brogdon, at 13.20% and 12.43%, respectively. These results suggest Boston had a fairly

balanced contribution in this game. It is also interesting to observe that Grant Williams had

a GCP of 6.34% in 28.7 minutes, whereas Luke Kornet recorded a higher GCP of 9.12% in

15.6 minutes. Because Kornet contributed more to the game in less playing time according

to (1), it is a sign that GCP may oﬀer insights into team building or game management

for player personnel oﬃcials within basketball organizations. For reference, Boston did not

record a CHGD or DLBR in this game, so the categorical weight for Boston, (3), was

For Philadelphia, we see that Joel Embiid recorded a game-high GCP of 25.30% in 38.6

minutes. Based on the histogram of non-zero GCPs for all players in the 2022-2023 NBA

regular season (i.e., Figure 2), we see that Joel Embiid had a 99.54% percentile non-zero

GCP game. The next highest player for Philadelphia is James Harden, with a GCP of

21.79%. It is interesting to see that Philadelphia had two players with GCPs over 20%,

whereas Boston had only one in Tatum. Indeed, Philadelphia had only two more players

above a 10% GCP, in Tobias Harris and Tyrese Maxey, at 11.86% and 11.53%, respectively.

In comparison with Boston, we can see that Philadelphia was more reliant on less players

than Boston. This again illustrates some of the added insights of the GCP metric. For

reference, Philadelphia did not record a OBOX in this game, so the categorical weight for

Philadelphia, (3), was

2.2 Return on Investment

With the GCP methodology suﬃciently established, it is now possible to proceed to the ROI

calculations. The ﬁrst step is deriving the SGV in dollars, which may then be allocated

to each player via GCP. Hence, with a player’s salary serving as a time zero investment to

Tatum Williams Horford Smart White Brogdon Hauser Kornet Muscala Griﬃn

MIN 37.8 28.7 34.6 30.2 40.4 27.7 3.3 15.6 13.4 8.3

FG2O 5 2 1 5 5 5 0 0 0 0

FG2X 7 1 1 3 3 7 0 1 0 0

FG3O 2 2 3 2 4 2 0 0 0 0

FG3X 6 2 7 5 6 2 1 0 1 0

FTMO 3 0 0 1 4 2 0 0 0 0

FTMX 2 0 0 2 0 2 0 0 0 0

PF 2 3 4 4 3 0 0 0 0 1

STL 3 0 0 1 0 0 0 0 0 0

BLK 0 0 0 0 2 0 0 1 0 1

TOV 2 0 0 3 2 1 0 0 0 0

BLKA 4 0 0 0 0 2 0 1 0 0

PFD 4 2 0 5 4 5 0 1 0 0

POSS 72 53 65 58 74 52 9 30 25 12

SAST 0 0 3 1 1 0 0 2 1 0

DEFL 2 0 0 3 0 0 0 0 0 0

CHGD 0 0 0 0 0 0 0 0 0 0

AC2P 0 5 10 0 3 2 0 7 3 0

C3P 4 0 5 2 2 2 0 3 0 0

OBOX 0 0 0 0 0 0 0 1 0 0

DBOX 0 0 1 0 0 0 0 0 1 1

OLBR 2 0 1 0 0 1 0 0 0 1

DLBR 0 0 0 0 0 0 0 0 0 0

DFGO 3 10 11 6 5 4 1 5 2 5

DFGX 4 4 8 3 6 9 0 4 3 1

DRV 10 3 1 10 9 14 0 0 0 0

ODIS 1.4 1.0 1.2 1.1 1.5 1.0 0.2 0.6 0.5 0.2

DDIS 1.0 0.8 0.9 0.9 1.2 0.8 0.1 0.5 0.5 0.2

TCH 73 25 56 66 70 52 1 8 9 10

APM 32 13 31 35 40 21 0 6 7 10

PASR 52 17 32 52 49 40 1 3 1 4

AST2 2 0 0 0 1 1 0 0 0 0

PAST 14 4 11 9 7 7 0 0 0 0

OCRB 0 1 1 0 0 0 0 2 0 1

AORC 9 2 3 3 1 2 0 2 0 3

DCRB 0 0 1 0 0 0 0 0 1 2

ADRC 6 3 6 5 8 6 0 2 3 2

GCP 0.2064 0.0634 0.1320 0.1402 0.1425 0.1243 0.0037 0.0912 0.0380 0.0582

Table 2: Game contribution percentage illustration: Boston Celtics. The statistical totals

for the April 4, 2023 game between the Philadelphia 76ers and the Boston Celtics for Boston

and ultimate GCP calculation using (1). Players with no recorded statistics or inactive players are

not reported. The statistics were pulled from National Basketball Association (2023d). The ﬁeld

abbreviations may be found in Table 1.

the realized 82-game regular season cash ﬂows, we are able to employ standard ﬁnancial

return calculation methods. In this way, our approach shares some similarity with the

aforementioned Tunaru et al. (2005), as the number of points recorded by each player in

Field Harris Tucker Embiid Maxey Harden Melton Niang McDaniels House Jr. Reed

MIN 34.43 27.45 38.6 39.63 40.02 19.17 15.52 15.1 0.83 9.25

FG2O 1 1 20 1 3 0 0 1 0 1

FG2X 3 1 4 3 5 1 1 1 0 2

FG3O 1 3 0 1 4 0 0 2 0 0

FG3X 3 0 1 3 5 3 2 1 0 0

FTMO 0 0 12 0 2 0 0 0 0 0

FTMX 0 0 1 0 0 0 0 0 0 1

PF 4 4 3 5 1 2 0 1 0 1

STL 0 0 0 0 1 1 0 0 0 1

BLK 0 0 2 1 2 0 0 1 0 1

TOV 1 2 3 4 0 0 0 0 0 0

BLKA 1 0 1 0 1 0 0 1 0 0

PFD 0 0 9 2 5 0 0 0 0 1

POSS 64 51 73 75 73 37 29 28 3 15

SAST 1 1 1 0 0 0 0 0 0 1

DEFL 0 0 0 0 4 1 0 0 0 2

CHGD 0 0 0 0 1 0 0 0 0 0

AC2P 1 0 7 2 1 4 0 1 1 2

C3P 1 4 5 2 3 1 1 3 0 1

OBOX 0 0 0 0 0 0 0 0 0 0

DBOX 1 1 2 1 0 0 0 0 0 0

OLBR 0 0 0 0 1 0 1 0 0 0

DLBR 0 0 1 2 0 0 0 0 0 0

DFGO 3 4 12 3 7 7 2 4 0 1

DFGX 6 6 13 7 9 9 2 2 1 3

DRV 1 0 10 3 17 1 1 1 0 1

ODIS 1.2 1.0 1.2 1.4 1.3 0.7 0.6 0.6 0.0 0.4

DDIS 1.1 0.9 1.2 1.4 1.1 0.6 0.5 0.5 0.1 0.3

TCH 31 19 75 62 100 16 17 19 0 8

APM 21 14 33 48 63 11 14 12 0 4

PASR 14 13 59 49 83 10 9 9 0 3

AST2 1 0 0 0 0 0 0 0 0 0

PAST 1 0 7 1 15 1 0 2 0 1

OCRB 0 0 1 0 0 0 0 0 0 1

AORC 0 1 2 0 2 0 1 1 0 4

DCRB 3 0 2 0 0 0 0 0 0 0

ADRC 5 3 19 9 10 0 1 7 0 1

GCP 0.1186 0.0657 0.2530 0.1153 0.2179 0.0524 0.0372 0.0503 0.0026 0.0871

Table 3: Game contribution percentage illustration: Philadelphia 76ers. The statistical

totals for the April 4, 2023 game between the Philadelphia 76ers and the Boston Celtics for

Philadelphia and ultimate GCP calculation using (1). Players with no recorded statistics or

inactive players are not reported. The statistics were pulled from National Basketball Association

(2023d). The ﬁeld abbreviations may be found in Table 1.

Tunaru et al. (2005) is translated into a Game Score. Our GCP methodology diﬀers the

Game Score of Tunaru et al. (2005), however, and we do not employ an option valuation

framework that relies on a geometric Brownian motion assumption (as mentioned previously,

we also focus on basketball rather than football (i.e., soccer)). We elaborate on our ﬁnancial

methods as follows.

2.2.1 Currency Conversion

Mechanically, currency conversion calculations are straightforward once the benchmark items

are identiﬁed; it is nothing more than a unit conversion. In this case, we desire to convert

a single NBA game unit into a dollar value of player compensation using the sum total of

player salary. This diﬀers from attempting to estimate the dollar value of an NBA game

generally, which would rely on factors such as ticket sales, television revenue, and other items

outside the performance of the players on the court. To do so, we’ll borrow from the gold

standard, in which a country’s basic monetary unit is deﬁned in terms of the weight of gold

specie (Hughes and Cain, 2011). Rather than specie, we will pin the total dollar amount

of player compensation to twice the number of NBA regular season games (i.e., the total

number of single team game units or GCP opportunities). This is because we are assuming

a regular season investment horizon. Speciﬁcally, there are 1,230 NBA regular season games,

each of which has two participants within T . Hence, we ﬁnd the SGV through the direct

conversion

SGV =

2 × 1230

, (5)

where S is the total dollar value of player compensation for all players active on NBA

rosters for the regular season. The choices behind (5) have been made largely for illustrative

purposes and have understandable limitations. For example, we assign all games the same

value, which may not be appropriate, especially as teams are gradually eliminated from play-

oﬀ contention. Further, to paraphrase a refreshing spin on a standard NBA pundit platitude

regarding the diﬀerence between a regular season and play-oﬀ game: there are 82-game

players, and there are 16-game players. (This phrasing is generally attributed to Draymond

Green (Mahoney, 2019).) In other words, the best players are paid for play-oﬀ games, and

so our regular-season based conversion would be missing this important component of player

on court performance. We expand on these points further in Section 4.

2.2.2 Financial Details

We now brieﬂy review how to calculate the realized return for a sequence of ﬁnancial cash

ﬂows. Because we know the initial investment (i.e., a player’s salary) and subsequent cash

ﬂows (i.e., a player’s vector of GCPs multiplied by the SGV), we will utilize the internal rate

of return methodology (e.g., Berk and Demarzo, 2007, §4.8). Consider the time line of cash

ﬂows illustrated in Figure 1. For simplicity, we assumed each cash ﬂow, CF

, . . . , CF

, is paid

on equally-spaced intervals. This assumption may be relaxed, a point we address more fully

in Section 4. Further, we assumed the time zero cash ﬂow, CF

, is the initial investment.

Because we are performing a realized return calculation (i.e., after the completion of the

regular season), all CF

, 0 ≤ i ≤ n are known at the onset of the problem. The return on

investment is the rate, r, such that

i=1

(1 + r)

. (6)

Aside from very simpliﬁed versions of (6), the computation of r will require the use of

optimization software (we have found the irr function in the R package jrvFinance (Varma,

2021) useful for this purpose).

Let us now interpret (6) within the context of an NBA regular season. The time zero

cash ﬂow (i.e., the initial investment) is a player’s salary. From the perspective of the NBA

team it is a negative cash ﬂow. Because we focus on an NBA regular season, it is natural to

assume N = 82 (though it is possible a player traded during the NBA regular season may

appear in more than 82 games, such as Mikal Bridges in the 2022-2023 NBA regular season).

To ﬁnd the return cash ﬂows, CF

, 1 ≤ i ≤ 82, we may use (1) and (5). Formally, let p

∗

represent an active NBA player on team t

∗

∈ T and let g

∗

= {g

∗

, . . . , g

∗

} be the ordered

. . .

Figure 1: Cash ﬂow time line. A classical illustration of a sequence of ﬁnancial cash ﬂows.

Within the context of the NBA, we assume CF

represents the season salary and is thus a negative

cash ﬂow to the organization. The remaining cash ﬂows, CF

through CF

represent the dollar

conversion of the player’s on court production, which may be estimated using (1) and (5). Observe

≥ 0 for 1 ≤ i ≤ N by (1) and (5). Because we assume a traditional NBA regular season for

illustration, N = 82 (though this may be adjusted to meet an analyst’s needs). For simplicity,

we assume the games are played at equally spaced intervals, though this assumption may also be

relaxed. See Section 4 for further discussion.

sequence of games in G of which t

∗

appeared. Then,

i,p

∗

= SGV × GCP

∗

. (7)

By deﬁnition of (1) and (5), it is clear CF

i,p

∗

≥ 0 for all 1 ≤ i ≤ N and p

∗

. Hence, the

contractual return on investment for p

∗

is the rate, r

∗

, such that

0,p

∗

= SGV

i=1

GCP

∗

(1 + r

∗

)

. (8)

We remark that any player traded during the regular season will require the standard adjust-

ments to (7) (we make these adjustments for all results in Section 3). We also remark brieﬂy

that the framework in (8) may be adjusted for enhanced precision. For example, rather

than assume a player’s salary is a time zero lump sum payment, the true timing of salary

payments may be incorporated into (6). Similarly, there is no need to assume all games are

played on equally spaced intervals, and the true dates and time calculations may be made

more precise. Further, we consider only on court performance in the form of GCP, but it

is not unreasonable to credit oﬀ court revenue to players, such as with team jersey sales.

Lastly, N may be extended to also include play-oﬀ games, and the SGV or GCP metrics may

be adjusted to ﬁt an analysts’ preference. As a ﬁnal comment, the nature of (8) naturally

assigns more weight to early season performance, which may also be adjusted by reordering

or weighting the games to meet an analysts’ needs. It is the framework we propose that we

feel is of general value. Further discussion on potential enhancements or customization may

be found in Section 4.

3 Results

As an illustration, we now apply the methods of Section 2 to the pool of players participating

the 2022-2023 NBA regular season. We ﬁrst brieﬂy discuss the data and how it was obtained.

Next, we present cumulative sums of complete regular season GCPs. This is done to help val-

idate the GCP metric itself and demonstrate it has utility irrespective of player salary data.

Finally, the section concludes by presenting ROI calculations, the ultimate purpose of this

study. In support of reproducible research, the complete compiled data and replication code

may be found on a public github repository at https://github.com/jackson-lautier/nba roi.

3.1 Data

Our data comes from two publicly available sources. The ﬁrst is the statistics page of

the NBA (National Basketball Association, 2023d). Because of the extensive nature of the

statistical categories ultimately utilized in the GCP calculation, we found the python package

nba api (Patel, 2018) of enormous value. Indeed, we compiled a novel dataset of box scores

of the form of Tables 2 and 3 for all 1,230 games of the 2022-2023 NBA regular season by

designing a custom game-by-game query wrapper for Patel (2018). The second is a complete

list of player salaries for the 2022-2023 NBA regular season from HoopsHype (2023) (with one

supplement for the player Chance Comanche (Spotrac, 2023)). Both of these sources were

combined into a novel dataset that includes both on court game-by-game performance in the

form of Tables 2 and 3 and player salary data. To obtain the data and replication code, please

navigate to the public github repository at https://github.com/jackson-lautier/nba roi.

3.2 Absolute Game Contribution Percentage

The ﬁrst set of results is a histogram of all non-zero GCPs recorded for the 2022-2023 NBA

regular season, which is available in Figure 2. The histogram spans 25,892 GCP realizations,

and it helps us get a sense of the distribution of this novel metric. Speciﬁcally, we can

see that GCP realizes a peak near 10%, with a tail skewed to the right. The maximum

realized GCP was by Luka Donˇci´c at 33.8%, which occurred against the New York Knicks

on December 27, 2023. The game was notable because Donˇci´c scored 60 points while also

recording 21 rebounds and 10 assists. It was the ﬁrst 60-point game in the history of the

Dallas Mavericks, a career high in rebounds for Donˇci´c, and, historically, the ﬁrst 60-

20-10 game in NBA history (Associated Press, 2022). As a bit of informal veriﬁcation for

the GCP metric, the maximum player salary ranges from 30-35% of the salary cap, subject

to years of service and other performance-based criteria (National Basketball Association,

2018). Hence, having a maximum realization of GCP for all players within the 30-35% range

is in this sense intuitively pleasing. (We note the GCP of Section 2.1 was developed without

regard to the 30-35% maximum salary; it is a satisfying coincidence.)

As a next set of results, we demonstrate how GCP may be used to assess the tipping

point of a player who performs very well but has a tendency to miss games against a player

that performs only reasonably well but does so consistently. The diﬃculty of comparing a

high-performing player with many missed games against an average-performing player with

few missed games has been a frequent source of consternation within the discourse of NBA

pundits (for example, Lowe (2020) and Mannix and Beck (2023) frequently cite games missed

as reasoning for preferring some players over others). Because a player receives a zero GCP

for any missed game (see Figure 3), we may ﬁnd the break even point by taking a running

tally of GCP for the period in question, such as the entire 2022-2023 NBA regular season. In

eﬀect, we are taking a present value of all GCPs at an interest rate of 0%. That is, for active

NBA player p

∗

on team t

∗

∈ T with g

∗

= {g

∗

, . . . , g

∗

} representing the ordered sequence of

250

500

750

0% 10% 20% 30%

Game Contribution Percentage

Number of Games

Figure 2: Game contribution percentage histogram. A distributional plot of the 25,892

non-zero GCP realizations for all players in the 2022-2023 NBA regular season. The GCP was

computed using the methods of Section 2.1. For reference, the maximum realized GCP was by

Luka Donˇci´c at 33.8%, which occurred against the New York Knicks on December 27, 2023. This

compares favorably to the 30-35% maximum player salary allowable under the NBA’s Collective

Bargaining Agreement (National Basketball Association, 2018).

games in G of which t

∗

appeared, we have

PVGCP

∗

GCP

∗

. (9)

As with (7), the adjustments to (9) are natural for any players traded over the time period

in question. We emphasize that (9) is directly comparable for all NBA players and does not

require standardization, such as per 100 possessions. This allows for analysts to use a single

metric to understand the impact of a player’s missed games, rather than computing a metric,

standardizing it, and then attempting to perform additional missed game value judgments

(e.g., Lowe, 2020; Mannix and Beck, 2023).

Table 4 presents the top ﬁfty players in terms of PVGCP for the 2022-2023 NBA regular

season. We can see the top ﬁve performers are Damontas Sabonis, Nikola Joki´c, Joel Embiid,

Luka Donˇci´c, and Bam Adebayo. In general, our PVGCP metric arrives at a similar list of

top performers, as measured by the 2022-2023 Kia NBA Most Valuable Player award voting

(Associated Press, 2023a) and 2022-2023 Kia All-NBA selections (Associated Press, 2023b).

The PVGCP metric prefers Sabonis as the top performer, whereas Embiid won the Kia NBA

Most Valuable Player award. Table 4 has Embiid ranked 3rd in terms of PVGCP, though

Embiid was the top per game GCP performer. Further, the PVGCP metric has Sabonis at a

clear top spot, but he received only one 4th place MVP vote and 24 5th place votes. Hence,

it is not unreasonable to suggest that our GCP methodology is able to capture Sabonis’

consistent high level of contribution to his team’s on court performance and availability in a

way that other popular advanced metrics may overlook (that said, the win shares approach

(Sports Reference LLC, 2022) had Sabonis ranked second behind Joki´c (Sports Reference

LLC, 2023a)). Aside from win shares, no other Table 4 metric had Sabonis higher than 7th.

Further, all comparative metrics reported in Table 4 have Nikola Joki´c as the top performer,

which suggests that these popular advanced metrics may rely on similar overall approaches

and not oﬀer enough diversity of perspective. For completeness, we note Berri and Bradbury

(2010) oﬀers a critique of sports metrics proposed outside the scope of academic peer-review.

In this regard, we emphasize again that GCP is a measure of a player’s total contribution

to his team’s on court performance; it does not attempt to parse out “good” and “bad”

performance (review Section 2.1 as needed). This helps explain why players like Alperen

S¸eng¨un and Nikola Vuceˇci´c have high values of PVGCP despite playing for teams in the

Houston Rockets and Chicago Bulls that amassed paltry win percentages of 0.268 and

0.488, respectively (National Basketball Association, 2023c). As a further reﬂective note, it

appears PVGCP is partial to the traditional big man in that there is a healthy representation

of centers with high games played that were not recognized on many NBA award ballots

(e.g., Vuceˇci´c, S¸eng¨un, Claxton, Gobert, Zubac, Porzi¸n

‘

gis, Valanˇci¯unas, Plumlee, P¨oltl,

Looney, and Okongwu). Then again, the importance of the center position has been long

established in basketball treatments (e.g., Oliver, 2004, pg. 40), and more generally its depth

of representation in Table 4 is a useful insight for NBA player personnel decision-makers

tasked with allocating a capped player salary pool.

It is interesting to observe that there are multiple ways to obtain an impressive PVGCP.

As we’ve established, it is clear that players with any missed games will be directly penalized

in (9) in a way that diﬀers from metrics based on cumulative on court statistics. Nonetheless,

it is possible for a player to perform so well in games played that they can amass a high

PVGCP despite accumulating many missed games. With PVGCP, we can obtain this exact

inﬂection point. This is the value of treating missed games as defaults, and it may oﬀer

useful insights on its own merit. Consider Figure 3, which compares Anthony Davis and

Brook Lopez. From Table 4, we can see that Davis and Lopez accumulated nearly identical

PVGCPs at 11.86 and 11.83, respectively. Davis did so in 56 games (i.e., 26 defaults) whereas

Lopez did so in 78 games (i.e., only 4 defaults). The visual representation in Figure 3 makes

the diﬀerence in consistency readily apparent. In other words, Lopez, through his consistent

availability and steady performance in 78 games was able to reach the same level of PVGCP

as Davis for the 2022-2023 NBA season. Because Lopez earned $13,906,976 in comparison

to Davis at $37,980,720 for the 2022-2023 NBA season (HoopsHype, 2023), this information

may be of interest to NBA player personnel decision makers. (Davis had a very strong 2023

NBA postseason, which is an important consideration not made within this analysis.) We

arrive at the formal ROI calculations in Section 3.3.

3.3 Return on Investment

The ﬁnal component of our eﬀort and the ultimate purpose of this study is to combine the

absolute GCP results of Table 4 with each player’s salary to perform a contractual realized

ROI calculation in the form of (8). The ﬁrst step is to calculate the SGV proposed in (5).

Rank Player GP PVGCP GCPpg PER WS BPM VORP RAPTOR

1 Domantas Sabonis 79 16.81 0.213 23.50 12.60 5.80 5.40 8.66

2 Nikola Joki´c 69 15.04 0.218 31.50 14.90 13.00 8.80 20.31

3 Joel Embiid 66 14.81 0.224 31.40 12.30 9.20 6.40 12.82

4 Luka Donˇci´c 66 14.24 0.216 28.70 10.20 8.90 6.60 12.98

5 Bam Adebayo 75 14.10 0.188 20.10 7.40 1.50 2.30 5.69

6 Giannis Antetokounmpo 63 13.62 0.216 29.00 8.60 8.50 5.40 9.31

7 Evan Mobley 79 13.61 0.172 17.90 8.50 1.70 2.50 3.85

8 Nikola Vuceˇci´c 82 13.50 0.165 19.10 8.30 2.70 3.20 1.91

9 Julius Randle 77 13.01 0.169 20.30 8.10 3.70 3.90 5.64

10 Alperen S¸eng¨un 75 12.94 0.173 19.70 5.20 1.40 1.90 5.18

11 Jayson Tatum 74 12.88 0.174 23.70 10.50 5.50 5.10 8.99

12 Pascal Siakam 71 12.54 0.177 20.30 7.80 3.10 3.40 4.50

13 Shai Gilgeous-Alexander 68 12.36 0.182 27.20 11.40 7.30 5.60 9.86

14 Anthony Edwards 79 12.34 0.156 17.40 3.80 1.00 2.10 6.42

15 Nic Claxton 76 12.25 0.161 20.80 9.20 3.10 2.90 5.57

16 Rudy Gobert 70 12.22 0.175 18.90 7.80 0.70 1.40 5.25

17 Ivica Zubac 76 12.15 0.160 16.70 6.70 -0.90 0.60 2.15

18 Trae Young 73 12.00 0.164 22.00 6.70 3.30 3.40 9.12

19 Anthony Davis 56 11.86 0.212 27.80 9.00 6.30 4.00 9.77

20 Brook Lopez 78 11.83 0.152 18.40 8.00 2.10 2.50 8.70

21 Paolo Banchero 72 11.57 0.161 14.90 2.40 -1.50 0.30 -0.42

22 Kristaps Porzi¸n

‘

gis 65 11.44 0.176 23.10 7.70 4.30 3.40 8.24

23 Scottie Barnes 77 11.35 0.147 15.50 5.00 0.40 1.60 4.62

24 Jonas Valanˇci¯unas 79 11.34 0.144 19.30 5.80 -0.40 0.80 0.55

25 Mason Plumlee 79 11.29 0.143 19.60 7.90 2.20 2.20 3.20

26 De’Aaron Fox 73 11.18 0.153 21.80 7.40 2.50 2.70 7.19

27 Jalen Brunson 68 11.16 0.164 21.20 8.70 3.90 3.50 8.14

28 Jakob P¨oltl 72 11.16 0.155 21.00 6.00 1.90 1.90 3.45

29 DeMar DeRozan 74 11.14 0.151 20.60 8.50 2.00 2.60 7.38

30 Zach LaVine 77 11.04 0.143 19.00 7.10 1.90 2.70 5.53

31 Jarrett Allen 68 11.00 0.162 19.90 9.50 2.40 2.40 4.53

32 Fred VanVleet 69 10.94 0.159 17.00 6.50 2.50 2.90 10.01

33 Donovan Mitchell 68 10.76 0.158 22.90 8.90 6.30 5.00 9.45

34 Mikal Bridges 82 10.73 0.131 16.80 7.50 1.70 2.80 6.76

35 Jaylen Brown 67 10.68 0.159 19.10 5.00 1.30 2.00 4.12

36 Kevon Looney 82 10.61 0.129 17.80 8.70 2.10 2.00 6.09

37 Draymond Green 73 10.59 0.145 12.20 4.70 0.80 1.60 6.09

38 Spencer Dinwiddie 79 10.56 0.134 16.00 6.30 0.70 1.80 4.56

39 CJ McCollum 75 10.54 0.140 15.60 4.30 0.80 1.90 3.59

40 Dejounte Murray 74 10.49 0.142 17.00 4.70 1.00 2.10 3.07

41 Jordan Poole 82 10.46 0.128 14.60 3.20 -1.90 0.10 -0.44

42 Franz Wagner 80 10.44 0.130 15.90 5.40 -0.10 1.30 7.24

43 Jimmy Butler 64 10.40 0.162 27.60 12.30 8.70 5.80 10.11

44 Onyeka Okongwu 80 10.39 0.130 19.40 7.10 0.80 1.30 3.50

45 Damian Lillard 58 10.34 0.178 26.70 9.00 7.10 4.90 11.52

46 Jalen Green 76 10.30 0.136 14.50 1.80 -2.10 0.00 1.75

47 Ja Morant 61 10.30 0.169 23.30 6.00 5.70 3.80 8.39

48 Russell Westbrook 73 10.30 0.141 16.10 1.90 0.20 1.20 1.37

49 Darius Garland 69 10.29 0.149 18.80 7.60 2.40 2.70 8.95

50 James Harden 58 10.26 0.177 21.60 8.40 5.40 4.00 9.22

Table 4: Top performers: Absolute game contribution percentage. The top 50 performers

in terms of (9) for the 2022-2023 NBA regular season. For reference, we also present the number

of games played (GP), GCP per game (GCPpg), standard player eﬃciency rating (PER) (Sports

Reference LLC, 2023a), win shares (WS) (Sports Reference LLC, 2023a), box plus/minus (BPM)

per 100 possessions (Sports Reference LLC, 2023a), value over replacement player (VORP) (Sports

Reference LLC, 2023a), and regular season wins above replacement (RAPTOR) (FiveThirtyEight,

2023) for each player. The high value in each column has been noted in bold.

10%

20%

30%

Game Number

Game Contribution Percentage

Anthony Davis (PVGCP: 11.86; Per Game GCP: 0.2118)

10%

20%

30%

Game Number

Game Contribution Percentage

Brook Lopez (PVGCP: 11.83; Per Game GCP: 0.1517)

Figure 3: Game contribution percentage comparison. A game-by-game plot of GCP for

Anthony Davis (top) and Brook Lopez (bottom) for the 2022-2023 NBA regular season. Both

Davis and Lopez registered nearly an identical PVGCP (i.e., (9)) at 11.86 and 11.83, respectively,

despite a large diﬀerence in games played (56 versus 78, respectively). Because GCP is a single

game calculation, it treats missed games as defaults. Hence, Davis missed enough games and Lopez

played enough games to register a similar level of cumulative contribution as measured by PVGCP.

Because Lopez earned $13,906,976 in comparison to Davis at $37,980,720 for the 2022-2023 NBA

regular season (HoopsHype, 2023), this information may be of interest to NBA player personnel

decision makers.

Based on our data of 547 active NBA players for the 2022-2023 NBA season, we have S =

$4,472,678,188. Thus, SGV = $1,818,162. To avoid skewed calculations from players on

10-day contracts, we set a minimum games played requirement of 25 games. This limits

the calculation pool to 423 players. The top and bottom 50 performers in terms of ROI,

r, via (8), have been compiled in Tables 5 and 6, respectively. There are some interesting

observations.

We begin with the top performers. Immediately, we see that the highest salary in Table 5

is $4.215M, which belongs to Tyrese Haliburton. Because this salary is well below the mean

(median) player salary of $10.022M ($5.122M) for all players playing at least 25 games during

the 2022-2023 NBA regular season, it is clear that the biggest returns belong to players signed

to small value contracts that also contribute meaningfully in terms of on court production.

In other words, the ROI calculation prefers players with a small initial investment (i.e., CF

in Figure 1) that produce valuable game-by-game output (i.e., CF

, 1 ≤ i ≤ 82 in Figure 1).

This insight is perhaps elementary, but the methods we propose lead to a direct framework to

identify which players have outperformed their salaries and by how much, neither of which is

a straightforward calculation. If we combine this information with the NBA team salary cap

restrictions, then it may be used to identify market ineﬃciencies in hopes of optimizing team

roster construction. On the player side, this information may be used in upcoming contract

negotiations. (It is notable that a number of players in Table 5 have signed contracts with

large raises for the upcoming 2023-2024 NBA season: e.g., Tre Jones, Max Strus, Austin

Reaves, Jock Landale, Desmond Bane, Gabe Vincent, Jordan Poole, Shake Milton, Tyrese

Haliburton (Associated Press, 2023c)). Additionally, it is of interest to observe that there

is limited overlap with Table 4. Indeed, only Alperen S¸eng¨un and Jordan Poole appear in

both tables. This again highlights the importance of the initial investment in calculating an

ROI with (8).

The lowest returns in Table 6 oﬀer another set of interesting observations. As expected,

there are many large contracts in Table 6, many of which are well above the 75th percentile

salary of $13.64M for all players playing at least 25 games during the 2022-2023 NBA regular

season. As the opposite reasoning of the previous paragraph would suggest, it requires much

stronger on court performance (i.e., CF

, 1 ≤ i ≤ 82) to overcome a much higher initial

investment (i.e., CF

). In addition, there are many highly decorated NBA players in Table 6,

such as Stephen Curry, LeBron James, Kevin Durant, and Giannis Antetokounmpo. This

may be surprising at ﬁrst glance, but we oﬀer a few reasonable explanations. First, many

players in Table 6 missed games in the 2022-2023 NBA regular season. Quite simply, it

Rank Player Salary GP PVGCP ROI (%)

1 Tre Jones $1.783 68 8.228 0.132

2 Kevon Harris $0.509 34 1.778 0.122

3 Nick Richards $1.783 65 6.766 0.113

4 Ayo Dosunmu $1.564 80 6.921 0.108

5 Max Strus $1.816 80 7.336 0.106

6 Anthony Lamb $0.695 62 4.734 0.096

7 Christian Koloko $1.500 58 3.851 0.095

8 Austin Reaves $1.564 64 6.594 0.094

9 Jock Landale $1.564 69 5.546 0.094

10 Jose Alvarado $1.564 61 5.475 0.092

11 Jaden McDaniels $2.161 79 8.587 0.087

12 Daniel Gaﬀord $1.931 78 9.111 0.086

13 Kevin Porter Jr. $3.218 59 8.968 0.086

14 Kenyon Martin Jr. $1.783 82 7.208 0.086

15 Santi Aldama $2.094 77 6.385 0.080

16 Desmond Bane $2.130 58 7.823 0.079

17 Bol Bol $2.200 70 5.524 0.077

18 Alperen S¸eng¨un $3.375 75 12.943 0.077

19 Drew Eubanks $1.968 78 8.166 0.077

20 Herbert Jones $1.785 66 7.614 0.076

21 Jordan Goodwin $1.280 62 5.189 0.075

22 Naji Marshall $1.783 77 6.417 0.073

23 Immanuel Quickley $2.316 81 8.902 0.073

24 Gabe Vincent $1.816 68 6.048 0.073

25 Tyrese Maxey $2.727 60 7.274 0.073

26 Dennis Smith Jr. $2.133 54 5.776 0.068

27 Jaylen Nowell $1.931 65 4.538 0.067

28 Terance Mann $1.931 81 6.528 0.066

29 Kenrich Williams $2.000 53 5.004 0.065

30 Orlando Robinson $0.386 31 2.111 0.063

31 Aaron Wiggins $1.564 70 4.695 0.062

32 Naz Reid $1.931 68 6.862 0.060

33 Troy Brown Jr. $1.968 76 5.707 0.060

34 Isaiah Stewart $3.433 50 6.489 0.059

35 Jeremiah Robinson-Earl $2.000 43 3.277 0.059

36 Walker Kessler $2.696 74 9.751 0.059

37 Duane Washington Jr. $0.629 31 1.735 0.058

38 Wenyen Gabriel $1.879 68 5.852 0.057

39 John Konchar $2.300 72 5.006 0.057

40 Jordan Poole $3.901 82 10.461 0.056

41 Shake Milton $1.998 76 5.524 0.056

42 Andrew Nembhard $2.244 75 6.998 0.056

43 Damion Lee $2.133 74 4.725 0.054

44 Isaiah Jackson $2.574 63 5.796 0.054

45 Isaiah Livers $1.564 52 3.818 0.054

46 Keldon Johnson $3.873 63 8.391 0.053

47 Tyrese Haliburton $4.215 56 7.964 0.053

48 Javonte Green $1.816 32 2.074 0.052

49 Trendon Watford $1.564 62 5.130 0.051

50 Jericho Sims $1.640 52 3.731 0.049

Table 5: Top 50 performers: Return on investment. The top 50 performers in terms of (8)

for the 2022-2023 NBA regular season, based on a minimum of 25 games played. For reference, we

also include the player salary (HoopsHype, 2023) in millions, games played (GP), and PVGCP, as

calculated with (9).

is diﬃcult to overcome a large initial investment with many subsequent zero cash ﬂows.

Second, we do not include playoﬀ games in the calculations for Table 6. If NBA personnel

decision makers put a premium on playoﬀ performance (a very reasonable supposition),

then the calculations in Table 6 are missing an important component of the contractual

value of the highest paid NBA players. Similarly, we only consider on court performance,

and we ignore oﬀ court value vis-´a-vis jersey sales, ticket sales, television revenue, and other

potential pecuniary production that is a likely income component to teams rostering the

NBA’s most popular players. We attempted to value on court performance only by design,

but this is a straightforward adjustment to the ROI framework we propose. Additional

related discussion may be found in Section 4. As a ﬁnal reference point, the highest 2022-

2023 salary was $48.07, which belonged to Stephen Curry. Assuming all 82 games played,

the break-even IRR implies a per game cash ﬂow of $0.586M. Assuming an SGV of $1.818M,

as calculated above, this implies a per game GCP of 32.24%. Again, this is quite close to the

maximum player salary of 30-35% per the NBA’s CBA (National Basketball Association,

2018) and is an additional informal validation of our approach.

As a ﬁnal curiosity of the ROI framework we propose, it is of interest to examine a scatter

plot of ROI by salary. In other words, player compensation in the NBA is eﬀectively formulaic

and prescribed by the National Basketball Association (2018). Thus, for players bracketed

within certain salary ranges, it is useful to identify which players generate the relative best

contractual ROI. We do exactly this in Figure 4. The best relative performers are at the top

of the resulting hockey stick shape, e.g., by increasing player salary: Tre Jones, Kevin Porter

Jr., Franz Wagner, Evan Mobley, Brook Lopez, Domantas Sabonis, Nikola Joki´c, Giannis

Antetokoumpo, and Russell Westbrook. Conversely, the worse relative performers are at the

bottom of the hockey stick shape, e.g., Bryn Forbes, Patty Mills, Landry Shamet, Richaun

Holmes, Duncan Robinson, Kyle Lowry, Andrew Wiggins, and Bradley Beal. Furthermore,

the overall shape of the scatter plot in Figure 4 is itself instructive. Because it is diﬃcult for

higher salary players to generate a break-even ROI based only on regular season on court

performance, Figure 4 implies that a considerable component of the expectation for maximum

salary players is play-oﬀ performance. As a ﬁnal caveat, the results will likely change with a

diﬀerent single game metric, diﬀerent game values, or methods that go beyond just on court

Rank Player Salary GP PVGCP ROI (%)

423 Derrick Rose $14.521 27 1.23 -0.080

422 John Wall $47.346 34 3.51 -0.070

421 Evan Fournier $18.000 27 1.33 -0.047

420 Andrew Wiggins $33.617 37 4.76 -0.039

419 Ben Simmons $35.449 42 5.33 -0.038

418 Garrett Temple $5.156 25 0.52 -0.037

417 Duncan Robinson $16.902 42 2.10 -0.032

416 Richaun Holmes $11.215 42 1.53 -0.032

415 Karl-Anthony Towns $33.833 29 4.58 -0.031

414 Davis Bertans $16.000 45 1.62 -0.030

413 Khris Middleton $37.984 33 3.63 -0.029

412 Bradley Beal $43.279 50 7.11 -0.026

411 Stephen Curry $48.070 56 8.72 -0.023

410 LeBron James $44.475 55 9.15 -0.022

409 Kyle Lowry $28.333 55 6.81 -0.022

408 Zion Williamson $13.535 29 4.67 -0.022

407 Klay Thompson $40.600 69 7.26 -0.022

406 Gordon Hayward $30.075 50 5.49 -0.022

405 Paul George $42.492 56 9.24 -0.021

404 Tobias Harris $37.633 74 8.33 -0.020

403 Bryn Forbes $2.298 25 0.71 -0.020

402 Michael Porter Jr. $30.914 62 6.29 -0.020

401 Collin Sexton $16.700 48 4.66 -0.020

400 Wendell Moore Jr. $2.307 29 0.53 -0.020

399 Furkan Korkmaz $5.000 37 1.13 -0.020

398 Kawhi Leonard $42.492 52 7.98 -0.019

397 Joe Harris $18.643 74 4.85 -0.019

396 Boban Marjanovic $4.101 31 0.80 -0.019

395 Damian Lillard $42.492 58 10.34 -0.018

394 Patty Mills $6.479 40 1.68 -0.018

393 Matthew Dellavedova $2.629 32 0.68 -0.018

392 Brandon Ingram $31.651 45 6.60 -0.017

391 DeAndre Jordan $10.734 39 3.11 -0.017

390 Devin Booker $33.833 53 8.52 -0.017

389 Myles Turner $35.097 62 9.60 -0.017

388 Al Horford $26.500 63 6.92 -0.016

387 Kevin Durant $44.120 47 7.86 -0.016

386 Steven Adams $17.927 42 6.66 -0.016

385 Kira Lewis Jr. $4.004 25 0.91 -0.015

384 Gary Harris $13.000 48 3.17 -0.015

383 Robert Covington $12.308 48 3.33 -0.015

382 Doug McDermott $13.750 64 4.07 -0.015

381 Landry Shamet $9.500 40 2.83 -0.015

380 Chris Paul $28.400 59 7.52 -0.015

379 Jimmy Butler $37.653 64 10.40 -0.014

378 Jrue Holiday $34.320 67 9.82 -0.014

377 Nicolas Batum $19.700 78 5.70 -0.014

376 Jamal Murray $31.651 65 9.22 -0.014

375 Zach LaVine $37.097 77 11.04 -0.013

374 Giannis Antetokounmpo $42.492 63 13.62 -0.013

Table 6: Bottom 50 performers: Return on investment. The bottom 50 performers in

terms of (8) for the 2022-2023 NBA regular season, based on a minimum of 25 games played. For

reference, we also include the player salary (HoopsHype, 2023) in millions, games played (GP), and

PVGCP, as calculated with (9).

performance. Further discussion may be found in Section 4.

Brook Lopez

Domantas Sabonis

Evan Mobley

Franz Wagner

Giannis Antetokounmpo

Kevin Porter Jr.

Nikola Jokic

Russell Westbrook

Tre Jones

Andrew Wiggins

Bradley Beal

Bryn Forbes

Duncan Robinson

Kyle Lowry

Landry Shamet

Patty Mills

Richaun Holmes

10%

0 10 20 30 40 50

Player Salary (Millions)

Return on Investment (ROI)

Figure 4: Relative return on investment by salary. A scatter plot of contractual ROI by salary

via (8) for the 2022-2023 NBA regular season. Because player salary is generally deterministic by

National Basketball Association (2018), this plot allows for relative comparisons within each salary

bracket. For example, for players in the $30M-$35M range, Nikola Joki´c generated a higher relative

regular season ROI than Andrew Wiggins. The mean line was generated by the loess function in

R Core Team (2022). The scatter plot shape is of interest, too, as it demonstrates maximum salary

players generally struggle to produce a break-even ROI based on regular season performance only.

4 Discussion

The NBA is big business, and no small part is due to the over $4.4 billion in annual player

compensation (HoopsHype, 2023). Given the salary cap restrictions of the NBA (National

Basketball Association, 2018), it is of paramount importance to team on court success to

appropriately compensate players for on court performance. Despite this, there are no known

studies that present a framework to measure a player’s contractual ROI. This study is thus

the ﬁrst known attempt.

Our approach unfolds in ﬁve parts. We ﬁrst decide on an investment time horizon over

I. Select Time

Period

Decide on a mea-

surement time

horizon (e.g., one

NBA regular sea-

son)

II. Estimate

GCP

Estimate a player’s

game contribution

percentage (e.g.,

GCP or an alter-

native) for each

game over the time

period in I

III. Estimate

SGV

Estimate a dollar

value of each game

in the measurement

time horizon (each

game need not have

the same value)

IV. Create Cash

Flows

Take an element-

wise product of the

vectors in II and

III to create a se-

ries of realized cash

ﬂows per player

over the measure-

ment time horizon

V. Perform ROI

Calculations

Treat the player

salary as an in-

vested (negative)

cash ﬂow with IV

as the realized

(positive) cash

ﬂows to perform

the desired ﬁnan-

cial analysis

Figure 5: NBA contractual ROI estimation framework summary.

which performance will be measured. The next step is computing a GCP metric. (The

GCP we propose in Section 2.1, via (1), is itself a novel contribution to the ﬁeld of on

court basketball player assessment metrics. Because (1) is calculated per game, cumulative

metrics such as PVGCP, via (9), allow analysts to assess the impact of missed games in a

single calculation (e.g., Figure 3). This has long been a known issue in the NBA (Wimbish,

2023). Additionally, PVGCP may oﬀer a fresh perspective on player evaluation, given the

general consensus of the other popular player evaluation metrics reported in Table 4; i.e.,

PER, WS, BPM, VORP, and RAPTOR unanimously ranking Joki´c ﬁrst, whereas PVGCP

ranks Sabonis ﬁrst.) After calculating GCP, the third step is to estimate the dollar value

of each NBA game in the measurement period (e.g., the SGV). Fourth, the GCP and SGV

calculations are combined to convert a player’s on court per game performance into a series

of realized cash ﬂows. From this, the ﬁfth and ﬁnal step is to perform standard ﬁnancial

calculations by using the player’s salary as invested (i.e., negative) cash ﬂows and the newly

created income (i.e., positive) cash ﬂows from step four. Our novel framework is summarized

in Figure 5.

The potential value of our proposed framework is illustrated in Figure 4, which may be

used by NBA player personnel decision makers and NBA player agents alike in contract

negotiations. Additionally, voters for NBA regular season awards may be interested in the

results of Table 4 or 5. Indeed, the Kia NBA Most Valuable Player award seems like a

good candidate for the consideration of PVGCP or ROI-type calculations. In terms of

forecasting, it is not diﬃcult to see how player on court projections may be used to produce

a distribution of GCP realizations, which may then be used to estimate the dollar or trade

value of draft picks or swaps or for potential trades more generally. Further, because player

contracts are highly regulated by the NBA CBA (National Basketball Association, 2018),

the ROI calculation methods herein may also be used for validation and fairness purposes

(e.g., Figure 2 and the break-even calculations of Section 3.3 suggest the maximum salary

restriction of 30-35% of a team’s salary cap appears reasonable). GCP may also be used

in sports injury-related or performance-based studies. For example, Page et al. (2013) look

at the eﬀect of minutes played and usage on a player’s production curve over the course of

their career. Within the model, the Game Score (Sports Reference LLC, 2023b) is used as a

measure of production. Our GCP oﬀers an alternative measure for a similar analysis.

In closing, we again emphasize the main contribution of this study is a framework to

measure realized contractual ROI for NBA players. As such, some simplifying assumptions

have been made, and it is possible our methodology may be customized or enhanced. For

example, the ﬁelds we select for the GCP calculation in Table 1 are just one such proposal.

These may be easily edited to meet the likely diﬀering views of NBA analysts (NBA teams

may also possess more detailed player evaluation data than what is publicly available, which is

a further motivation for alternative ﬁeld selections). Further, in (1), we use a simple, uniform-

like weighting system for the importance of each ﬁeld in Table 1. Alternative weighting

schemes are also possible. For example,

Ozmen (2016) analyzes the marginal contribution of

game statistics across various levels of competitiveness in the Euroleague to win probability.

Hence, a similar analysis could be utilized to vary the weighting scheme of (1), if desired.

Instead, additional precision may be used to assign the weights within GCP, such as reﬁning

the quality of a ﬁeld-goal attempt (e.g., Shortridge et al., 2014; Daly-Grafstein and Bornn,

2019) or accounting for peer (i.e., teammate) and non-peer (i.e., opponent) eﬀects (e.g.,

Horrace et al., 2022). Even more, the GCP may be ignored altogether and replaced with an

alternative per game evaluation metric. As long as the percentage and per game properties

hold, many alternatives to GCP are valid.

Beyond changes to the GCP metric, the ROI methods of Section 2.2 may be enhanced or

customized, too. For example, we assume the entire player salary is a time zero investment.

Instead, the actual payment dates of a player’s salary may be used. In the same way,

the actual game dates may be used instead of assuming 82 equally spaced per game cash

ﬂows. Further, we use a uniform weight for each game, and the nature of (8) implicitly

weights early season games more heavily than later season games. As an alternative, it

may be desirable to assign diﬀerent weights to each game based on its importance (i.e., the

proverbial “big game”). For example, Teramoto and Cross (2010) is an an example of how

weighting schemes may diﬀer for playoﬀ games versus regular season games in the NBA. Or,

to avoid the implicit weighting of (8), it may be prudent to randomize the order of the games

and calculate a distribution of realized ROI calculations. Indeed, the SGV methodology of

(5) is quite rudimentary and is thus ripe for additional study. Furthermore, we consider only

regular season games. While this is natural for regular season award considerations, there is

the obvious curiosity of how the calculations in Section 3.3 would change with the inclusion

of playoﬀ games or even oﬀ court revenue, such as jersey sales. We close with a hopeful note

in that the suggestions of this and the previous paragraph may motivate additional study.

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