The Wins Produced

Calculation
The following is a step-by-step guide to the Wins Produced calculation.
As noted below, these steps are detailed in Stumbling on Wins, The Wages of Wins, and in Berri (2008).
And more information is also offered at The Wages of Wins Journal

The example provided here focuses on Bob Lanier and the 1977-78 Detroit Pistons.

Preliminary Step A:
Link wins to offensive and defensive efficiency.
This simple model was noted by both Dean Oliver (2004) and John Hollinger
(2002). In Berri (2008) this model is developed mathematically. For here,
though, we are going to simply take the link between wins and the efficiency
measures as given. [One can read Berri (2008) for the math].

Here is the specific model linking winning percentage to offensive and

defensive efficiency.
The model was estimated with data from 1977-78 to 1990-91.
Data taken from Basketball-Reference.com

Dependent Variable is Winning Percentage

Independent Variable Coefficient t-statistic
Offensive Efficiency 3.442 62.6
Defensive Efficiency -3.447 -60.2
Constant term 0.535 10.4
Adjusted R2 = 0.93

Where
Offensive Efficiency = Points Scored divided by Possessions Employed (PE)
Defensive Efficiency = Points Surrendered divided by Possessions Acquired (PA)

Where
PE = FGA + 0.47*FTA + TO – REBO
PA = DFGM + 0.47*DFTM + REBD + DTO + REBTM

Where
FGA = Field Goal Attempts FTA = Free Throw Attempts
TO = Turnovers REBO = Offensive Rebounds
DFGM = Opponent’s Field Goals DFTM = Opponent’s Free Throws
Made Made
REBD = Defensive Rebounds DTO = Opponent’s Turnovers
REBTM = Team Rebounds
The formulation for PE and PA is explained in Berri (2008).
The value for FTA and DFTM is explained in Berri (2008)
REBTM refers to Team Rebounds that change possession. This calculation is detailed in the book and Berri (2008)

Preliminary Step B:
Determine the value, in terms of wins, of points and possessions.
This is done by differentiating the above wins model with respect to Points,
Points Surrendered, PE, and PA.

Table One
The Value of Points and Possessions
Variable Label Marginal Value
Points Scored PTS 0.032
Possessions Employed PE -0.032
Points Surrendered DPTS -0.032
Possessions Acquired PA 0.033

Preliminary Step C:
With the value of PTS, DPTS, PE, and PA determined, we can now ascertain
the value of all the individual elements of offensive and defensive efficiency
 (i.e. PTS, FGA, ORB, etc…). These values are detailed in The Wages of Wins.
The model estimated for the paperback, though, employed data from 1991-92
through the 2006-07 season. One should note that across the earlier time
period the values for the individual statistics are basically the same.

One should also note the values for blocked shots and assists are not taken
from the efficiency model. Further regressions are used to get at these two
factors. For details one is referred to Berri (2008) and The Wages of Wins.

The value of personal fouls, again as detailed in The Wages of Wins and Berri
(2008), is calculated from the value of the opponent’s free throws made.
Specifically, we first determine the percentage of personal fouls a player
committed on a team. We then multiply this percentage by the number of
free throws the opponent of a team made. For example, Bob Lanier
committed 9.3% of Detroit’s personal fouls in 1977-78. Detroit’s opponents
made 1,662 free throws, so Lanier is charged with 155.3 FTM(opp.).

Table Two
Value of Player and Team Statistics
Player Variables Marginal Value
Three Point Field Goals Made (3FGM) 0.064
Two Point Field Goals Made (2FGM) 0.032
Free Throws Made (FTM) 0.017
Missed Field Goals (FGMS) -0.032
Missed Free Throws (FTMS) -0.015
Offensive Rebounds (REBO) 0.032
Defensive Rebounds (REBD) 0.033
Turnovers (TO) -0.032
Steals (STL) 0.033
Opponent's Free Throws Made [FTM(opp.)] -0.017
Blocked Shots (BLK) 0.019
Assists (AST) 0.022
Team Variables Marginal Value
Opponent's Three Point Field Goals Made [3FGM(opp.)] -0.064
Opponent's Two Point Field Goals Made [2FGM(opp.)] -0.032
Opponent's Turnovers [TO(opp.)] 0.033
Team Turnovers (TOTM) -0.032
Team Rebounds (REBTM) 0.033

CALCULATING WINS PRODUCED

Step One:
Calculate the value of a player’s production (PROD).

The three point shot did not exist in 1977-78 so this value can be ignored. But
the other statistics were tabulated.

PROD = 2FGM*0.032 + FTM*0.017 + FGMS*-0.032 + FTMS*-0.015 +

REBO*0.032 + REBD*0.033 + TO*-0.032 + STL*0.033 + FTM(opp.)*-0.017
+ BLK*0.019 + AST*0.022

For Bob Lanier in 1977-78 the calculation would be as follows:

Lanier PROD = 622*0.032 + 298*0.017 + 537*-0.032 + 88*-0.015 +

197*0.032 + 518*0.033 + 225*-0.032 + 82*0.033 + 155.3*-0.017 + 93*0.019
+ 216*0.022 = 28.57

Step Two:
Adjust for teammate’s production of blocked shots and assists and
calculate P48

Blocked shots and assists do not impact wins directly. Neither of these stats
are a part of offensive or defensive efficiency. But each stat, as detailed in
The Wages of Wins, do have an impact on factors that are part of offensive
and defensive efficiency. In calculating PROD the player was credited with
the value of his block shots and assists. Now we have to account for the
impact of teammates blocked shots and assists on the player’s productivity.

To do this we calculate MATE48. For each team we take the accumulation of

blocked shots and assists and multiply each stat by the corresponding value
found in Table Two. We then determine the value a team creates from its
blocked shots and assists per 48 minutes played (by dividing the value of
blocked shots and assists by total minutes played and multiplying this by 48).

For example, the Pistons in 1977-78 blocked 330 shots and accumulated 1840
assists. Given the value of blocked shots (0.019) and assists (0.022), and
19,855 minutes played, we do the following calculation:

Per 48 minute value of blocked shots and assists = [(330*0.019+

1840*0.022) / 19,855] * 48 = 0.1145.

The average NBA team in 1977-78 had a per 48 minute value of blocked shots
and assists of 0.1305. MATE48 is simply the difference between the team
value and the league average.

MATE48 = Per 48 minute value of a team’s blocked shots and assists –

Average per 48 minutes value of blocked shot and assist

Pistons MATE48 = 0.1145 – 0.1305 = - 0.016

MATE48 is incorporated into each player’s value by subtracting MATE48

from each player’s PROD per 48 minutes. The outcome of this calculation is
called P48.

Lanier P48 = [(PROD / Minutes Played)*48] – MATE48 = [(28.57 /

2,311)*48] – (-0.016) = 0.609

Table Three
Value of MATE48 in 1977-78
Team MATE48
Atlanta -0.009
Boston -0.010
Buffalo -0.009
Chicago -0.001
Cleveland -0.016
Denver 0.007
Detroit -0.016
Golden State 0.002
Houston -0.010
Indiana -0.002
Kansas City -0.006
Los Angeles 0.009
Milwaukee 0.015
New Jersey 0.000
New Orleans 0.006
New York 0.015
Philadelphia 0.015
Phoenix 0.013
Portland 0.000
San Antonio 0.017
Seattle -0.013
Washington -0.007

The average value, in absolute terms, of MATE48 is 0.009. The average

value of PROD48 in the league is 0.304. MATE48 has very little impact on
our assessment of individual players. The correlation coefficient between
PROD48 and P48 in 1977-78 was 0.9986.

Step Three:
Incorporate team defense and calculate adjusted P48.

From Table Two we see that there are five factors tracked for the team that
are not tracked for individual players. These include 3FGM(opp.),
2FGM(opp.), TO(opp.), TOTM, and REBTM. Each of these statistics are
tracked for the team, but not assigned to individual players.

These are team defensive factors, and these are allocated across the players
according to the minutes the player plays. In other words, we treat defense
as a team activity, not an individual action.

This approach allows us to differentiate players who play on good and bad
defensive teams. But the data limitations prevent us from differentiating
between players who are relatively better or worse on an individual team. It
may be possible to utilize plus-minus data to overcome this limitation, but
until that happens, we utilize DEFTM48 in our evaluation of individual
players.

The calculation of DEFTM48 begins with the Team Defense Adjustment.

Team Defense Adjustment = [(2FGM(opp.)*-0.032 + TO(opp.)*0.033 +

TOTM*-0.032 + REBTM*0.033)/Minutes Played]*48

Pistons Team Defensive Adjustment = [(3688*-0.032 + 853*0.033 + 18*-

0.032 + 437.7*0.033)/19,855]*48 = -0.1839

To calculate DEFTM48 we compare each team’s defensive adjustment to the

league average.

DEFTM48 = League Average Team Defensive Adjustment - Team Defensive

Adjustment

Pistons DEFTM48 = -0.1734 - -0.1839 = 0.010

DEFTM48 is incorporated into each player’s value by subtracting DEFTM48

from each player’s P48. The outcome of this calculation is called Adj. P48.

Lanier Adj. P48 = 0.609 - (0.010) = 0.599

Table Four
Value of DEFTM48 in 1977-78
Team DEFTM48
Atlanta -0.030
Boston 0.006
Buffalo 0.005
Chicago 0.014
Cleveland -0.008
Denver 0.014
Detroit 0.010
Golden State -0.001
Houston 0.011
Indiana 0.004
Kansas City -0.002
Los Angeles 0.011
Milwaukee -0.001
New Jersey -0.022
New Orleans 0.017
New York 0.004
Philadelphia -0.001
Phoenix -0.014
Portland -0.018
San Antonio 0.013
Seattle -0.025
Washington 0.010

The average value, in absolute terms, of DEFTM48 is 0.011, so again this is a

very small adjustment. And as we saw with MATE48, DEFTM48 has very
little impact on our assessment of individual players. The correlation
coefficient between P48 and Adj. P48 in 1977-78 was 0.9977.
Step Four:
Adjusting for position played.

The average value for Adj. P48 is 0.304. But this value is not the same across
all positions. As noted in The Wages of Wins, centers and power forwards get
rebounds and tend not to commit turnovers. Guards are the opposite. The
nature of basketball is that teams need guards, small forward, and big men.
Given nature of the game, players have to be compared to their position
averages. These are reported in Table Five.

Table Five
Value of Adj. P48 Across Positions
Position Average Adj. P48
Centers and Power Forwards 0.420
Small Forwards 0.286
Guards 0.196

Previously averages were calculated for all five positions. Centers and power
forwards tend to have the same averages across time. Furthermore, it is
sometimes not clear who is the power forward or the center. Hence, it
doesn’t appear that much is lost if we simply treat centers and power
forwards as the same position. A similar argument can be offered for
shooting guards and point guards. Basically, what we see is that big men are
different from guards and that needs to be noted in the evaluation of players.
Trying to differentiate positions further seems unnecessary.

One last note…as detailed below, the average productivity of a big man in
1977-78 is higher than what we see today. And the productivity of guards
was lower in the 1970s. It was once believed that you needed a dominant big
man to compete in the NBA. Certainly these results suggest that was true
three decades ago.

To incorporate the position averages we need to identify the position each

player plays. For most players this is easy. For a few, though, it can be more
challenging.

For the 1977-78 season I am began with position data that was provided by
Dean Oliver.

Table Six
Position Data for the Detroit Pistons in 1977-78
Minutes Position Position
Pistons 77-78 Played Number Code Height Weight
Bob Lanier 2,311 5.0 C 6-11 256
Leon Douglas 1,993 4.5 FC 6-10 230
John Shumate 2,170 4.5 FC 6-9 235
Ben Poquette 626 4.5 FC 6-9 235
Howard Porter 107 4.5 FC 6-8 220
Marvin Barnes 269 4.5 FC 6-8 210
Willie Norwood 260 3.5 F 6-7 220
Al Eberhard 576 3.5 F 6-6 225
Jim Bostic 48 3.0 SF 6-7 225
Gus Gerard 805 2.5 GF 6-8 200
Ralph Simpson 739 2.5 GF 6-5 200
M.L. Carr 2,556 1.5 G 6-6 205
Chris Ford 2,582 1.5 G 6-5 190
Al Skinner 1,274 1.5 G 6-4 195
Jim Price 839 1.5 G 6-3 195
Wayman Britt 16 1.5 G 6-2 185
Kevin Porter 127 1.5 G 6-0 175
Eric Money 2,557 1.5 G 6-0 170

It is important to note that positions in basketball are not like baseball or

football. In baseball and football we can tell position by where a player
appears on the field. In basketball, though, position designations are more
arbitrary. Consequently, two analysts looking at the same team may
designate positions differently.

Here is the process I followed for the 1977-78 season.

1. Minutes are equal at each position
2. In general, players are allocated across the center and forwards position
according to Oliver’s designation and then by height and weight.
3. At the guard positions again we look at position designation, height, and
weight. But I also consider number of assists per minute. The players who
get more assists are generally considered point guards (although given that
we are not differentiating between guards with respect to the league
averages, the distinction between shooting and point guards is not
important).

Given this process, here is my allocation for the Pistons in 1977-78.

Table Seven
Allocating Player across Positions
Centers Minutes at Position
Bob Lanier 2,311
Leon Douglas 1,660
3,971
Power Forwards
John Shumate 2,170
Ben Poquette 626
Leon Douglas 333
Marvin Barnes 269
Willie Norwood 260
Al Eberhard 206
Howard Porter 107
3,971
Small Forwards
M.L. Carr 2,556
Gus Gerard 805
Al Eberhard 370
Ralph Simpson 192
Jim Bostic 48
3,971
Shooting Guards
Chris Ford 1,311
Al Skinner 1,274
Jim Price 839
Ralph Simpson 547
3,971
Point Guards
Eric Money 2,557
Chris Ford 1,271
Kevin Porter 127
Wayman Britt 16
3,971

With positions ascertained, we can now calculate a player’s performance

relative to the position average. For Lanier the calculation would be as
follows:

Lanier Relative Adj. P48 = Adj. P48 – League Average Adj. P48 = 0.599 –
0.420 = 0.179

So per 48 minutes, Lanier produced 0.179 more wins than an average center.
Given that he played 2,311 minutes, we can now see that Lanier produced 8.6
wins more than the average center.

Before moving on, what about a player like Ralph Simpson? Simpson is
listed at small forward and shooting guard. To assess his productivity, we
need to compare Simpson to an average small forward and an average
shooting guard. This is done as follows:

Simpson’s Relative Adj. P48 at small forward = 0.084 – 0.286 = -0.202

Simpson’s Relative Adj. P48 at shooting guard = 0.084 – 0.196 = -0.112
We then weight these two calculations according to the time Simpson spent
at each position. After this calculation we see that Simpson, per 48 minutes,
produced 0.135 less than an average player at the position he played (so his
 Relative Adj. P48 was -0.135).

Step Five:
Calculating WP48 and Wins Produced

If we stop after Step Four we will have a player’s production relative to the
position average. What we want is a player’s Wins Produce per 48 minutes
(WP48) and his Wins Produced.

As noted in The Wages of Wins, to move from relative wins to absolute wins
you need to note the average number of wins produced by a player per 48
minutes. This is quite easy to calculate.

The average team will win 0.500 games. Since a team employs five players
per 48 minutes, the average player must produce per 48 minutes 0.100 wins.
Because teams do play overtime games once in awhile, the actual average
production of wins per 48 minutes is 0.099 (and one should note, all this is
true regardless of how you calculate Wins Produced).

Given what we know about an average player, WP48 is calculated as follows:

WP48 = Relative Adj. P48 + 0.099

For Lanier the calculation is as follows:

Lanier WP48 = 0.179 + 0.099 = 0.278

Lanier played 2,311 minutes. If he produced 0.278 wins per 48 minutes he

must have produced 13.4 wins for the season.

Lanier Wins Produced = WP48 / 48 * Minutes Played = 0.278/48 * 2,311

= 13.4

Or you can think of it this way. An average player would have produced 4.8
wins in Lanier’s minutes. We saw in Step Four that Lanier produced 8.6
wins more than the average center. Therefore Lanier’s Wins Produced must
be 13.4.

Table Eight reports the calculation for each player the Pistons employed in
1977-78. Again, an average team would win 41 games, and an average
position would produce 8.2 victories. Looking over the roster, it appears the
Pistons were only above average at center. Their weakest position was power
forward. Although John Shumate was above average at the (4) spot, the
remaining power forwards employed were well below average.

Table Eight
Calculating Wins Produced for the Pistons in 1977-78
Pistons Minutes at Position Adj. P48 Position Average Relative Adj. P48 WP48 Wins Produced
Centers
Bob Lanier 2,311 0.599 0.420 0.179 0.278 13.4
Leon Douglas 1,660 0.353 0.420 -0.067 0.032 1.1
Position Totals 3,971 14.5
Power Forwards
John Shumate 2,170 0.454 0.420 0.034 0.133 6.0
Ben Poquette 626 0.225 0.420 -0.195 -0.095 -1.2
Leon Douglas 333 0.353 0.420 -0.067 0.032 0.2
Marvin Barnes 269 0.337 0.420 -0.083 0.016 0.1
Willie Norwood 260 0.205 0.420 -0.215 -0.116 -0.6
Al Eberhard 206 0.213 0.420 -0.207 -0.108 -0.5
Howard Porter 107 0.038 0.420 -0.382 -0.283 -0.6
Position Totals 3,971 3.4
Small Forwards
M.L. Carr 2,556 0.321 0.286 0.035 0.134 7.2
Gus Gerard 805 0.193 0.286 -0.092 0.007 0.1
Al Eberhard 370 0.213 0.286 -0.072 0.027 0.2
Ralph Simpson 192 0.084 0.286 -0.202 -0.103 -0.4
Jim Bostic 48 0.468 0.286 0.182 0.281 0.3
Position Totals 3,971 7.4
Shooting Guards
Chris Ford 1,311 0.246 0.196 0.050 0.149 4.1
Al Skinner 1,274 0.136 0.196 -0.060 0.039 1.0
Jim Price 839 0.161 0.196 -0.034 0.065 1.1
Ralph Simpson 547 0.084 0.196 -0.112 -0.013 -0.1
 Position Totals 3,971 6.1
Point Guards
Eric Money 2,557 0.138 0.196 -0.058 0.041 2.2
Chris Ford 1,271 0.246 0.196 0.050 0.149 3.9
Kevin Porter 127 0.305 0.196 0.109 0.208 0.6
Wayman Britt 16 0.113 0.196 -0.083 0.016 0.0
Position Totals 3,971 6.7
Team Totals 19,855 38.0

Although Lanier was clearly the most productive player on this team, Chris
Ford, M.L. Carr, and Shumate were above average. In fact, Lanier, Ford,
Carr, and Shumate produced 34.6 of this team’s 38.0 Wins Produced.

Table Nine
Ranking the Pistons of 1977-78 in terms of Wins Produced
Position Minutes Wins
Pistons Played Played ADJ P48 WP48 Produced
Bob Lanier 5.00 2,311 0.599 0.278 13.4
Chris Ford 1.51 2,582 0.246 0.149 8.0
M.L. Carr 3.00 2,556 0.321 0.134 7.2
John Shumate 4.00 2,170 0.454 0.133 6.0
Eric Money 1.00 2,557 0.138 0.041 2.2
Leon Douglas 4.83 1,993 0.353 0.032 1.3
Jim Price 2.00 839 0.161 0.065 1.1
Al Skinner 2.00 1,274 0.136 0.039 1.0
Kevin Porter 1.00 127 0.305 0.208 0.6
Jim Bostic 3.00 48 0.468 0.281 0.3
Gus Gerard 3.00 805 0.193 0.007 0.1
Marvin Barnes 4.00 269 0.337 0.016 0.1
Wayman Britt 1.00 16 0.113 0.016 0.0
Al Eberhard 3.36 576 0.213 -0.021 -0.3
Ralph Simpson 2.26 739 0.084 -0.036 -0.6
Willie Norwood 4.00 260 0.205 -0.116 -0.6
Howard Porter 4.00 107 0.038 -0.283 -0.6
Ben Poquette 4.00 626 0.225 -0.095 -1.2
Totals 19,855 38.0

As noted, the summation of Wins Produced for this team was 38.0. And the
Pistons actually did win 38 games in 1977-78. Table Ten reports for each
team the summation of Wins Produced and actual wins. As one can see, the
average difference – in absolute terms – is 2.3 wins. Again, Wins Produced
is based on a model connecting wins to offensive and defensive efficiency. So
the small difference between actual wins and the Summation of Wins
Produced simply reflects the fact that the efficiency metrics do indeed
explain team wins in the NBA.

Table Ten
Reviewing the Accuracy of Wins Produced in 1977-78
Actual Summation of Difference in
Team Wins Wins Produced Absolute Terms
Atlanta 41 40.9 0.1
Boston 32 36.1 4.1
Buffalo 27 31.3 4.3
Chicago 40 38.7 1.3
Cleveland 43 42.6 0.4
Denver 48 43.4 4.6
Detroit 38 38.0 0.0
Golden State 43 42.0 1.0
Houston 28 30.4 2.4
Indiana 31 34.6 3.6
Kansas City 31 36.3 5.3
Lakers 45 48.2 3.2
Milwaukee 44 40.0 4.0
New Jersey 24 26.2 2.2
New Orleans 39 36.2 2.8
New York 43 40.1 2.9
Philadelphia 55 54.8 0.2
Phoenix 49 51.0 2.0
Portland 58 57.2 0.8
San Antonio 52 49.9 2.1
Seattle 47 45.3 1.7
Washington 44 45.3 1.3
Average Difference 2.3

Here are the top 50 players in Wins Produced in 1977-78. Notice that big
men dominate the rankings. Again, it was widely believed that you needed a
 dominant big man to compete in the NBA back in the 1970s. The Wins
Produced calculations are consistent with that belief.

Table Eleven
The Top 50 Players in 1977-78
Rank Position Games Minutes Wins
Wins Produced Top 50 Player Team Played Played Played Adj. P48 WP48 Produced
1 Kareem Abdul-Jabbar LA Lakers 5.00 62 2,265 0.758 0.438 20.6
2 Artis Gilmore Chicago 5.00 82 3,067 0.605 0.284 18.1
3 Bill Walton Portland 5.00 58 1,929 0.771 0.451 18.1
4 Dave Cowens Boston 5.00 77 3,215 0.576 0.255 17.1
5 Wes Unseld Washington 5.00 80 2,644 0.626 0.305 16.8
6 Marques Johnson Milwaukee 3.58 80 2,765 0.547 0.283 16.3
7 George Gervin San Antonio 2.00 82 2,857 0.367 0.270 16.1
8 Marvin Webster Seattle 5.00 82 2,910 0.580 0.259 15.7
9 David Thompson Denver 2.00 80 3,025 0.340 0.243 15.3
10 Adrian Dantley Indiana-LA Lakers 3.00 79 2,933 0.428 0.241 14.7
11 Bob McAdoo New York 5.00 79 3,182 0.526 0.205 13.6
12 Bob Lanier Detroit 5.00 63 2,311 0.599 0.278 13.4
13 Swen Nater Buffalo 5.00 78 2,778 0.552 0.231 13.4
14 John Lucas Houston 1.00 82 2,933 0.311 0.215 13.1
15 Bobby Jones Denver 4.00 75 2,440 0.565 0.244 12.4
16 Foots Walker Cleveland 1.00 81 2,496 0.335 0.238 12.4
17 Julius Erving Philadelphia 2.88 74 2,429 0.411 0.235 11.9
18 Moses Malone Houston 5.00 59 2,107 0.589 0.269 11.8
19 Don Buse Phoenix 2.00 82 2,547 0.312 0.216 11.4
20 Rich Kelley New Orleans 5.00 82 2,119 0.577 0.257 11.3
21 Dan Issel Denver 5.00 82 2,851 0.507 0.187 11.1
22 Charles Dudley Golden State 1.00 78 1,660 0.412 0.316 10.9
23 Clifford Ray Golden State 4.88 79 2,268 0.550 0.229 10.8
24 Dan Roundfield Indiana 4.15 79 2,423 0.534 0.213 10.7
25 Walter Davis Phoenix 2.99 81 2,590 0.376 0.191 10.3
26 John Drew Atlanta 3.00 70 2,203 0.405 0.218 10.0
27 Paul Westphal Phoenix 1.00 80 2,481 0.289 0.192 9.9
28 Kevin Porter Detroit-New Jersey 1.00 82 2,813 0.266 0.169 9.9
29 Billy Paultz San Antonio 5.00 80 2,479 0.504 0.184 9.5
30 Norm Van Lier Chicago 1.86 78 2,524 0.276 0.179 9.4
31 Elmore Smith Cleveland 5.00 81 1,996 0.545 0.224 9.3
32 Bob Gross Portland 3.00 72 2,163 0.392 0.206 9.3
33 Truck Robinson New Orleans 3.73 82 3,638 0.405 0.120 9.1
34 Sam Lacey Kansas City 5.00 77 2,131 0.523 0.202 9.0
35 Elvin Hayes Washington 4.00 81 3,246 0.451 0.130 8.8
36 Butch Beard New York 1.00 79 1,979 0.306 0.210 8.6
37 Randy Smith Buffalo 2.00 82 3,314 0.220 0.123 8.5
38 Kermit Washington Boston-LA Lakers 4.28 57 1,617 0.567 0.246 8.3
39 Sonny Parker Golden State 2.97 82 2,069 0.376 0.192 8.3
40 Ricky Sobers Indiana 1.00 79 3,019 0.225 0.129 8.1
41 Chris Ford Detroit 1.51 82 2,582 0.246 0.149 8.0
42 Gus Williams Seattle 1.00 79 2,572 0.246 0.149 8.0
43 Darryl Dawkins Philadelphia 5.00 70 1,722 0.543 0.222 8.0
44 Cedric Maxwell Boston 3.20 72 1,213 0.526 0.313 7.9
45 Steve Hawes Atlanta 4.21 75 2,325 0.484 0.163 7.9
46 Mike Gale San Antonio 1.53 70 2,091 0.277 0.181 7.9
47 Bernard King New Jersey 3.04 79 3,092 0.313 0.122 7.9
48 Quinn Buckner Milwaukee 1.00 82 2,072 0.274 0.177 7.7
49 Fred Brown Seattle 2.00 72 1,965 0.273 0.176 7.2
50 Dave Twardzik Portland 1.00 75 1,820 0.285 0.189 7.2

CALCULATING WINS PRODUCED FOR

2006-07
The basic wins model was estimated with data from the 1991-92 through the
2006-07 season.
 Here are the values for the player and team statistics (notice how similar
these values are to what we saw in Table Two)

Table Twelve
Value of Player and Team Statistics
1991-92 to 2006-07
Player Variables Marginal Value
Three Point Field Goals Made (3FGM) 0.06493
Two Point Field Goals Made (2FGM) 0.03207
Free Throws Made (FTM) 0.01770
Missed Field Goals (FGMS) -0.03364
Missed Free Throws (FTMS) -0.01516
Offensive Rebounds (REBO) 0.03364
Defensive Rebounds (REBD) 0.03344
Turnovers (TO) -0.03364
Steals (STL) 0.03344
Opponent's Free Throws Made [FTM(opp.)] -0.01759
Blocked Shots (BLK) 0.01755
Assists (AST) 0.02228
Team Variables Marginal Value
Opponent's Three Point Field Goals Made [3FGM(opp.)] -0.06454
Opponent's Two Point Field Goals Made [2FGM(opp.)] -0.03188
Opponent's Turnovers [TO(opp.)] 0.03344
Team Turnovers (TOTM) -0.03364
Team Rebounds (REBTM) 0.03344

Given the values in Table Twelve, here are the steps in calculating Wins
Produced

Step 1: Calculate PROD

PROD = 3FGM*0.065 + 2FGM*0.032 + FTM*0.018 + FGMS*-0.034

+ FTMS*-0.015 + REBO*0.034 + REBD*0.033 + TO*-0.034 +
STL*0.034 + FTM(opp.)*-0.018 + BLK*0.018 + AST*0.022

Step 2: Adjust for MATE48 and calculate P48

PROD48 = [PROD/Minutes Played]*48

P48 = PROD48 – MATE48

Here are the values for MATE48 in 2006-07

Table Thirteen
Value of MATE48 in 2006-07
Team MATE48
Atlanta -0.00658
Boston -0.00603
Charlotte 0.00367
Chicago 0.00790
Cleveland -0.00316
Dallas -0.00432
Denver 0.01220
Detroit 0.00498
Golden State 0.01531
Houston -0.00390
Indiana -0.00023
LA Clippers 0.00553
LA Lakers 0.00641
Memphis -0.00297
Miami -0.00080
Milwaukee -0.00497
Minnesota 0.00251
New Jersey 0.00720
New Orleans -0.01261
 New York -0.01705
Orlando -0.00990
Philadelphia -0.00373
Phoenix 0.02064
Portland -0.01290
Sacramento -0.00873
San Antonio 0.00577
Seattle -0.00575
Toronto 0.00235
Utah 0.01373
Washington -0.00457

Note: For 2006-07, the average value for blocked shots and assists per 48
minutes was 0.11004.
The average value for MATE48, in absolute terms, was .00723.

Step Three: Adjust for DEFTM48 and calculate Adj. P48

Adj. P48 = P48 – DEFTM48

Here are the values for DEFTM48 in 2006-07

Table Fourteen
Value of DEFTM48 in 2006-07
Team DEFTM48
Atlanta -0.004838
Boston -0.011380
Charlotte -0.008978
Chicago -0.025093
Cleveland -0.020608
Dallas -0.016380
Denver 0.019057
Detroit -0.015784
Golden State 0.011894
Houston -0.008566
Indiana -0.014493
LA Clippers -0.000473
LA Lakers 0.006892
Memphis 0.027201
Miami 0.007541
Milwaukee 0.016586
Minnesota 0.006528
New Jersey -0.002011
New Orleans 0.008044
New York 0.012923
Orlando -0.026345
Philadelphia 0.001006
Phoenix 0.014891
Portland -0.002966
Sacramento 0.012344
San Antonio -0.014198
Seattle 0.016748
Toronto 0.010224
Utah -0.016428
Washington 0.016661

Note: For 2006-07, the average value for the Team Defensive Adjustment
was -0.1885.
The average value for DEFTM48, in absolute terms, was 0.01257.

Step Four: Adjust for position played

Relative Adj. P48 = Adj. P48 – League Average Adj. P48

Here is the average Adj. P48 at each position in 2006-07. Notice that
relative to 1977-78, big men are less productive and guards and small
forwards are now more productive.
 Table Fifteen
Value of Adj. P48 Across Positions
Position Average Adj P48
Centers and Power Forwards 0.37593
Small Forwards 0.26309
Guards 0.23884

Step Five: Calculate WP48 and Wins Produced

WP48 = Relative Adj. P48 + 0.09910

Wins Produced = WP48/48 * Minutes Played

Here is the accuracy of Wins Produced for the 2006-07 Season

Table Sixteen
Reviewing the Accuracy of Wins Produced in 2006-07
Actual Summation of Difference in
Team Wins Wins Produced Absolute Terms
Atlanta 30 28.3 1.7
Boston 24 31.8 7.8
Charlotte 33 31.2 1.8
Chicago 49 54.3 5.3
Cleveland 50 51.3 1.3
Dallas 67 60.2 6.8
Denver 45 45.2 0.2
Detroit 53 52.3 0.7
Golden State 42 39.9 2.1
Houston 52 54.0 2.0
Indiana 35 34.3 0.7
LA Clippers 40 39.5 0.5
LA Lakers 42 41.2 0.8
Memphis 22 27.5 5.5
Miami 44 38.6 5.4
Milwaukee 28 29.2 1.2
Minnesota 32 31.4 0.6
New Jersey 41 39.0 2.0
New Orleans/Oklahoma City 39 36.8 2.2
New York 33 33.6 0.6
Orlando 40 42.9 2.9
Philadelphia 35 32.9 2.1
Phoenix 61 60.8 0.2
Portland 32 29.7 2.3
Sacramento 33 36.0 3.0
San Antonio 58 63.5 5.5
Seattle 31 33.2 2.2
Toronto 47 43.4 3.6
Utah 51 48.6 2.4
Washington 41 39.6 1.4
Average Difference 2.5

Here is the Top 50 in Wins Produced for the 2006-07 season.

Unlike what we saw for the 1977-78 season, big men are not as dominant in today’s game.

Table Seventeen
The Top 50 Players in 2006-07
Rank Position Games Minutes Wins
Wins Produced Top 50 Player Team Played Played Played Adj. P48 WP48 Produced
1 Jason Kidd New Jersey 1.00 80 2,933 0.545 0.405 24.8
2 Kevin Garnett Minnesota 4.30 76 2,995 0.607 0.330 20.6
3 Dwight Howard Orlando 5.00 82 3,023 0.602 0.325 20.5
4 Tim Duncan San Antonio 4.42 80 2,726 0.631 0.355 20.1
5 Shawn Marion Phoenix 3.54 80 3,010 0.535 0.310 19.5
 6
7 Steve
CarlosNash
Boozer Phoenix
Utah 1.00
4.05 76
74 2,682
2,557 0.488
0.622 0.348
0.345 19.4
18.4
8 Dirk Nowitzki Dallas 4.15 78 2,820 0.583 0.306 18.0
9 Marcus Camby Denver 5.00 70 2371 0.632 0.356 17.6
10 LeBron James Cleveland 3.05 78 3,190 0.432 0.262 17.4
11 Tyson Chandler New Orleans/Oklahoma City 5.00 73 2,525 0.598 0.321 16.9
12 Ben Wallace Chicago 5.00 77 2,697 0.557 0.281 15.8
13 Kobe Bryant LA Lakers 2.03 77 3,140 0.375 0.234 15.3
14 Luol Deng Chicago 3.04 82 3,071 0.401 0.232 14.9
15 Manu Ginobili San Antonio 2.00 75 2,060 0.469 0.330 14.1
16 Emeka Okafor Charlotte 4.74 67 2,329 0.567 0.290 14.1
17 Elton Brand LA Clippers 4.40 80 3,077 0.490 0.213 13.6
18 David Lee New York 4.00 58 1,731 0.654 0.378 13.6
19 Amare Stoudemire Phoenix 4.96 82 2,689 0.516 0.240 13.4
20 Chauncey Billups Detroit 1.00 70 2,533 0.391 0.252 13.3
21 Chris Paul New Orleans/Oklahoma City 1.00 64 2,353 0.410 0.270 13.2
22 Chris Bosh Toronto 5.00 69 2,658 0.505 0.228 12.6
23 Vince Carter New Jersey 2.72 82 3,126 0.339 0.192 12.5
24 Andre Iguodala Philadelphia 2.44 76 3,062 0.345 0.195 12.4
25 Al Jefferson Boston 4.91 69 2,319 0.529 0.252 12.2
26 Dwyane Wade Miami 1.97 51 1,931 0.431 0.291 11.7
27 Andris Biedrins Golden State 5.00 82 2,382 0.512 0.235 11.7
28 Kevin Martin Sacramento 1.94 80 2,818 0.337 0.198 11.6
29 Pau Gasol Memphis 4.92 59 2,133 0.536 0.259 11.5
30 Gilbert Arenas Washington 1.42 74 2,942 0.319 0.180 11.0
31 Josh Howard Dallas 3.00 70 2,455 0.378 0.214 10.9
32 Gerald Wallace Charlotte 3.52 72 2,640 0.420 0.198 10.9
33 Jason Terry Dallas 1.54 81 2,846 0.323 0.183 10.9
34 Andre Miller Denver-Philadelphia 1.06 80 2965 0.314 0.174 10.7
35 Tony Parker San Antonio 1.00 77 2,499 0.334 0.194 10.1
36 Tracy McGrady Houston 2.65 71 2,539 0.344 0.188 9.9
37 Kirk Hinrich Chicago 1.29 80 2,839 0.307 0.167 9.9
38 Baron Davis Golden State 1.00 63 2,221 0.349 0.209 9.7
39 Samuel Dalembert Philadelphia 5.00 82 2,535 0.455 0.178 9.4
40 Jeff Foster Indiana 5.00 75 1,740 0.533 0.257 9.3
41 Deron Williams Utah 1.00 80 2,950 0.289 0.149 9.2
42 Dikembe Mutombo Houston 5.00 75 1,289 0.613 0.336 9.0
43 Josh Childress Atlanta 3.00 55 2,024 0.372 0.208 8.8
44 Caron Butler Washington 3.07 63 2,474 0.342 0.170 8.7
45 Ruben Patterson Milwaukee 3.06 81 2,508 0.337 0.166 8.7
46 Ron Artest Sacramento 3.35 70 2,641 0.360 0.156 8.6
47 Drew Gooden Cleveland 4.00 80 2,238 0.458 0.181 8.4
48 Tayshaun Prince Detroit 3.07 82 3,001 0.307 0.135 8.4
49 Corey Maggette LA Clippers 2.77 75 2,291 0.335 0.176 8.4
50 Rashard Lewis Seattle 3.33 60 2,348 0.373 0.171 8.4

REFERENCES

Berri, David J. 2008. “A Simple Measure of Worker Productivity in the National Basketball Association.” In The Business of Sport; eds.
Brad Humphreys and Dennis Howard, 3 volumes, Westport, Conn.: Praeger: 1-40.

Berri, David J. and Martin B. Schmidt. 2010 Stumbling on Wins: Two Economists Explore the Pitfalls on the Road to Victory in
Professional Sports. Financial Times Press (Princeton, N.J.)

Berri, David J., Martin B. Schmidt, and Stacey L. Brook. 2006. The Wages of Wins: Taking Measure of the Many Myths in Modern
Sport. Stanford University Press. Paperback edition released in 2007.

Hollinger, John. 2002. Pro Basketball Prospectus 2002. Washington D.C.: Brassey’s Sports.

Oliver, Dean. 2004. Basketball on Paper. Washington D.C.: Brassey’s.