The Wins
Produced Calculation
The
following is a step-by-step guide to the Wins Produced calculation.
As noted
below, these steps are detailed both in The Wages of Wins and in Berri (2008).
The steps
in the book, though, left out the math. So
hopefully the following example (with the math) will be helpful.
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 Made |
DFTM = Opponent’s Free Throws 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
|
Pistons 77-78 |
Minutes Played |
Position Number |
Position 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 |