01
A scorer uses chances that belong to the whole team.
Same scorer. Same twenty points.
Thought experiment+2 made× missed○ available to a teammate
Twenty possessions in the team’s shared budget
Simplification: one shot ends each possession; no offensive rebounds, free throws, or turnovers. This demonstrates opportunity cost, not a full player valuation. Paper: p. 417.
02
A rebound can preserve the chance without changing the score.
Same points. Same number of possessions.
Sequence comparison · Not a time scaleFirst shot goes in1 shot · 2 points
One possession
Make+2 points
OpponentNext possession
Miss, then recover2 shots · 2 points
One possession
Miss0 points
ReboundKeep the ball
Make+2 points
OpponentNext possession
One possession1 shot · 2 points
Make+2 points
Score on the first shotOpponentNext possession
One possession2 shots · 2 points
Miss0 points
Rebound0 points
Make+2 points
Keep the ball.
Another shot within this possession.
Another shot within this possession.
OpponentNext possession
Both routes end with two points and the ball going to the opponent.
Same miss. Different team gets the next chance.
Hypothetical alternativesOpponent gets the rebound
Bulls’ possession
Jordan misses0 points · −0.025 credit
Opponent’s next possession
Opponent reboundsNo rebound credit for Rodman
Opponent can shootThe Bulls’ chance ends.
Rodman gets the rebound
Bulls’ same possession
Jordan misses0 points · −0.025 credit
Rodman rebounds0 points · +0.058 credit
Bulls can shoot againThe chance survives.
Table 5, pp. 417–418. Credits isolate the miss and rebound entries, before tempo, defense, and position adjustments. They are not live changes in win probability. The 1990s NBA reset the clock to 24 seconds after an offensive rebound; the 14-second rule began in 2018.
Why not simply add −0.025 and +0.058 and declare the sequence profitable?
Those two entries total +0.033, but they omit other terms in Berri’s accounting, including the shot-attempt charge assigned through team tempo. The useful basketball comparison is recovering the ball versus losing it after a miss. That does not establish that missing and recovering is better than making the original shot.
03
An assist and a turnover are not equal opposites.
Assist
A passTeammate scores
Turnover
Ball lostOpponent gets it
Keep six assists. Add turnovers.
Berri’s accounting · Two statistics onlyCredit for helping teammates score Six assists, unchanged
Assist
Assist
Assist
Assist
Assist
Assist
Debit for giving the ball away
Table 5, p. 417: one assist +0.014; one turnover −0.042. Bar widths compare these model credits, not points scored or possessions. The six assists still happened; adding turnovers does not erase their baskets.
Why not count every good and bad action equally?
Illustration using Table 5 · pp. 412–417
Two assists. One turnover. Is that a positive contribution?
Keep the actions fixed. Change how they are valued.
Why does Berri use unequal weights? He starts from how scoring and possession relate to winning, estimates those relationships from team data, and derives the value of each statistic. He does not assume that one assist cancels one turnover.
The equal-weight tally illustrates the assumption Berri criticizes on p. 412; it is not a reconstruction of a complete competing rating. The two-assist subtotal omits shooting and other contributions. Table 5 gives assist +0.014 and turnover −0.042. These are estimated relationships, not exact effects of every play.
A pass and a screen can both help. Which gets an entry?
Illustration · Extends the paper’s recorded statistics
Two ways A helps B score.
A passes to B
A passes → B shoots
B makes it: +2 points
A screens for B
A blocks the defender’s path → B gets room to shoot
B makes it: +2 points
In the paper: B’s two-pointer has a +0.026 entry; A’s recorded assist has +0.014. There is no separate screen entry (Table 5, pp. 417–418). Only these entries are shown.
Our question: the screen’s benefit may appear in B’s shooting, but how much belongs to A? These invented plays do not establish equal help or a ranking error. Berri leaves the causes of productivity, including team chemistry, for further research (p. 423).
Technical method and limits
The reported regressions contain 114 observations from 1994–1995 through 1997–1998. Berri estimates two linked equations for winning percentage and opponent scoring using three-stage least squares, with team-specific fixed effects. Several inputs are ratios, including assists per turnover; derivatives yield component values. These are rounded published estimates, not a refit or a claim that every live turnover costs exactly three assists regardless of game context.
04
What did you do—and what did your situation supply?
Each stage adds an adjustment to the preceding calculation. Compare Jordan and Malone as you move through the five stages.
Credit per 48 player-minutes
Table 6, p. 420: published rounded rates × 48. Intermediate values are not complete win estimates. The baseline illustration uses 0.10 per full-game role; the paper’s rounded 0.0021 per minute becomes 0.1008. This rounding prevents exact reconstruction of its reported season totals.
05
Ordinary rebounding is already in the baseline. Rodman supplies the surplus.
For Rodman’s mix of center and power-forward minutes, Berri estimates an average player would collect 8.8 rebounds per game. Rodman actually averaged 15.0, as reported in the paper.
How much of that surplus could you take away?
Sensitivity illustrationMove the slider to reduce his rebound credit. The rest of his estimated contribution stays fixed.
8.8
Position baseline≈13.5
Matches Jordan15.0
Rodman’s actual
Position baseline≈13.5
Matches Jordan15.0
Rodman’s actual
Rebounds per game
8.8 expected from his positional mix
Rodman: Estimated season wins
Vertical marker: Jordan’s 16.44 wins · Scale 0–22
P. 421 and Table 9. Berri attributes 18.4 wins to Rodman’s 6.2-rebound surplus, within 20.79 total estimated wins. This illustration scales that reported contribution proportionally and leaves 2.39 wins in the other terms. It does not recompute the offensive/defensive rebound mix, team response, or position baselines.
Does Rodman’s extra rebound give the Bulls an extra rebound?
Illustration · Two assumed alternatives, not Rodman data
Same missed Bulls shot. Who gets the loose ball?
Compare two situations. In one, an opponent is next to the ball. In the other, a Bulls teammate is.
Each column is a separate hypothetical situation. We assume who gets the ball without Rodman; the paper does not report how often either situation occurred.
The slider above changes his recorded rebounds. It cannot tell us who would have collected them instead. Removing his rebound credit and removing team possessions are different experiments.
In the 1999 paper: measured productivity and its causes are distinct (p. 423). Later context: Berri discusses teammate influences in “NBA Babble Babble” (2007). No later formula is applied here.
06
Jordan produced more in total. Rodman produced more per minute.
1998 playoffs. The equal-time comparison holds each player’s estimated production rate fixed.
Remove the extra minutes. See who leads.
Table 10 + equal-time illustrationCredit at 722 minutesCredit from extra minutes
Table 10, p. 422: Jordan 872 minutes / 3.86 wins; Pippen 836 / 3.76; Rodman 722 / 3.65. The blue/orange split applies each player’s season-average estimated rate to 722 minutes and the remaining minutes. It is not a record of which particular minutes produced the wins. Equal-time estimates are arithmetic comparisons, not forecasts of different rotations.
07
The miss is visible. Its individual cause may not be.
A defender can challenge a shot—get a hand up and make it harder—without blocking it. Berri’s data record the miss, but do not name that defender. A recorded block does name the player.
Same missed shot. Three alternative versions.
1 · What happens on court
2 · What enters the model
3 · Who receives this miss’s credit
Same +0.013 total credit. Only its allocation can change.
Pp. 418–419, Table 5, and notes 20–23. Simplified five-player team with equal total minutes. Only the opponent-miss component changes; rebounds and other entries are held fixed. A blocked miss is removed from the shared defensive pool to avoid counting it twice.
The limitation is specific, not “the model ignores defense.”It accounts for team defense, but cannot distinguish every player’s role in producing it. Berri also acknowledges that some blocked shots would have missed anyway.
08
Do the player estimates add up to the team’s results?
Berri checks the sum of player estimates against team wins across the 1997–1998 regular season and playoffs combined. That is why Chicago has 77 wins here, rather than its familiar 62 regular-season wins.
Regular season + playoffs
Actual wins, combined
Sum of player estimates
Table 11, pp. 422–423. Season breakdowns: Chicago’s season record; Utah’s regular season and playoff results.
2.6 wins is the average miss—not a limit on the misses.
Across 29 teams, the estimates miss actual wins by 2.6 wins on average, counting high and low errors alike.
Utah · exact at published precision
0.0 wins off
Chicago · estimate too low
4.7 wins off
Detroit · estimate too high
7.4 wins off
Three examples; the average uses all 29 teams.
Detroit is one of the largest misses.Four of 29 teams miss by more than five wins: Boston (5.2), Philadelphia (5.3), Detroit (7.4), and Vancouver (7.4). Detroit and Vancouver tie for the largest error. The paper reports these discrepancies but does not diagnose Detroit’s.
Is 2.6 wins a small error? Compare it with ignoring team differences.
Our calculation · Using all 29 teams in Table 11
How far is the estimate from the actual result?
Chicago won 77 games. Berri estimates 72.3: a gap of 4.7 wins. Smaller gaps mean closer estimates.
Compare his model with a crude alternative: give every team 43.4 wins, the average actual total across all 29 teams.
Distance from actual wins · bar scale 0–40 wins
Average gap across all 29 teams wins
Three selected teams above; the average uses all 29. Bars show absolute error on the same 0–40-win scale. Actual totals include regular season + playoffs. The constant calculation uses the unrounded mean, 43.448… wins.
This is a low bar to clear. The constant ignores team strength and playoff games played. Beating it does not establish superiority over another player-rating method or accuracy on future seasons.
Inspect the 29 inputs and calculations
| Team | Actual | Berri | Constant |
|---|
This comparison is added for this explainer; Berri does not report this benchmark in Table 11. A competitive benchmark would require another method tested on the same outcomes under the same conditions.
The team totals support the model. What else would establish the player rankings?
Berri treats the team-level agreement as evidence that his Jordan, Malone, and Rodman estimates are accurate. The weights, team adjustments, and position comparisons provide his rationale for allocating credit. The question is how independently the final check tests that allocation.
Our interpretation · Scope of the paper’s evidence
Match the question to the evidence.
Interpretation of pp. 418–423, not a further test performed in this explainer. The 2.6-win team error is not an uncertainty interval for a player. “Untested here” refers to this paper’s Table 11 check, not to all of Berri’s subsequent research.
Open questions worth exploring next
- When a player collects an additional rebound, how often does the team gain control it would otherwise have lost, versus another teammate losing the rebound credit?
- How do shot difficulty, shot creation, and teammates’ spacing alter the meaning of identical box-score lines?
- How sensitive are the rankings to estimated position minutes and the assignment of team-level terms?
- Would the same weights and allocation rules work on seasons not used to construct them?