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LUMA Basketball Research

Introducing ARC v3 Adjusted Regularized Contribution

An NBA player’s actual impact per 100 possessions against the average possession.

The ARC board →
One-pager · Full paper coming soonLOKI one-pager →LOKI board →ARC board →Research →

What ARC v3 is

ARC v3 is the third and latest model of Adjusted Regularized Contribution: an expected value prior Bayesian RAPM (EV-RAPM).

ARC v3 is built on 29 seasons of play-by-play (1997–98 to 2025–26): 33,735 games, 835,979 stints, 6.3 million possessions and 6.7 million points, across 2,781 players.

Whereas the prior renditions of ARC (ARC v1 and v2) standardized the box-score valuation and RAPM separately and added them together with z-scored weights outside the solve, ARC v3 is Bayesian. It uses the box-score valuation as a starting estimate of a player's skill, a prior, within the solve. The more evidence a player has, through his minutes and lineup data, the more he can deviate from the expected-point valuation of his box-score actions.

This Bayesian blend treats the actualized production of a player as foundational context, then adds the signal on/off data provides. The abstraction on/off data provides fills in the pieces of context the box-score valuation may have missed, in direct proportion to how much evidence there is.

Instead of fitting box-score actions to RAPM, ARC prices the added possession value of every box-score action (r = .56 with RAPM over the same seasons).

Why count instead of fit → Expected Box Value RAPM

Season-end top 102025–26
  1. 1Shai Gilgeous-AlexanderOKC+12.9
  2. 2Nikola JokićDEN+11.5
  3. 3Kawhi LeonardLAC+11.0
  4. 4Victor WembanyamaSAS+10.7
  5. 5Giannis AntetokounmpoMIL+10.2
  6. 6Luka DončićLAL+7.6
  7. 7Jimmy Butler IIIGSW+6.6
  8. 8Stephen CurryGSW+5.8
  9. 9Chet HolmgrenOKC+5.7
  10. 10Donovan MitchellCLE+5.7
1998–992025–26

2-year ARC · played 55%+ of games over the two seasons

Why plain plus-minus fails

2008–09 LakersKobe BryantLamar Odom
+/-+659+695
Net on/off, per 100+11.9 ± 4.5+18.6 ± 3.5
ARC v3 (2-year)+6.9+5.1
Kobe on/off +11.9 ±4.5Odom on/off +18.6 ±3.5Kobe+1.72,227vs +2.0Both+17.63,348vs +0.9Odom+10.21,082vs −2.6Neither−14.8822vs −3.7
2008–09 Lakers · net per 100 possessions · possessions · vs = opponents’ ARC

Two main components

ARC v3 can be separated into two main components.

Individual skill (formerly Box+)

The possession-by-possession accounting of a player's box-score production can also be read as his individual skill, irrespective of on/off lineup data. Individual skill is the starting point for each player: before ARC looks at a single lineup, every player is rated at what his own recorded actions are worth.

In 2025–26, the average NBA possession was worth 1.16 points. Each action is credited with how much it changed that expectation.

average possession · 1.16Missed three−0.86shooterOffensive rebound+0.86rebounderMade two, assisted+0.84shooter and passer1.160.301.162.002 points
Simplified illustration · 2025–26 league averages

Lineups (Impact)

Contemporary implementations of RAPM start every player at zero, the league average, until there is enough lineup data to prove otherwise. ARC uses individual skill as the starting point until lineups prove otherwise, then uses every stint since 1997–98 (a stretch with the same ten players on the floor).

How they come together

Both components come out of one solve. Individual skill enters as the prior; lineups are what the stints add to it. The model also sets, inside the same solve, how much a point of box-score valuation is worth on the court, for offense and for defense.

ARC = individual skill + lineups
Individual skill and lineups go in; one rating comes out.

Why expected value accounting > RAPM regression for description

Read

Raw box actions may be too lossy to use for prediction, but they are uniquely positioned to describe what happened.

You wouldn’t want to take that and regress it. For description, ARC posits that it is not ideal to take those box-score actions, account for actualized production, and then regress it to RAPM. RAPM is known for being extremely lossy year to year, even at 1,000 possessions, and for dealing with issues of collinearity and proper credit allocation.

The expected valuation of box-score actions can act as a structural foundation for once again quantifying what a player actually did, as far as we can tangibly capture within a game. It has the most direct outcome, and the most direct effect we can measure, on the net margin.

  • Decomposable and open rather than opaque. There are no opaque numbers and coefficients: the number stays decomposable down to the granular actions, play types, shot zones, and skills that make up the overall score.
  • No big-man bias (some high-usage creator bias, which we posit).
2019–20 to 2025–26, 2-year viewRAPMBPM (box score only)ARC v3
Describes the season: player on/off (r²).77.35.75
Describes the season: lineup net (r²).26.08.23
Holds from one 2-year window to the next (r).43.76.62
Holds for players who changed teams (r).36.71.52

ARC v3 is the best of both worlds.

r²: how much of what happened the ratings explain (0 to 1). r: how closely a player's rating in one 2-year window matches the next (1 is a perfect match).

Decomps, decomps, decomps

Another distinctive part of Adjusted Regularized Contribution, and what separates it from other box-prior RAPMs, is that it is fully decomposable rather than an opaque number. ARC can be used not only to compare players as a whole, but to see the underlying context and story of how a player impacts the game, possession by possession.

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Each node is the exact sum of its children (to rounding). Points per 100 possessions against the average possession. Switch the split: it is the same number, read another way.

Each split is exact; the parts add up to the rating. The measured skills are the one tab that does not add up: they describe the player, as context.

ARC = O-ARC + D-ARC ARC = individual skill + lineups ARC = shot value + possession value shot value = selection + conversion possession value = retention + generation

What offensive conversion is worth → the note

How to read ARC

ARC divides credit among individuals based on what actually happened in a given season or time period. It is not predictive.

A player with an ARC of 0 can be understood to have a neutral effect on their team’s expected point valuation per 100 possessions. This is because, intuitively, minutes are going to better players. The average possession is mostly defined by rotation players. Thus ARC is functionally in units of points above the rotation player. The average ARC of all 582 players on the 2025–26 2-year board is −0.9.

-6-4-20+2+4+6+8+10+120 = average possessionTop 10#1–10+8.0Stars#11–30+4.1Starters#31–150+1.3Rotation#151–300−0.6Bench#301–450−2.2Deep bench#451–582−3.5
Every player on the 2025–26 2-year board, grouped by rank. Hover a dot to see who it is; the bar and the number at the right are the tier’s median.

ARC solved over a player’s entire career. Past seasons weigh more than in any other view, but recent games still count the most. The box score keeps a long memory; lineups turn over faster.

How much each season counts
this−1−2−3−4−5−6−7
Box scoreLineupshover a block for its share
The view
Seasons in the solvethe whole career
This season’s sharebox score 11% · lineups 29%
A season counts half as muchbox score: 6 seasons back · lineups: 2 seasons back
Reliability
Next season’s game margins explained (R²).166
Snapshotsevery week, every season since 1997–98

How the different views function

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Conclusion

We here at LUMA Basketball Research posit that ARC is a great metric for properly describing what happened over a given time period. ARC struggles a lot to anticipate growth or regression in players, down to their granular skills and the intersection of their talents. That is exactly where LOKI comes in.

Read the LOKI one-pager →