Lineup chemistry: when five players beat the sum of their parts

Our RAPM model is additive on purpose. It fits one offensive and one defensive number per player by ridge regression over every reconstructed possession, coding the five players on offense +1 and the five on defense -1, with points per 100 possessions as the target. Nothing in that setup has a term for two players enjoying each other's company. The model's prediction for any stint is plain arithmetic: add the five offensive ratings, subtract the five defensive ones.

Chemistry is what that arithmetic misses. Take every stint a particular five-man unit played, ask the model what it expected, compare that to what the unit actually did, and average the differences weighted by possessions. Statisticians call the leftover a residual. A positive residual is a surplus in points per 100 possessions: the unit scored more, or allowed less, than its own ten-man arithmetic said it should. A negative one means the unit underperformed its talent.

The important thing to hold onto is that a residual is a leftover, not a measurement of fit. It contains genuine chemistry. It also contains everything else the additive model could not see.

Raw five-man net ratings, the kind you get from a standard lineup table, tell you what happened without asking who it happened against. A backup unit that spends its minutes across from other backup units will look better than it is. A starting five that draws the other team's best group every night will look worse.

The residual sidesteps this without any extra machinery. The model's prediction already contains the five opponents, with a minus sign in front of them. Run into a strong opposing five and the predicted net rating drops accordingly, so simply matching that lower bar produces a chemistry near zero and beating it produces a positive one. Opponent adjustment is not a correction applied afterward. It falls out of how the number is defined.

The adjustment is only as good as the model's opinion of those opponents, and it covers who was on the floor rather than the circumstances they were in. Rest, travel, an injury that developed mid-game and garbage-time minutes all land in the residual along with everything else.

Five-man units accumulate possessions slowly. Even a team's most-used starting five plays a small share of the season intact, and the great majority of the combinations a team fields over a year never play enough possessions together to say anything about. Across a sample that short, a handful of contested threes falling or not falling moves net rating by more than any plausible chemistry effect could.

The Ringer's "Five Reasons NBA Lineup Data Is Lying to You" (April 2023) cites Kostya Medvedovsky's calculation that a five-man unit's offensive rating takes roughly 550 possessions to stabilize and its defensive rating roughly 850, thresholds most units never reach. The same piece makes the selection-bias point that matters most here: coaches stop playing units that lose. So the units with enough minutes to analyze are a survivorship-filtered sample that skews positive before you have computed anything.

We only publish chemistry for units with enough shared possessions, which is why some lineups on the site carry no chemistry value at all. That threshold suppresses the worst of the noise. It does not remove it. Read chemistry as a careful description of what already happened, not as a forecast of what will happen next.

The honest use of this number is narrow, and narrower than the word "chemistry" invites. It is a flag, not a verdict.

Computing a lineup residual requires knowing the exact five players on the floor for every stint of every game. There is no public lineup feed for recent seasons, so we rebuild it from scratch out of play-by-play (stats.nba.com playbyplayv3) plus box scores, tracking every substitution and reconciling the result against the official record.

The check on that reconstruction is per-player minutes. Ours match the official box score to within half a second for every game, across nine seasons from 2017-18 through 2025-26. Chemistry inherits that coverage, because it is computed on the same stints.

The second requirement is a possession-level model whose prediction you can subtract, and that comes free once RAPM is already fit on the same data. The full specification for both, including the ridge setup and the honest caveats on single-season RAPM, is on the methodology page.

Whether NBA lineups exceed the sum of their parts is a real research question with real published work behind it, and it is worth reading rather than taking our word. Stephen Devlin and David Uminsky used spectral analysis to identify group contributions in NBA lineups. A separate line of work frames the problem as cooperative game abstractions, evaluating and rewarding teamwork directly. John Chen has written a clear practitioner walkthrough of lineup value models and where additivity breaks, and Danny Leese approached the same question by clustering players into archetypes and scoring the combinations.

The recurring theme across that work is that additive player ratings already explain a great deal of what a lineup does, and that the synergies left over are identifiable rather than dominant. A residual is one of the simplest ways to see that for yourself: if chemistry were enormous, RAPM would be a much worse model than it is.

The player ratings underneath our chemistry number are RAPM and IPM, which belong to the same family of prior-informed impact metrics as EPM (Taylor Snarr) and LEBRON (BBall Index). DARKO (Kostya Medvedovsky) reaches the same goal by a different route, a Bayesian box-score projection updated game by game. What is missing from the shelf is not the idea, it is a place to look the number up. The papers compute synergy on their own samples and stop, and the tools that publish lineup tables publish unadjusted net ratings. We compute the residual against our own RAPM fit and publish it for every qualifying five-man unit across all nine seasons. As far as we can tell, we are the only site that does.