Forecasting Quarterback Performance Using Multilevel Regression

A rookie quarterback with four career starts and a ten-year veteran with a hundred should not be forecast the same way, and multilevel regression is the modeling tool built specifically to handle that difference correctly, not by ad hoc rule of thumb.

Two Bad Defaults: Pooling Everyone or Pooling No One

Forecasting an individual quarterback’s next-season performance runs into a tension between two flawed defaults. The first, complete pooling, ignores who the quarterback is entirely and forecasts every player using the same league-wide average — accurate on average across the whole league, but useless for distinguishing a genuinely elite passer from a replacement-level one. The second, no pooling, fits each quarterback a fully separate model using only his own career data — responsive to real individual differences, but dangerously overconfident for any player with a short track record, where a small sample of starts can produce a wildly noisy estimate that looks precise but is not.

Multilevel regression — also called hierarchical or mixed-effects regression — sits between these two extremes deliberately. It estimates a league-wide (or position-wide) distribution of quarterback performance at one level, and each individual quarterback’s deviation from that distribution at a second level, fitting both simultaneously from the same data instead of picking one level and ignoring the other.

Partial Pooling: Weighting the Blend by How Much Data Exists

The mechanism that makes this work is called partial pooling, and the intuition behind it is straightforward: a forecast for a given quarterback should be a weighted blend of his own individual history and the league-wide average, with the weight on his own history determined by how much reliable data actually exists about him. A rookie with four starts has a small, noisy individual sample, so the model leans more heavily on the league-wide distribution for his forecast — not because the model assumes rookies are all the same, but because there is not yet enough individual evidence to override the wider pattern with confidence. A veteran with several full seasons of starts has a large enough individual sample that the model lets his own history do most of the work, with only a small pull toward the average.

Critically, this weighting is not a fixed rule set by hand — it emerges from the model’s estimate of how much variance exists at each level (between quarterbacks generally, and within a single quarterback’s own game-to-game results), which is why multilevel regression is often preferred over a manually chosen shrinkage rule: the data determines how aggressively to shrink individual estimates toward the group; an analyst does not guess at a fixed cutoff for “enough starts to trust.”

The Classic Illustration, From Outside Football

The clearest historical demonstration of this shrinkage principle predates football analytics entirely. Bradley Efron and Carl Morris, in a 1975 paper in the Journal of the American Statistical Association, applied the closely related James-Stein estimator to a simple forecasting problem: predicting the rest-of-season batting average for 18 Major League Baseball players using only their first 45 at-bats of the 1970 season. They did not use each player’s own early-season average as the forecast; instead they shrank every player’s average toward the group average across all 18 players, with players whose early samples were furthest from the group average shrunk the hardest.

The shrunk estimates dramatically outperformed the unshrunk ones — the paper reported a total squared prediction error of roughly 0.027 for the shrinkage estimator against roughly 0.086 for the naive individual-average approach, a difference of more than three-fold. The exception, notably, was Roberto Clemente, whose early-season average was both extreme and — as it turned out — an accurate reflection of a genuinely exceptional hitter; shrinkage improved the average prediction across all 18 players substantially while costing a small amount of accuracy for the one player whose individual sample happened to be right all along. That asymmetry — shrinkage helps on average even when it occasionally overcorrects for a real outlier — carries over directly to quarterback forecasting: pooling toward the league average will occasionally undersell a rookie who turns out to be genuinely exceptional, while still producing better forecasts on average across the full population of quarterbacks being projected.

Applying the Same Principle to Quarterback Forecasting

A multilevel model for forecasting quarterback performance follows the same structure, adapted to football-specific data. A practical example, described in a technical write-up by data scientist Samuel Rome applying Bayesian hierarchical modeling to fantasy football scoring projections, builds a model where each player’s projection is a population-level baseline (informed by variables such as a rolling multi-game average, opponent defensive strength by position, and home-or-away status) adjusted by a player-specific term drawn from a shared distribution — the same partial-pooling structure as the batting-average example, applied to a much richer set of predictors.

For quarterback performance specifically, a comparable multilevel setup could model a passing-efficiency statistic (such as EPA per dropback or adjusted net yards per attempt) as a function of age, experience, and starter status at the population level, with a random effect per quarterback capturing individual ability beyond what those shared predictors explain. Age curves are a natural fit for this structure: a multilevel model does not assume every quarterback ages identically — it can let the age effect itself vary by player while still pooling information across the whole sample of quarterbacks to estimate what a typical age curve looks like — useful specifically because most individual quarterbacks do not play enough seasons at every age to estimate their own personal age curve with any precision.

Nested Groups: Quarterbacks Within Teams, Teams Within Seasons

Football data rarely has just one grouping level worth accounting for, and multilevel regression handles nested structure naturally. A quarterback’s performance is shaped partly by the quarterback himself and partly by the team around him — the offensive line, receiving corps, and play-calling scheme — so a fuller model can nest quarterback-level effects inside team-level effects inside season-level effects, letting each level pool information appropriately instead of forcing a single flat model to treat “which team a quarterback plays for” as just another unrelated predictor. Textbook treatments of the method, such as Andrew Gelman and Jennifer Hill’s Data Analysis Using Regression and Multilevel/Hierarchical Models, describe this as one of the central reasons multilevel models spread well beyond their original applications in education and biostatistics into any domain with a natural grouping structure — students within classrooms within schools maps directly onto plays within quarterbacks within teams.

What This Buys Over a Single Flat Regression

The practical payoff of a multilevel approach over a single regression fit to every quarterback-season pooled together is twofold. First, forecasts for players with limited data are less likely to be wildly overconfident, because the model is explicitly aware of how much individual evidence supports each player’s own estimate. Second, the model produces this correction automatically and consistently across every player in the dataset; an analyst does not have to manually decide, player by player, how much to discount a small sample — a decision that is easy to make inconsistently or with hindsight bias once actual results are known. The same logic extends past quarterback forecasting to any football projection built on uneven sample sizes across players or teams, which is most of them.

The predictor variables feeding a multilevel quarterback model are only half the problem — the uncertainty in whatever underlying performance statistic gets forecast, such as a small-sample EPA-per-dropback figure, compounds with the model-level shrinkage described here. And once a forecast is produced, grading it properly after the season ends — checking calibration, not just whether a single prediction happened to land — is what actually reveals whether the partial-pooling approach improved on a simpler method or merely looked more sophisticated.