What is correlation in DFS?

Correlation in DFS is the degree to which two players' fantasy outcomes move together. A QB's touchdowns are his receiver's touchdowns — their fantasy outcomes are positively correlated (coefficient ~0.55). A QB and an opposing defense move inversely — negatively correlated (coefficient ~-0.4). Correlation coefficients drive stacking, bring-back, and portfolio construction across every DFS sport.

How does correlation affect DFS lineup ceiling?

A correlated stack has a heavier-tailed joint distribution than the same-mean uncorrelated players. Concretely: a QB (mean 20, ceiling 30) + WR (mean 15, ceiling 25) at 0.55 correlation has a 90th-percentile combined outcome roughly 15-20% higher than the sum of independent 90th percentiles. That gap is where tournament wins come from.

Which DFS sports have the highest player-pair correlations?

MLB (batting-order-adjacent hitters at 0.4-0.6), NFL (QB-WR at 0.5-0.6), NHL (linemates at 0.5-0.55), soccer (attacker + creator on the same team at 0.4-0.5). NBA has the lowest team-sport correlations (teammate coefficients hover around 0.15-0.25) because scoring events don't chain as tightly. Individual sports (PGA, MMA, NASCAR) have near-zero correlations between competitors.

Why don't point projections capture correlation?

Point projections output a single number per player — the expected value. They can't represent joint distributions across correlated players because a single number has no variance information. Adding two point projections implicitly assumes independence, which systematically underprices the joint upside of correlated stacks. Correlated Monte Carlo simulation is the fix.

How does DFS Simulator use correlation?

Every sport has a per-sport correlation matrix baked into the simulator config. Monte Carlo iterations sample correlated outcomes (a QB's big game correlates with his WR's big game across every iteration), producing a joint distribution across the entire lineup that respects the real-world scoring dependencies.

DFS Correlation Deep Dive: The Math That Makes Stacking Work

By DFS Simulator TeamPublished July 31, 202611 min read

Correlation is the mathematical structure that makes DFS stacking work. Every DFS sport has known position-pair correlation coefficients that reflect real-world scoring dependencies — QB touchdowns are WR touchdowns; batting- order-adjacent hitters share rally events; NHL linemates share goals and assists. Simulation that respects those coefficients prices stacks accurately; point projections that assume independence systematically underprice them.

Correlation gets treated as intuition in most DFS content — "stack your QB with his receiver because they score together." That's true but incomplete. Correlation is a specific mathematical quantity (Pearson coefficient between -1 and 1) with specific effects on lineup ceiling distributions. Understanding the math is what separates heuristic stacking from optimized stacking.

Correlation coefficients by sport

NFL: QB-WR (same team) ≈ 0.55; QB-TE (same team) ≈ 0.45; QB-RB (same team) ≈ 0.15; QB-DST (same team) ≈ -0.3; QB-DST (opposing) ≈ +0.2.
MLB: batting-order-adjacent hitters (positions 1-2, 2-3, etc.) ≈ 0.4-0.5; positions 3-5 (heart of the order) ≈ 0.5-0.6; pitcher vs opposing bats ≈ -0.7 (never roster).
NHL: same-line skaters ≈ 0.5-0.55; same-team defenseman + top-line skater ≈ 0.35; opposing goalie vs stacked line ≈ -0.6.
NBA: teammates ≈ 0.15-0.25 (weak); game-total participants (both teams' stars in a pace-up game) ≈ 0.3.
Soccer: forward + attacking midfielder (same team) ≈ 0.45; full defense + goalkeeper (same team) ≈ 0.5-0.6 for clean-sheet outcomes.
PGA / MMA / NASCAR: essentially zero between competitors. Field sports don't stack via correlation.

The joint-distribution math

For two players with means μ₁, μ₂ and standard deviations σ₁, σ₂ at correlation ρ, the joint distribution's 90th-percentile combined outcome exceeds the sum of independent 90th percentiles by approximately:

Ceiling boost ≈ (2ρσ₁σ₂)^(1/2) — the covariance term that independent-distribution math loses. At ρ = 0.55 with typical DFS standard deviations, that's a 15-20% boost. At ρ = 0.15 (weak NBA correlation), it's under 5%. This is why NFL and MLB stacks are more rewarding than NBA stacks.

Why independence-based projections fail

A point projection for a QB (23 points) and his WR (16 points) adds to 39. That's the sum of means, which is correct for the joint mean. But the sum-of-independent- 90th-percentiles vs the joint 90th percentile diverge — the joint 90th percentile is higher. Cash-game construction uses means (independence is fine); GPP construction uses ceilings (independence is systematically wrong).

This is why every serious DFS operator ships correlated Monte Carlo simulation. Independence-based tools produce cash-game-competitive lineups but structurally underprice GPP-winning stacks.

Negative correlation and bring-backs

Not all correlation is positive. A QB's fantasy points move INVERSELY with his opposing defense's fantasy points (roughly -0.3 correlation). A pitcher's points move inversely with the opposing team's bats (-0.7 correlation). Understanding negative correlation prevents "auto-fail" stacks — never roster a QB and his opposing defense in the same lineup.

Bring-backs exploit a specific correlation pattern: the stack's universe (a shootout game script) correlates positively with the OPPOSING team's attackers benefiting from the same script. The QB-WR stack's 30-point ceiling universe is (with high probability) a universe where the opposing WR also went off — bring-back captures that correlated upside.

Portfolio-level correlation

A 20-lineup portfolio has correlation structure across lineups, not just within them. Two lineups sharing 6 of 9 players are 66% correlated — a bad slate for one is a bad slate for both. Exposure caps enforce portfolio- correlation limits so no single game script determines more than a bounded fraction of your portfolio's outcome. See exposure caps explained for the caps math.

DFS stacking strategy — the general theory of stacking correlation drives
Monte Carlo simulation explained — how the simulator samples the correlated distributions
NFL DFS strategy — where correlation coefficients are highest
MLB DFS stacking — batting-order correlation deep-dive

DFS Correlation Deep Dive: The Math That Makes Stacking Work

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