The Average Tells You Where. Only the Variance Tells You Who Wins.
A number that doesn’t move can’t predict anything.
Imagine two statistics you might use to guess which of two teams will win. The first, Predictor A, is nearly the same for every team — everyone scores about eight. The second, Predictor B, is all over the map — some teams at two, some at twenty. They have the same average. They are not remotely equally useful. Predictor A cannot separate a winner from a loser, because both teams have basically the same value; it cancels out. Every ounce of predictive power lives in Predictor B, the one that varies.
That is the whole idea in one picture. When you are looking for what drives a result, you are really looking for what moves. Chase the biggest number and you will keep landing on things that are the same for everyone — comforting, prominent, and useless for telling anybody apart.
The variance of a total is the sum of its parts.
Variance has a precise definition — the average squared distance from the mean — and one property that does most of the work: for pieces that move independently, the variance of a sum is the sum of the variances. If an outcome is built by adding up components (a fantasy score, a team’s run total, a portfolio’s return), then the swing of the whole is governed by the swings of the parts, and the biggest-variance parts dominate. A component that barely moves contributes almost nothing to where the total lands, no matter how many points it is nominally worth.
The same logic runs through any prediction model. A predictor’s contribution to the outcome scales with its coefficient times its own variance — so two variables with the same relationship to the result are not equally useful; the one that varies more pulls more weight. A predictor pinned at a constant has zero variance and therefore zero influence, however important it seems in theory.
One honest guardrail, so this is not misused: variance is necessary but not sufficient. A number that swings wildly but has nothing to do with the outcome is not a predictor — it is just noise, and loud noise at that. The useful inputs are the ones that both vary and track the result. Fantasy football is the unusually clean case where that second condition comes for free, because the categories literally add up to the score; in the messier real world, you still have to check that the thing that moves is moving with what you are trying to predict.
The full treatment: variance, covariance, and explained spread.
How variance is defined and used — standard deviation, covariance, the way a regression apportions the outcome’s variance among predictors, and the R² that measures how much of it you have explained — is developed in The Sports Page’s companion statistics textbook, a free, open, graduate-level text, with the R code to compute and decompose a variance yourself. Read it free here — the same “read, play, learn” idea, one rung deeper.
Where this concept shows up in The Sports Page
- The “variance is king” fantasy issue — a matchup is decided in the high-swing slots (a receiver’s good week is ten times a bad one), never in the steady ones. The anchor case.
- The “own mean” franchise pieces — a team’s average tells you its level; its variance around that mean tells you whether it’s a steady contender or a boom-or-bust wildcard.
- The “pull the goalie” issue — the sequel: variance drags every matchup toward the coin flip, so the favorite smothers it and the underdog goes hunting for it.
- The Objective Function (Concept No. 24) — the necessary partner: whether swing helps or hurts you depends entirely on what you are trying to maximize.
- Communicating Uncertainty (Concept No. 18) — the sibling: variance is the spread you are obligated to report, not hide.
- Rates of Change (Concept No. 21) — a related trap: each derivative you take amplifies variance, which is why higher-order signals are noisier.