Frequently Asked Questions

How to read a distribution, and what it does and does not claim.

What does each chart show?

Every chart is a histogram of outcomes from hundreds of simulated games. The horizontal axis is the result (a final margin, a game total, a player’s yardage), and the height is how often that result occurred across the simulation. The vertical line marks the market’s number. After the game, we overlay the realized outcome so you can see where it fell within the projected distribution.

Why publish a distribution rather than a single projection?

Football is a high-variance process, and a point estimate conceals that variance behind false precision. The same matchup, simulated a thousand times, yields a broad range of results. Reporting the full distribution, its center and its spread, shows not only the most likely outcome but how probable each alternative is, and exactly where the market’s line sits within it.

What do the mean and median toggles represent?

Two measures of central tendency. The median is the fiftieth percentile, the outcome with half the simulated results above it and half below, and the most direct comparison to a betting line. The mean is the expected value, which a skewed distribution pulls toward its longer tail. The two diverge only when the curve is asymmetric, which is often where the more interesting reads live. We default to the median.

How do I read a divergence from the line?

By comparing the model’s implied probability to the market’s. If the simulated distribution places roughly 58 percent of its mass above a given total while the posted line implies about 52 percent, that gap is where the model and the market disagree. The signal is the divergence between the two probabilities, not the point estimate, and it is a probabilistic lean rather than a certainty.

A player projected for 70 yards gained 30. Was the model wrong?

Not necessarily. A projection describes expected output across many similar matchups, not a forecast of one game, and it carries a substantial standard deviation. A receiver who averages 65 yards will, in a given week, plausibly post 20, 45, or 110. The appropriate test is calibration over a season, whether results fall within the projected percentiles at the expected frequency, not whether any single outcome matches the mean.

The distribution looks wide. Does that indicate low confidence?

No. Width reflects the inherent variance of the matchup, not uncertainty in the model. A genuinely close game should produce a wide, high-variance distribution; a mismatch should produce a tight one. A narrow curve is not a better curve, only a more lopsided game.

Why are some selections labeled “confidence”?

The label reflects the magnitude of the divergence between the model’s projection and the market line. A larger gap denotes a stronger probabilistic lean and is flagged accordingly; a marginal one is not. The designation measures separation from the line, not assurance of the result. We are pursuing honest, well-calibrated probabilities over a full season, not issuing guarantees.

Why might a projection change from one day to the next?

Two reasons. First, the inputs move: as injuries, weather, and depth charts are updated through the week, the simulation re-runs on the current information, so a distribution can shift before kickoff. Second, the model itself is under active development. We refine the underlying simulation between releases, and a refinement can move the projected curve. Each page is stamped at the bottom with the model version and the date it was last updated; if a figure has moved while the inputs have not, the model version is the place to look.

Where and when are forecasts published?

Each week’s forecasts are published to Substack subscribers before kickoff, while they are still forecasts. Once the games are final, that same forecast opens free on this site, set beside the realized result, so anyone can see how it read the week. Subscribers get it early; everyone can check it afterward.

Will there be losing weeks?

Yes. A sound long-run approach still has losing weeks and cold stretches; that is the nature of a high-variance process, not a failure of the method. The model is built to be judged over a full season, not a single Sunday. The standard we hold ourselves to is calibration across a season-long sample, and an honest public record of every week, winning and losing alike.

Is any of this betting advice?

No. Tiresias is a statistical analysis tool, not financial advice. Every figure we publish is a probability distribution derived from simulation, not a prediction of an actual outcome. Sports wagering carries genuine financial risk; never stake more than you can afford to lose. Restricted to those 21 and older, where legal. If gambling has become a problem for you, contact the National Council on Problem Gambling at 1-800-522-4700.