Team KR is the rating. A game is the collision of two of them.
A game is not won by the higher Team KR alone. The matchup, the field position, the coaching, the officiating, and the variance all move the outcome, and the simulation is where they are played out. It runs the two rosters through a drive-and-play model on the correct engine, N times, and returns a distribution, a win probability, a spread, a total, and a scoreline spread, because a single football game is high-variance and turnover-driven and a distribution is the only honest answer. It plays the teams it is handed and never re-grades them, and it credits only what the data supports: no momentum, no altitude myth, no false precision.
Run it a thousand times, because one game is high-variance.
A composite matchup, Team A favored. The engine does not hand back one score. It runs the two rosters through the drive-and-play model N times and returns the whole shape of what could happen.
The distribution is the answer. A favorite by three-and-a-half still loses better than a third of the time, and the engine reports the band rather than a single score. Deterministic given a seed, auditable and reproducible. Believable over impressive: a wide honest distribution beats a confident single number.
Illustrative on the real multi-run distribution (N runs to a win probability, spread, total, and scoreline, deterministic given a seed, wide honest bands). Composite matchup, demonstration figures.
The rating sets the baseline. The matchup bends the drive.
The higher Team KR is favored. But the game is not the gap in the ratings, it is the way the two rosters actually collide, drive by drive.
The modifiers target the expected-points differential and the rates, never a KR, and compose multiplicatively under a joint bound so a stack cannot compound without limit and the upset stays possible. Turnovers are the primary single-game driver at about five expected points each, interceptions skill-driven and fumble recovery near a coin flip, so a season regresses a lucky margin. The higher rating is favored. The matchup decides by how much, and sometimes whether.
Illustrative on the real matchup model (the expected-points bridge, field position, the three interaction classes, the trench and weak-link and strong-link matchups, bounded and jointly bounded, turnover leverage). Composite matchup, demonstration figures.
The actors, the weather, and the market, credited only from evidence.
Close games are decided at the margins, and the engine credits only the margins the data actually supports. The actors enter as actors, the weather as an environment, and the myths do not enter at all.
The late-game mechanics that decide close football, the two-minute drill, the four-minute offense, the timeout state, and overtime on the level's own rules, are modeled explicitly, the postseason applies a bounded favorite-separation, and the engine surfaces the key matchup notes in plain language. Model the margins that decide games, and refuse to invent the ones that do not exist.
Illustrative on the real actor and context layers (coaching, officiating, the evidence-based situational factors, the not-modeled myths, injury attrition, the market calibration and the edge). Composite matchup, demonstration figures.
A game is not a rating, it is the collision of two ratings under the rules, the clock, the field, and the matchup, and the honest way to report a collision this variance-heavy is a distribution, never a single score. The engine plays the two teams it is handed, on one engine, thousands of times, and the higher rating wins most of the runs, but the tail where the underdog wins is real and the ratings themselves allow it, because a game is decided as much by the trench mismatch, the coverage hole attacked every drive, a five-expected-point turnover, the weather, and a fourth-down decision as by the gap in Team KR. So the matchup bends the drive within bounds that never let it rewrite the ratings, field position carries the hidden value of the third phase, and coaching and officiating enter as the in-game actors they are and not as multipliers on the roster. And the engine credits only what the data supports: it models the margins that decide games and refuses to invent momentum or an altitude edge or a narrative the numbers do not carry. The arrow runs one way, the simulation never writes back to an evaluation, and the answer is always a band with its confidence attached. Favor the favorite, and respect the tail, because that is where the games actually live.
Collide the ratings. Report the distribution.
Simulation plays two rosters through a drive-and-play model on the matchup, the field, the actors, and the variance, and returns a win probability, a spread, a total, and a scoreline spread, never a single score and never a change to a rating.