How Monte-Carlo simulation projects baseball games
By George Boyle · Updated 2026-08-21 · The Sport Stack
A Monte Carlo projection simulates an event thousands of times and reports how often each outcome occurred, rather than calculating a single expected result. For sports it matters because the distribution is the useful part: knowing a team scores 24 points on average tells you far less than knowing how often they clear 27.5.
Distributions, not point estimates
A baseball game is a chain of discrete events — plate appearances — each with probabilities that depend on who is batting, who is pitching, the park, and the game state. A Monte-Carlo engine plays that chain forward: it samples an outcome for every plate appearance, walks runners, records outs, and finishes the game. Then it does that thousands of times.
The output is not “Yankees 5, Red Sox 4” but a distribution: how often each team wins, how the total runs spread, how often a specific hitter records two hits. Markets price distributions — a total of 8.5 is a claim about tail mass, not an average — so a model that produces distributions can be compared to prices directly.
What goes in decides what comes out
The engine is only as good as its per-matchup probabilities. Ours are built from projected player rates (regressed toward league behavior in proportion to sample size), the actual confirmed lineup, platoon splits, park factors, weather, umpires, and a bullpen model that knows who is available tonight. Every one of those inputs moves the simulated distribution in a measurable way.
Crucially, the whole thing is graded: nightly projections are archived and compared to what actually happened — mean absolute error on runs, Brier score on win probabilities — and the calibration receipts are public. A projection system that never grades itself is a marketing page.
What simulation cannot do
Simulation quantifies the uncertainty inside its assumptions; it cannot fix wrong assumptions. If the input rates are biased, ten thousand simulations produce a very precise wrong answer. That is why calibration against actuals, honest uncertainty labels, and market anchoring where the market is demonstrably better all matter more than raw simulation count.
Written by George Boyle, who builds The Sport Stack — the models, the public ledger and these explainers. Corrections and questions: hello@thesportstack.io. Who runs this.