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Model Literacy · Lesson 3 of 9

Monte Carlo Simulation

What does "10,000 simulations" actually tell me?

Intermediate9 min readUFC / MMA

Rolling the dice on purpose

Some questions have no clean formula: what share of bankrolls survive 500 bets, how often a fight reaches the judges, how a game's remaining innings could play out. Simulation answers them by playing the process thousands of times with random draws from a model, then counting.

$0$427$854$1281$1708300 bets
300 simulated bankrolls, 53% at 1.95. The spread is the answer: a thin edge produces a wide fan of plausible results.

Reading an outcome share

A simulated outcome share is the fraction of simulations that ended a certain way. It inherits every assumption in the model — nothing more.

Worked example · reading a simulator panel
  1. A matchup shows 58% for Fighter A, with 31% of simulations ending by decision.
  2. Read: under the simulator's assumptions, 31 in 100 simulated fights reached the judges.
  3. Do not read: "this fight will go to a decision" or "the fight will last 15 minutes".
An outcome share is a distribution, not a pick. The single most common outcome is usually less likely than all the others combined.

The Fight Simulator lesson applies this to the PropBetEdge UFC simulator, which separates the simulation outcome share from the PBE Fight Model's win probability.

More simulations do not mean more truth

simulation error ≈ √(p(1 − p) / n)
p = 0.30, n = 10,000 → ±0.9 pts (95%)
Limitations

Ten thousand draws make the arithmetic precise, not the model. If the inputs are wrong, the simulation reports the wrong answer to one decimal place. Quantities the model was never validated on — exact finish round, exact finish time — stay unreliable no matter how many simulations run.

Build intuition in the Monte Carlo simulator.