Monte Carlo Simulation in Cycling: From a Number to a Probability
A single time prediction is always wrong. What matters is the distribution of possible outcomes — and simulation is how you get it.
The principle
Instead of one value for wind, power and rolling resistance, you define a plausible spread for each input. Then you draw thousands of random samples, compute the segment time each time, and look at the distribution of results.
Which uncertainties matter
Not every input is equally uncertain. Wind forecast and daily form dominate; tyre pressure is noise.
- wind speed: typically ±20 to 30 percent several hours out
- wind direction: ±15 to 25 degrees
- daily form: ±3 to 5 percent power
- execution and line choice: ±1 to 2 percent time
The distribution answers the questions
The share of simulations faster than your best time is the PR probability. The share below the KOM time is the KOM probability. The 10th and 90th percentiles form a confidence band around the expected time.
That is the decisive improvement over a bare number: you learn not only what will likely happen, but how certain it is.
How many runs?
Around 1000 runs give stable probabilities. Small probabilities such as a sub-one-percent KOM chance need more, otherwise the result is noisy. A few hundred are enough for a quick hourly preview.
In short
Not "you will ride 3:01", but "2:56 to 3:03 with a 72 percent PR chance" — that is how you decide rationally.
Frequently asked questions
Does simulation make the prediction more accurate?
The expected value stays similar. What you gain is a statement about uncertainty — and that is what you need for a decision.
What if the spreads are wrong?
Then probabilities are over- or under-confident. Calibration against real attempts is mandatory.