What is Monte Carlo simulation?
Monte Carlo simulation is a computational technique that uses repeated random sampling to model the probability of different outcomes in a system that involves uncertainty. Named after the famous casino district in Monaco, the method was originally developed during the Manhattan Project in the 1940s to solve neutron diffusion problems. Today it is used across finance, engineering, insurance, and — critically for us — sports investing portfolio management.
The core idea is simple: instead of trying to predict a single future for your portfolio, you simulate thousands of possible futures. Each simulation randomly replays your position history (or a model of future positions) with realistic variance. The result is not one line on a graph, but a cloud of thousands of lines, each representing a plausible path your portfolio could follow. From that cloud you can extract percentile bands, ruin probabilities, and confidence intervals that tell you far more than any single-point estimate ever could.
Think of it this way: if you have a 55% win rate at average returns of 1.90, your expected value is positive. But expected value tells you nothing about the journey. How deep could your drawdowns get? What is the probability of losing 40% of your portfolio before doubling it? Monte Carlo answers these questions by letting you observe the full distribution of possible paths, not just the average.
Why static portfolio projections fail
Most investors think about their edge in terms of expected value: "I have a 3% edge, so over 1,000 positions at $100 each I should make $3,000." This is mathematically correct on average, but it is dangerously incomplete. Expected value is a single number — the mean of a distribution. It tells you nothing about the variance around that mean, and variance is what kills portfolios.
An investor with a genuine 3% edge can still experience drawdowns of 30% or more over several hundred positions. If that investor has sized their allocations too aggressively relative to their portfolio, a perfectly normal losing streak can trigger ruin before the edge has time to manifest. Static projections treat the future as if it will follow the expected value line smoothly upward, but real trading outcomes are jagged, volatile, and often terrifying in the short term.
Monte Carlo simulation replaces this false certainty with honest uncertainty. Instead of saying "you will make $3,000," it says "there is a 90% chance your portfolio will be between $800 and $6,200 after 1,000 positions, with a 4% chance of hitting a 40% drawdown along the way." That second statement is infinitely more useful for making real decisions about allocation sizing and risk management.
How to run a Monte Carlo simulation on your position history
The basic procedure for running a Monte Carlo simulation on a trading record involves several steps. First, you need your historical data: the returns you invest, the outcomes, and your allocation sizes. From this data you extract the distribution of returns per position — not just the mean and standard deviation, but ideally the full shape of the distribution, including how fat the tails are (more on this below).
Next, you generate a large number of simulated sequences. For each simulation, you draw random position outcomes from your estimated distribution and apply them sequentially to a starting portfolio. Typically you want at least 1,000 simulations, though 10,000 gives smoother percentile estimates. Each simulation produces a portfolio curve over time, and from the collection of all curves you can compute statistics at any point: the median portfolio, the 5th percentile (your downside risk), the 95th percentile (your upside potential), and the probability of ruin (hitting zero or some minimum threshold).
For example, suppose you have a record of 500 positions with an average edge of 2.5% and standard deviation of returns of 1.0 per unit. Running 1,000 simulations of the next 500 positions might show that the median portfolio grows by 25 units, but the 5th percentile path is actually down 8 units at some point along the way. Without the simulation, you might have assumed smooth growth. With it, you know to prepare for potential valleys.
Confidence bands and percentile ranges explained
The output of a Monte Carlo simulation is typically visualized as a fan chart or confidence band. The central line represents the median outcome (the 50th percentile), and shaded bands extend outward to show the range of outcomes at various confidence levels. A common setup uses bands at the 10th/90th percentiles (the 80% confidence interval) and the 5th/95th percentiles (the 90% confidence interval).
Interpreting these bands correctly is crucial. The 5th percentile line does not represent the worst case — it represents the outcome that is worse than 95% of simulations. There is still a 5% chance of doing worse than that line. For portfolio management decisions, the 5th percentile is often the most important number: it tells you what your portfolio could look like in a realistically bad scenario. If the 5th percentile path shows a 50% drawdown, you need to ask yourself whether you can psychologically and financially survive that.
The width of the confidence bands also conveys critical information. Wide bands mean high uncertainty — your actual outcome could vary enormously from the expected value. Narrow bands mean the outcome is more predictable. As a general rule, higher volume (more positions) and lower variance per position produce narrower bands. This is why professional investors obsess over position volume: it is not just about accumulating edge, it is about narrowing the confidence interval around that edge.
Heavy tails and regime persistence: why naive simulation falls short
A common mistake in Monte Carlo simulation is assuming that position outcomes follow a normal (Gaussian) distribution. In reality, sports investing returns exhibit fat tails — extreme outcomes (both positive and negative) occur more frequently than a normal distribution predicts. A combined position that hits at 8.0 returns or a devastating losing streak of 12 positions are both more likely in practice than Gaussian models suggest.
Yoseri's simulation engine addresses this by using Student-t distributions with calibrated degrees of freedom to model the heavy tails observed in real trading data. The Student-t distribution has a parameter (degrees of freedom) that controls how fat the tails are. Lower degrees of freedom mean fatter tails and more extreme outcomes. By fitting this parameter to your actual position history, the simulation produces more realistic worst-case scenarios.
Additionally, Yoseri incorporates regime persistence — the empirical observation that winning and losing streaks tend to cluster more than pure randomness would predict. This can be due to model quality fluctuations, market condition changes, or sport seasonality. The simulation engine models this autocorrelation, which means the simulated drawdowns are deeper and more sustained than a naive independent-position simulation would produce. The result is a more conservative and realistic estimate of downside risk, which is exactly what you want when making portfolio decisions.
Why every serious investor should simulate before sizing up
The most dangerous moment in an investor's journey is when things are going well. After a profitable stretch, the temptation to increase allocation sizes is enormous. But increasing allocations without understanding the full range of possible outcomes is how profitable investors blow up their portfolios. Monte Carlo simulation provides the discipline check: before you double your unit size, simulate 1,000 futures at the new allocation level and look at the 5th percentile drawdown. If you cannot stomach that drawdown, you are not ready to size up.
Simulation also helps you set realistic expectations. Many investors quit too early because their results do not match their expected value projection. But if they had run a simulation first, they would have seen that their current results are well within the normal range of variance. Understanding the width of the confidence bands prevents premature abandonment of a profitable strategy.
For a deeper exploration of how variance affects your portfolio trajectory and the math behind simulated outcomes, read our guide on simulating variance in portfolio management. Combining simulation output with disciplined allocation sizing is the foundation of sustainable long-term profitability.