What is Monte Carlo Analysis? It is a random process used to solve difficult problems

For example, a statistician will tell you there’s a one-third chance of X (or a 95% chance of Y) occurring in a given year. However, many others feel that standard deviation doesn’t give them a “real feel” for the actual risk of that investment. Here, we present some more “intuitive” measures of risk. In particular, we want to help you better understand the behavior of your bankroll – especially when coping with difficult periods.

Market Charts

We’ve all heard the phrase: “Every investment has its ups and downs.” We know that the stock market will earn positive returns in the long run. We also know that the stock market endures crashes and bubbles from time to time. Let’s take a look at some market charts.

Can you tell what this chart is?
The charts look similar, right? The first chart is actual stock market performance over the past few years; the second chart is the output of a Monte Carlo simulation. The charts demonstrate our ability to model the “market action” of any marketplace.

Monte Carlo Analysis

It’s fitting that “Monte Carlo” (one of the world’s gambling capitals) – is part of the name of a statistical tool/random process used by mathematicians and investment professionals: namely, “Monte Carlo Analysis.” Here – we come full circle and use this tool to study sports betting.

What is Monte Carlo Analysis? It is a random process used to solve difficult problems. Here’s an example to give this definition more color. Imagine that we want to compute the area of an irregularly shaped object. We can place a rectangle around this area and easily compute the rectangle’s area. We then “throw darts” at the rectangle. The area of the “odd-shape” can be computed as the percentage of darts that fall within the odd-shaped area times the area of the rectangle.

Parameters for our Monte Carlo Analysis of Sports Betting

We’ll use a Monte Carlo analysis to study the behavior of a sports betting account. For the purposes of our simulation, the Bet Size is 1% of the sports investor’s bankroll. The size of the bet doesn’t matter, but if you want to get a feel for things – you can use a bet size of \$100, with a bankroll of \$10,000. The sports investor bets just over 3 bets a day, making 100 bets in a quarter.

Behavior of Bankroll

The beauty of Monte Carlo analysis is that it allows us to closely study the ups and downs of an investment. We can run simulations for many years – and get a better understanding of the expectations and behavior of our portfolio. Here, we selected indicators that most sports investors would find useful.

Largest Decline

The percentage that your account declines from a recent peak is a good measure of pain. We can study how much your bankroll declines in a worse case scenario, based on simulations. This is “path dependent” – so that this statistic is not very robust. That is, over an infinite number of trials, there is a chance that your account will do worse than the figure we show.

Note, however, that we used a consistent Monte Carlo approach to study large declines. It is telling to see that even with a winning percent of 54%, it is likely that your account will decline by around –28% at some point. Note that if you bet more than 1% of your bankroll per bet, your decline will be larger than the figures we show (by the ratio of your bet size to 1%).