Monte Carlo Analysis and the Ups & Downs of Sports Investing

Guest Article by Researchers at
One of our goals – at and BettingCharts – is to make investing in sports a more legitimate asset class. is a sports information service and presents key statistics in the sports marketplace. Together, and perform hours of research and apply the same analytical tools as investment professionals.

We believe that there are ways to profit in sports investing. However, most investors – and in particular, sports investors – do not fully understand the risks involved with their investments. Most sports bettors figure that if they beat the magical 52.4% winning percentage (lower, depending on the vig), their accounts will grow continually. As financial professionals say: this is true in the “long run.” However, there will be some scary peaks and valleys.

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Investment Analysis

In the world of finance, investment professionals use a wide variety of risk measures – ranging from statistical terms such as standard deviation to risk/return ratios such as a Sharpe Ratio. One of the more commonly used risk measures is standard deviation. While standard deviation might mean something to certain investors, it means almost nothing to others.

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?

Chart 1 – Mystery Market #1

How about this chart?

Chart 2 – Mystery Market #2

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%).

Average Quarterly Decline

Using an “average of quarterly declines” is a more robust measure of risk. It also is perhaps more useful and practical for many sports investors, who might add money to their accounts periodically and “start fresh.” The Monte Carlo analysis allows us to see what kind of declines we would endure during an “average” quarter.

Percentage of Time Near Peak (or % of Time In Decline of More than 10%; 5%)

When investments are going well, everyone is happy. However, when things inevitably turn down, investors feel the pain. The “Largest Decline” and “Average Quarterly Decline” (in previous sections) measure the magnitude of the declines.

The “Percentage of Time Near a Peak” (or conversely, the % of Time in a Decline) measures how long we endure pain. We believe that many investors will find this indicator intuitively interesting. If we have an edge, we will tend to earn money in the long run. However, from time to time, we will suffer losses. For our statistical simulations, we studied the percentage of time we fall below a peak by worse than -5% and worse than –10%.

Table 1 – Monte Carlo Simulation Results

Win % Largest Decline Avg Qtr Decline % Time Below –10% % Time Below -5%
51.3% -82% -10.6% 72.3% 84.7%
52.0% -72% -8.6% 44.3% 63.8%
54.0% -28% -5.1% 8.1% 24.5%
57.0% -11% -2.5% 0.2% 2.3%

Summary: How Can You Use These Tables?

Table 1 can help you understand the ups and downs of sports investing. In particular, the table can be used to estimate the long-term performance of your sports betting methods. For example, if you bet 1% of your bankroll and hardly experience declines of more than -10% from recent peaks, then you might have a long-term winning percentage in the area of 57% (normalized for moneyline sports like baseball). However, if you regularly experience declines of -50% from peaks (while betting 1% on each play), you either have a slight edge in handicapping – or no edge at all. Here are some other notes:

  • Note that Table is based on a bet size of 1% of your bankroll (as well as 100 plays/quarter). You can “ratio up” results based on different sized bets and the number of bets you average a day.
  • If you do NOT have an edge in sports handicapping, you will experience huge ups and downs. Even if you have a slight edge (52%-53% winning percentage), you can expect declines of more than –50% at some point – and average quarterly declines of around –8%.
  • If you are able to achieve a 57% winning percentage, you will limit “bad case” declines to around –10% and will spend almost all of your time (97%+) at – or close to (within -5%) – your bankroll’s peak.

We do not guarantee that the trends and biases we’ve found will continue to exist. It is impossible to predict the future. Any serious academic research in the field of “market efficiencies” recognizes that inefficiencies may disappear over time. Once inefficiencies are discovered, it is only a matter of time before the market corrects itself.