Monte Carlo simulation is a mathematical technique that allows you to calculate the odds of different outcomes by running thousands of simulations. It’s used in finance, engineering, and many other fields to determine the probability on the range of possible inputs. In sports betting, Monte Carlo simulation is useful for determining the probability of wins, losses, point spreads, and more for teams and players. If you want to gain an edge in sports betting, understanding Monte Carlo simulation is key. I’ll walk you through how Monte Carlo simulation works and how you can apply it to sports betting to calculate probabilities like a pro.
The Basics Of Monte Calo Simulation For Sports Betting
Monte Carlo simulation is a method for solving math problems. It allows you to simulate the outcome of events that have an element of randomness.
How does it work? Basically, Monte Carlo simulation uses random numbers to simulate a model’s outcome many times over. Each simulation calculates the impact of risk and uncertainty to provide a range of possible outcomes. By running thousands of simulations, you can get a view of the overall risk and the likelihood of different outcomes.
In sports betting, it is used to find out the probability of different outcomes by simulating the event many times. For example, if you wanted to bet on a football match, a Monte Carlo simulation could simulate that match 10,000 times to estimate the likelihood of each team winning, losing or drawing. By changing variables like each team’s ability, home advantage or injuries, you can see how it impacts the probabilities.
Monte Carlo simulation allows you to make better decisions and find value bets since you have a better sense of the risks and probabilities. You should bet when the odds underestimate the true probability of an outcome, giving you an edge. Obviously you should avoid bets where the odds overestimate the probability of outcome.
While the simulation reduces uncertainty, it does not eliminate it. There is still an element of randomness in any sporting event. But by understanding the probabilities and risks better, you can make strategic bets that will pay off over the long run.
You can perform Monte Carlo simulations for sports betting using a spreadsheet program like Excel. No special software is required. You just need a spreadsheet, random number generator, and some basic formulas. Many tutorials are available online to walk you through setting up a basic simulation. Here you can find Microsofts support page to the introduction on Monte Carlo simulation. Or you can head out to YouTube and search for content how to use the simulation, there’s plenty of great videos that’ll get you started!
What Is Monte Carlo Simulation Used For?
Applying Monte Carlo Simulation to Improve Sports Betting Strategies
Using the Monte Carlo method analyzing your betting performance is key to make sure your betting system is working. You need to track your betting history with expected value and the odds you placed the bet. And preferably sample size of thousands.
How Monte Carlo Simulation Enhances Sports Betting Predictions
Monte Carlo simulation generates random variables to simulate the performance and risk of a system. In sports betting, it’s used to determine the probability of certain outcomes to help you make better bets.
How does it work? Monte Carlo simulation works by generating thousands of random variables based on the odds and probabilities of a sporting event. It then aggregates the results to estimate the most likely outcomes.
For example, say you want to bet on an NBA game between the Clippers and Lakers. The oddsmakers have the Lakers as 6-point favorites. Using historical data, you determine there’s a 60% chance the Lakers will win and cover the spread.
You set up a Monte Carlo simulation that will run 10,000 random variables based on those odds. It might look something like this:
- 6,000 times the Lakers win and cover
- 3,000 times the Lakers win but don’t cover
- 1,000 times the Clippers win
The simulation shows the most likely outcome is the Lakers winning and covering the spread. Remember, even when statistically Lakers win is the most likely outcome, placing a bet with let’s say 1.55 odds isn’t necessary a smart bet. Why? The fair odds in this scenario is 1/0.6 = 1.667. This means you have a negative expected value. Implied probability of 1.55 odds is calculated 1/1.55 * 100 = 64.5%. While the true odds Lakers winning is 4.5% lower.
Monte Carlo simulation is a powerful tool for sports bettors. If used properly, it can help turn betting into an investment with a positive expected value. But like any tool, it depends on the skill and knowledge of the person using it. If you want to learn more about the positive expected value aka +EV – which we and every bettor who’s goal is to actually make profit are all about – you can check our post about +EV
Determining How Many Simulations To Run
To determine how many Monte Carlo simulations to run for sports betting, there are a few factors to consider:
The more simulations you run, the more accurate your results will be. As a general rule of thumb, aim for at least 10,000 simulations for reliable estimates. For very complex models with lots of uncertainty, 100,000 simulations or more may be needed. This is the case in sports betting.
However, running too many simulations can be inefficient and time-consuming. At a certain point, the marginal benefit of additional simulations starts to drop off. Look for the point at which your key metrics, like expected value or win probability, start to stabilize. Once the results aren’t changing much with additional simulations, you’ve likely run enough.
The complexity of your model also impacts how many simulations to run. More complex models with lots of uncertain inputs generally require more simulations to achieve stable results.
Your confidence in the inputs and assumptions of the model should also be considered. The more uncertain or speculative the inputs, the more simulations you’ll need to account for variability. Conservative estimates for uncertain inputs will also require fewer simulations.
In the end, determining the right number of simulations comes down to balancing accuracy and efficiency for your particular needs. Start on the higher end of the range, around 10,000 to 100,000 simulations. Check how your key metrics change as you increase the number of simulations. Once the results start to stabilize and additional simulations yield little marginal benefit, you’ve found the sweet spot.
Mitigating Risks Through Monte Carlo Simulation In Sports Betting
To use Monte Carlo simulation for sports betting, first determine how much risk you’re comfortable with. If losing a few bets would wipe out your bankroll, your risk tolerance is low. If you can handle significant losses and continue betting, your tolerance is higher.
Once you know your risk tolerance, you can model different betting strategies. For example, say you’re considering a strategy of betting $100 on underdogs with odds of 3.0 or higher. You could run 10,000 simulations of following this strategy for a season. The results might show:
- The median outcome is losing $500
- There’s a 30% chance of losing over $2,000
- There’s a 20% chance of winning over $5,000
This helps you to visualize the risk and rewards in a longer run. The potential winnings are attractive but the chance of significant losses may be too high for your taste. You could then adjust the strategy, like reducing bet sizes or odds requirements. If you want to learn about optimal bet sizing, have a read about Kelly Criterion. This helps you to manage your bankroll balance and bet optimal sized bets.
Making Smarter Bets
Monte Carlo simulation can also help determine which types of bets offer the best risk-reward ratio for you. You may find:
- Betting underdogs in a particular sport or league is riskier than others.
- Spreads and totals is safer than moneylines.
- Betting on favorites to win by a narrow margin is optimal for your goals.
By simulating many possible bets, you can make smarter choices and build the optimal risk-managed betting strategy for your needs. While uncertainty is inherent in sports betting, Monte Carlo simulation gives you a useful tool for navigating it.
How accurate are the results?
The accuracy of Monte Carlo simulation depends on several factors, including:
- The quality of the data used – Reliable historical data will produce better results.
- The number of simulations run – More simulations mean more accurate probabilities. Thousands of simulations are typically needed.
- Properly weighting key factors – The simulation needs to account for things like home field advantage, weather, injuries, etc. Weighting these factors incorrectly will skew the results.
- Accounting for randomness – There is inherent randomness and unpredictability in sports. The simulation will never be 100% accurate but can still identify value bets.
- Considering correlations – The simulation needs to model how different events might impact each other. For example, how a team performing well in one area might boost performance in another.
- Making adjustments – Oddsmakers are also running simulations and adjusting odds based on the latest information. Bettors need to adjust their simulations accordingly to find edges.
With the right data and methodology, Monte Carlo simulation can be very useful for finding value in the sports betting market. But like any predictive model, it will never be perfect. Always bet responsibly!
Step-By-Step Guide Using Monte Carlo Simulation For Betting Analysis
Step 1: Data Collection and Preparation
Data collection: If you want to be profitable in sports betting, one of the most important aspects is to gather data on your progress. If you don’t have strategy on your bankroll management, betting sizes and expected value, you are most likely to lose in the long run. Make sure you keep track of Placed Bets, The Result of the Bet, Size of the Bet, The Bookmakers Odds, Estimated Fair Odds, and Expected Value. What ever you feel like would provide you more insight in the future the hone your strategy, keep track of it. For example, tracking Live bets and Cash Outs might be useful.
Bet tracking spreadsheet
Here’s what the template I personally use looks like, it’s very easy to use and provides all the information I need for myself. I’ve added the Expected Value column to keep track of my average expected value which should equal to yield in the long run. Credit to Australia Sports Betting. You can download the template here.
Step 2: Setting Up Excel
Create a New Worksheet: Open a new worksheet in Excel.
Organize Data: Organize your data in columns. You should have columns for Fixture / Event, Selection, Bet size, Bookmaker Odds, Estimated Fair Odds, Win probability, and Yield Based on Fair Odds, or Expected Value.
Here’s what my imported betting data on this Monte Carlo simulation looks like.
Calculate your yield by dividing your Net profit (or loss) by Total wagers. My Yield at the time of writing through 110 bets was 30.28%. Now that’s considered very high. And it is basically because of my small sample size and luck. Even though I do extensive research and use machine learning for wagers, such high yield is highly unlikely to maintain in the long run. But how do we measure the effects of luck? This is where Monte Carlo simulation comes in.
Calculate Estimated Fair Odds
You should always have your own estimated odds higher than the bookmaker odds. In other words, you need Expected Value. If you think there’s a 50% estimated probability of Barcelona winning, your Estimated Fair Odds is 1/0,5 = 2.00. So, any bookie odds above 2.00 gives you +EV. 2,05 has 5% or 0.05 +EV.
Step 3: Running a Monte Carlo simulation in Excel
- Calculate the expected probability of a win as a decimal between 0 and 1. Also known as inverse of the Fair Odds.
- Use Excel’s RAND function to generate a random number between 0 and 1 for each of your bets.
- Use IF function on a new column. Here I used simple binary 0 and 1 on a new column to determine the simulated outcome of the bet. If the RAND number is less than your estimated probability, the bet wins, if not, the bet loses.
- Next, on the Profit column another =IF function. Meaning, If the random number generated falls between 0 and the inverse of fair odds, the bet is won.
- Sum the individual profits and losses for all bets in the simulation to calculate the yield. And divide the profit total by the number of bets. You can create something like shown in the image below.
By pressing the F9 key, Excel will regenerate all the random numbers and new theoretical sample yield. On the picture above, I got yield of a 21% which is less than my 30.28% but still considered high. You could Press F9 over and over again and manually write down the yields, but we need thousands of simulations to come up with reliable results.
In order to do this, Use Excels Data Table function. You can find this Data > What If Analysis > Data Table
- Calculate your sample’s yield using a blank cell
- Choose the cells where you intend to display yield results for new simulations. Keep an empty column to the left. Decide the number of rows based on your simulation requirements.
Access Excel’s Data Table Feature. You will see a box like the one below. Designate a single cell reference in the “Column input cell” field. Opt for any cell except those you highlighted in the previous step.
For reliable results, aim for at least 1000 simulations. The more simulations you have, the more accurate your results will be. In this example I used 25000. If you are feeling adventurous, you can go for 100.000 and give your PC something to work with. This might take few minutes depending on your setup.
The larger your betting history, the more likely it is that the actual performance will be closer to expectation, assuming that your prediction methodology is working as it should.
Expected Value indicates the average return an investment can make after considering all the possibilities. My average Expected Value after 110 bets being 6.781%, the Yield should be as close as possible in order to validate my estimations for the Fair Odds.
Step 4: Calculate Z-Scores
In a new column, calculate the Z-scores. It is a statistical measurement of a score’s relationship to the mean in a group of scores. Average Yield and Standard Deviation of Yields can be calculated using Excel functions like AVERAGE() and STDEV().
You need both of these to calculate Normal Distribution and to form the bell curve graph on next step. Create a new column for Normal Distribution and do it for every simulated yield using formula as in my example =NORM.DIST()
Now you should have something like in the picture below. (+EV column not necessary just for comparison)
Step 5: Visualizing the Distribution
Create a histogram in Excel using the simulated yield and normal distribution data. This will show you the distribution of your potential profits based on the Monte Carlo simulation. Select the data and go to Insert > Charts > X Y (Scatter) chart. Adjust the axis settings so it’s easier for you to interpret.
Step 6: Analysis and Interpretation
Interpret the Distribution: Analyze the histogram to understand the distribution of potential profits. You’ll be able to see the likelihood of various profit levels and assess the risk associated with your betting strategy.
Compare to Actual Results: Compare your actual results to the simulated distribution. This can help you evaluate whether your actual performance falls within the expected range or if there are significant deviations.
Risk Assessment: Use the distribution to assess the potential risks and rewards of your betting strategy. You can identify the probability of hitting certain profit or loss levels.
Remember, while the Monte Carlo simulation provides insights into potential outcomes, it’s still based on probabilities. Past performance doesn’t guarantee future results, and the accuracy of your simulation will depend on the quality of your data and assumptions.
Additionally, consider factors such as bankroll management, consistency in betting size, and analyzing the reasons behind each bet’s outcome to refine your betting strategy further.
About my Monte Carlo findings:
According to my estimates, my Expected Value would be 6.781%. Also known as the average return a bet can make considering all the possibilities. Simulating those 110 bets, the average yield was 6.85%. This gives me confirmation of my +EV estimation process working so far.
But since the sample size is still small, I will recreate this Monte Carlo simulation after 1000 bets to see where we stand. Being currently at 123 bets, this will take about 6 months if I keep providing 5 bets a day.
Also worth noting, my current 61 percent win rate on all bets will most likely even out somewhere between 53-55. Therefore high expected value, betting strategy and bankroll management is key.
So there you have it, an inside look at how Monte Carlo simulation applies to sports betting. By running thousands of simulations, you can get a more accurate sense of the probabilities and make smarter bets. The next time you’re researching picks for the big game, consider using a Monte Carlo simulator to help determine which wagers are most likely to pay off. While it won’t guarantee you win every bet, it can give you an edge over time. And in a game where the odds always favor the house, any advantage you can get is worth finding.