POISSON DISTRIBUTION CALCULATOR

1. What is a Poisson Calculator?

A Poisson calculator, also known as a Poisson distribution calculator or Poisson probability calculator, is a mathematical tool often used in sports betting. Bettors use it to calculate the probability of the frequency of events occurring over a period of time.

The Poisson calculator is often used to calculate probabilities of propositional, or “prop”, bets 

"A prop bet, short for proposition bet, is a wager in sports betting not tied to the final score or outcome of a game."

- Action Network

For example, a bettor may want to know the probability of a soccer team having three shots on target in their next game. To help with this, the Poisson calculator would use two inputs, ‘expected average’ and 'proposition', to tell them the probability of that occurring.

If the probability calculated by the calculator is higher than the sportsbook's implied probability for that bet, this could indicate the bettor has an edge over the sportsbook.

We'll explain exactly how this works in the next section.

2. How Do I Use a Poisson Calculator? Worked Example

Here we'll show the six steps to using a Poisson calculator to calculate event probability, including a worked example.

1) Choose Bet Selection

Pick a selection from a sportsbook that you believe could be ‘Poisson’ (you think the sportsbook odds given may be undervalued). In our example, we're using the number of 3-point shot attempts by the Chicago Bulls in their next basketball game.

We know from research that on average, the number of 3-pointers the Bulls attempt in a game is 15.2. We can also see our sportsbook has offered moneyline odds of -115 for the Bulls to have at most 15.5 3-pointer attempts (meaning 0-15 attempts).

2) Input Expected Average

The expected average is the number of events we expect to occur. For our example, we'd input 15.2. In different examples, this could be the number of goals we expect a soccer team to score or touchdowns in a football game.

3) Input Proposition

This is the number of events specified by the sportsbook in the bet. In our case, we'd input 15.5.

4) View the Results

The calculator will automatically calculate the probability of the Bulls attempting at most 15.5 3-pointers. It will also show a full distribution of probabilities for your selection.

Using our example, we would see:

• More than 15.5 3-point attempts = 45.24%
• Less than 15.5 3-point attempts = 54.76%

5) Compare Odds

Now we've got the true probability percentage of our selection (54.76%) it's time to convert that to odds to see whether we have an edge over the sportsbook.

Using an implied probability calculator, we type in our 54.76% percentage and it shows us the American odds equivalent is -121.05.

When we compare this to the sportsbook's odds for this selection of -115, we can now see that the sportsbook has undervalued its odds.

This means that, statistically speaking, we have an edge over the sportsbook. In this case we would have a 2.4% edge.

6) Place the bet

You've now identified you have an edge over the sportsbook, and statistically speaking, are likely to have a profitable bet. If you're happy with the selection, all that's left to do is log into your sportsbook and place your bet.

Remember: Having an edge over the sportsbook does not guarantee a profit. It simply states in statistical terms, you are likely to receive a profit with this selection.

3. Do I Need to Know the Poisson Formula to Use the Calculator?

Simply put, no. Our Poisson calculator does all of the hard work for you.

This saves you the time, effort and potential confusion of worrying about complex math like standard deviation, lambda, variance, random variables, rate of success and more. 19th-century French mathematician, Siméon Denis Poisson, did that for us!

Instead, just follow the six steps above and you can use the Poisson distribution calculator easily and effectively when sports betting.

4. What are the Benefits of Using a Poisson Calculator in Sports Betting?

A Poisson calculator can have a wide range of benefits in the world of sports betting. Here are five of the most powerful:

1. Long-Term Profits: Identifies potential edge over a sportsbook, increasing the likelihood of profitable betting decisions in the long term.
   
   
2. Time-Saving: Rapidly determines the likelihood of a range of betting outcomes, hugely reducing the time it would take to follow the formula and find calculations manually.
   
   
3. Broad Application to Sports: Relies on a model that can be used in most sports to find event probability, from soccer goals to football touchdowns and basketball 3-pointers.
   
   
4. Stat-Backed: Uses a mathematical formula to produce a statistically backed answer, unlike less data-driven calculators like a parlay calculator and round robin calculator. This can reduce the unreliability of opinion or emotional betting.
   
   
5. Opportunity Identification: Our calculator doesn't just show a probability for one outcome, but shows a distribution of up to five probability percentages. This can help identify other potentially profitable bets you hadn't considered.

5. Are There any Limitations to Using a Poisson Calculator in Sports Betting?

Though the Poisson calculator can have a range of benefits to sports bettors, it's equally important to note the tools limitations. Five of the most significant are:

1. Inability to Factor in Context: Fails to incorporate contextual factors such as weather conditions, player injuries, or team morale.
   
   
2. Overlooking Tactical Changes: Does not account for tactical adjustments made during matches, impacting prediction accuracy.
   
   
3. Vulnerability to Outliers: Susceptible to outliers in data, which can skew predictions and compromise reliability.
   
   
4. Influenced by Personal Input: Exact averages for bet selections to input to the ‘expected average’ cell won't always be available to find. This can lead to assumed averages being used which can reduce accuracy.
   
   
5. Profits Aren't Guaranteed: Though it can be a valuable tool to increase long-term betting profitability, the Poisson probability distribution is not a fool-proof model and cannot guarantee returns.

6. 4 Strategies to Use Alongside/Instead of Poisson Betting

Though Poisson betting can be a helpful tool in a sports bettor's lineup, it's be no means the most popular (or effective) betting strategy.

Here are four alternatives to Poisson betting for maximizing returns and minimizing risk:

1) Matched Betting

Perhaps the most effective risk-free method of earning serious monthly profits, matched betting involves betting on every outcome of a sporting event to unlock a sportsbook promotion risk-free, before converting that into guaranteed profits.

This process can be made simple with the help of tools like a Dutch Matcher, Dutch Calculator and free bet conversion calculator.

2) Arbitrage Betting

Similarly, arbitrage betting involves betting on all outcomes of an event to remove risk. However, unlike matched betting, with arbing you don't unlock a free bet and instead aim to profit from inconsistencies in odds across different sportsbooks, with the help of an arbitrage calculator.

This can be an effective risk-free betting strategy, but does not offer the same opportunity to maximize guaranteed profits over a short that matched betting does.

3) Kelly Criterion Betting

Kelly Criterion betting is closer to Poisson betting in that it is more of a statistical model-based betting strategy that can support betting, rather than a risk-free process like matched betting and arbing.

It involves using a Kelly Criterion calculator to calculate the mathematically ideal stake to place on a bet in relation to its odds and your available bankroll.

4) Expected Value Betting

Expected value betting (or EV betting), like the above strategy, is also not a risk-free betting strategy, but more of a long-term model for increasing betting profits.

Similarly to Poisson, it involves identifying an edge over the sportsbook. However, it's more straightforward in that the expected value calculator uses odds, win probability and wager amount to calculate whether the selection is statistically profitable.

7. Get Started with Risk-Free Betting

If you want to stop spending valuable time doing painstaking calculations just to grow your profits gradually when sports betting (or worse yet, still run the risk of losing money entirely), it might be time you consider risk-free matched betting.

Matched betting is a rapidly growing betting strategy in the US, with more than 500,000 users in the states and Europe using the process to earn guaranteed profits in the $1,000s each month. At ProfitDuel, we're the experts in it, with over a decade of experience in the industry and 400,000+ members across the US and our European arm OddsMonkey.

Simply put matched betting involves strategically betting on every outcome of a sporting event in order to unlock a sportsbook promotion (such as a free bet) risk-free, before repeating the process using your promotion to guarantee winnings.

At ProfitDuel, we make this full process seamless and simple. Providing you with all of the software, strategies and one-to-one support to make $1,000s in your first month as a total beginner. Just ask our customers - their results speak for themselves.

The best part? We're offering 50% off your first month of Premium access, including all the software, strategies and support you need to level up your income from home.