Do you know why the house always wins eventually when it comes to casino games? With casino games, we are able to solve for the probability of any given outcome mathematically.

So, when you spin a roulette wheel, there’s a 1-in-38 chance of the ball landing on the number that you bet. The casino sets the odds so that correct picks pay out 36-to-1, and so the math works out in such a way that the house always has a significant advantage over the gamblers.

Fortunately for sports bettors, the probability of winning or losing a sporting event is less certain. Numerous factors influence the outcome, and without having definite expectations determined by the number of cards or dice, sportsbooks are forced to try and set the odds based on their own research.

Furthermore, when the bookmaker sets their line, they aren’t trying to accurately predict the probability of each outcome happening.

A sportsbook’s goal when they set the odds of a contest is to entice bettors to place an equal amount of wagers on each side, guaranteeing the book makes a profit.

So once they’ve crunched the numbers and predicted the probability of each outcome happening, they adjust the odds to bring in action on both sides. The odds that are set then carry a certain implied probability, which is the number we base our wagers on.

In order to become a successful sports bettor, you must do your own statistical analysis. The goal is to identify variables that have a strong influence on the outcome of a contest or event and calculate your individual probabilities for each possible result. The last step is to compare your percentages of likelihood against the implied expectations set by the bookmaker.

Winning sports gamblers only make a wager when a bet has positive value. A gamble is said to have value when the implied probability based on the odds is a lower percentage than the likelihood you calculated from your own analysis.

That’s the whole name of the game; if your math says that Team A will win this contest 45% of the time, but the odds mean Team A would only need to win 20% of the time to break even, that’s bet has value.

But how do we accurately determine the probability so that we have a number to compare against the odds? We have to create betting systems based on statistical analysis and probability distributions. This guide is meant to help you understand how handicapping is done and get you started.

When we talk about statistical analysis as it relates to sports betting, we are usually talking about regression analysis. Regression analysis is a set of processes used to determine the relationship between a dependent variable and one or more independent variables.

For the purposes of sports betting, the dependent variable is winning, while the independent variables can be any statistic recorded for the competition – for example, “passing completion percentage” or “rushing yards per game.”

So the way to use statistical analysis to our benefit when betting on sports is to identify factors that have a strong correlation to winning that aren’t immediately apparent to the betting public. It may take some time and lots of playing around with large sets of data, but the reward will be worth it.

With regards to statistics, you must understand that “significance” does not mean “important” or “vital.” Instead, a result is said to have statistical significance when it is unlikely to have occurred if there was no relationship between the two variables.

So, let’s say that our hypothesis is that “completion percentage” plays an influential role in whether an NFL team wins or loses. First, we’d want to find a dataset with a large quantity of historical NFL data.

Then we’d see how often the team with the higher completion percent also won the game. Depending on that answer, we’d have a percentage of statistical significance.

You can do this for lots of factors to get an idea of which variables impact winning and losing, and to what degree. The more statistically significant a variable is, the more likely you can trust it to correlate to winning.

Because there are always numerous variables at play at once, all of which impact the outcome of a game or contest to some degree, multiple regression analysis is the system most commonly used for sports betting.

Rather than just pick a single statistic, this system considers numerous regressions to predict a future outcome based on past data.

Here’s an example.

- The Houston Rockets have an upcoming home game against the New Orleans Pelicans.
- Regression 1: New Orleans won the last game these two teams played by two points. The game was in New Orleans.
- Regression 2: The Houston Rockets have won 90% of their games at home.
- Regression 3: The New Orleans Pelicans give up an average of 106 points per game on the road.
- Regression 4: The Houston Rockets win 98% of the games in which they score 102 or more.

The handicapper analyzes these regressions and extrapolates a predicted outcome. Based on the data, New Orleans is expected to have worse defense on the road, while the Rockets excel at home. Despite the Pelicans winning the most recent contest between the two teams, the data seems to suggest the Rockets will be taking the upcoming game in Houston.

The key to reliable regression analysis is having extensive historical data sets to manipulate. You want as many statistics available as possible, both for the teams and individual players. From there, you can begin narrowing your focus to specific factors that strongly correlate to precise outcomes.

Logistic regression is a method for analyzing data in which the outcome is determined by one or more independent variables. It solves problems such as “How does the probability of winning change for every additional three-pointer made above the average?”

Another example would be “Do three-point percentages, the total number of assists, and average margin of victory have an influence on the probability of winning?”

This form of analysis can be used to obtain an odds ratio despite having more than one explanatory variable. The calculated result is the impact the combination of variables has on the desired outcome, represented in an odds ratio.

Any time you are working with statistical analysis, you must remember that correlation does not necessarily mean causation. Just because two variables are correlated, that doesn’t mean that one variable caused the other.

Regression analysis can be used to find variables that correlate, like home field advantage and winning, but it cannot prove that winning is caused by playing at home.

Probability distributions are methods of providing the likelihood of the occurrence of different possible outcomes. Rather than just solving for the most probable outcome, they provide the likelihood of each possible result. Graphical models may then be used to represent the range of probabilities.

Bayesian networks are a type of graphical model that can be used to make predictive distributions. The networks are broken up into levels consisting of variables that may impact the outcome of a match.

For example, if we are trying to base our prediction on team strength, level one would be comprised of values for historical inconsistency, team performance, and average goals per game.

For level two, we would consider those previous factors, but also look at the injuries for each team. Then we forecast the two teams again based on this additional filter. Last, we look at things like how recently the teams have played and if they’re fatigued or motivated.

These additional variables are added to the other levels to comprise level three. We then make a final forecast.

Poisson distribution is a predictive method typically used in soccer or hockey betting, or for NFL prop bets based on things like sacks. Basically, anything in sports where stats are counted in increments of one and scoring is relatively rare.

It works by converting mean averages into a range of probabilities and can be used to predict, like the most likely score of a soccer match.

For example, let’s say Jadeveon Clowney is averaging 1.4 sacks a game. A prop bet being offered sets the over/under on total sacks for his upcoming contest at 1.5. You want to bet the over, which means you’ll need at least two sacks. You can use a Poisson calculator like this one to determine the probability.

The Poisson Probability values for this example are as follows.

- The probability of Jadeveon Clowney getting precisely 2 sacks with a mean rate of success of 1.4 is 0.242, or 24.2%.
- The probability of getting 2 or fewer occurrences (cumulative probability) is 0.833, or 83.3%.
- The probability of getting more than 2 occurrences is 0.167, or 16.7%.

Number of occurrences | Exact Probability | Cumulative Probability |
---|---|---|

0 | 0.247 | 0.247 |

1 | 0.345 | 0.592 |

2 | 0.242 | 0.833 |

So, as you can see, using Poisson Distribution can be enormously helpful when predicting outcomes for certain types of bets. Compare the probability of the events with the implied probability based on the odds, and you’ll know which side to pick on totals bets and specific props.

The binomial distribution is the probability of success and failure outcomes in an experiment that’s then repeated multiple times. The first variable is the number of times an analysis is performed and is represented by “n.” The second variable is the probability of a specific result and is represented by “p.”

These distribution methods can be utilized to predict your possible win and loss record in your future wagers. Let’s say, based on your betting system’s 60% winning percentage, you want to know your most likely record over the next 21 bets.

60% of 21 is 12.6, so our record should be 13-8. Using the binomial distribution calculator, we learn that even though 13-8 is the most likely record, it will actually only occur 17.4% of the time.

The likelihood of winning twelve games or less is 47.6%. However, the possibility of winning 13 or more games is 52.3%. These distribution methods can be an immense help with bankroll management.

When you go through stretches of time when you’re winning at a higher or lower rate, you can calculate the various possible outcomes and see that rather than betting more or less money, you’re best to stick to a staking plan and wait for the math to regress to the mean.

Statistical analysis and probability distributions are vital aspects of any successful handicapper’s method. Winning sports betting requires the ability to identify and exploit mispriced bets.

In order to accomplish this, you must be able to correctly predict an outcome’s probability of happening so that you can compare that percentage of likelihood with the implied expectation. Once you’ve developed an accurate predictive model, finding positive value to bet on is as simple as comparing two numbers.

Handicappers work to predict the future by studying the past. Using regression analysis, we comb through large data sets to find variables that seemed to correlate to wins or losses in past contests and predict future results based on those numbers.

So if we learn that the NFL team with the highest completion percentage has won 85% of the time in past games, we compare two teams’ respective completion percentages to predict who will win.

When we’ve calculated the most probable outcome, we can then take our calculations further and find the probability of all possibilities along a distribution graph. In our example above, the most likely result of the upcoming 21 games was a 13-8 record.

But ending that stretch at 13-8 was actually only predicted to happen 17% of the time. This is because finishing 12-9 or 14-7 is almost as probable as 13-8, and the further we get from the mean, the less likely the result. But there’s still some chance that records ranging from 21-0 to 0-21 can occur as well.

Knowing how to study and manipulate data for your benefit is the cornerstone of winning sports betting.

The more acquainted you get with statistical methods and probability models, the more natural your handicapping decisions will be.

The real work is in the constant searching for new variables that correlate to wins. It can be a time-consuming activity, but it’s sure to pay off once you get the hang of it.