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The accuracy of each approach is determined by looking at the average error in the predicted spread values versus the true spread values. The blue line represents the true spread, while the red and green lines represent the Bayesian and frequentist forecasts, respectively. Both forecasts correctly predict the spread to rise. However, the Bayesian approach does a better job, in this scenario, of being closer to the true spread values.

This will be a key distinction to make when it comes to betting strategies. Since I make betting decisions based on whether the spread is within the selected interval, I use an interval that allows me to incorporate more instances of waiting to bet until the future spread moves to a more advantageous position. The residuals do not seem to be completely normally distributed. This is due to the fact that the true spread can only move in increments of 0.

When looking at the rounded values of the spread, however, the residuals are more likely to be normally distributed. The p values for autocorrelation are all extremely high, indicating there is no autocorrelation. The residuals generally look like noise, with a few exceptions attributed to the nature of these data, and the ACF is within the bounds for all factors of the lag. After building two models, I chose to use the forecasts from the best performing model.

For each time-series, the error is the sum of the difference between each true spread and predicted spread. Each method had a vector of errors of errors. When looking at the error vectors, I removed 5 outliers where each model had error sums above total points. These massive errors that both models found are likely due to games that were affected extraordinary circumstances for which my model cannot account.

I did not use the time-series predictions for these 5 games for my simulations either. The odd start time could have caused odd betting patterns where there were way fewer bets in the last third of observations than normal. Typically the amount of cash increases more linearly. However, with such an early start time on a Sunday morning, combined with the fact that people often have plans on Saturday nights, there may be a massive influx of money very close to the start of the game, as people wake up just before the game starts — opposed to having a few hours to place bets before the game starts.

JAC right Throughout the Week. The dotted line is the decision point. The charts show that the odd start time games have a significantly more massive exponential increase in the amount of money bet directly after the decision point.

This makes these games tough to model. In addition, looking at the GB vs. DET game that was a massive outlier, star Green Bay Packers quarterback Aaron Rodgers was questionable to play throughout the week due to injury. He was finally announced as healthy late in the week. It is unclear the circumstances for the other three outliers. In addition, when looking at simply absolute error, the Bayesian DLM approach provided a lower median absolute average error, as seen in Table 3.

I gathered ten equally spaced data points from each of my data sets. One row of this data frame is shown in Section 6. While I considered using Poisson regression because the number of observations are a number of occurrences, the Poisson mixed linear and simple model did not fit the data as well as the linear mixed model, based on the diagnostics of the model. Week is a factor and random effect playoffs are treated here as week 0 , as certain weeks attract more bettors than other weeks.

The coefficients and diagnostics for this model are also shown in Section 6. The bookmakers open up betting on the game by placing an initial spread typically about a week before the game starts. I then wait until my decision point, forecast the spread for the rest of the week up until game time and provide a probability estimate for each team beating the spread. If betting on the game provides negative expected value based on the probability point estimate, I do not bet on the game, but I leave the opportunity open to bet later on in the week if a new, forecasted spread would make the advantageous to bet on.

If the game has positive expected value, I place my bet on the game at the decision point. However, if the future forecasted spread projects a new spread that is even more advantageous to bet on, then I will only place a portion of my bet at the decision point and wait to place the rest of my bet.

If the spread does in fact move as projected, I then place the rest of the bet the moment the spread hits my projections. Spread — The red indicates that the team has beat the spread and the black indicates that the team has failed to beat the spread. Some key decisions determine whether the actual spread itself was a major factor in predicting team performance against the spread. In Figure 3. For example, if the away team wins by 11 points, and the spread had the away team favored by 10 points, the y-variable in this scenario would be 1, as the away team performed one point better than the spread.

The x variable is the spread. The red points are the observations where the away team covered the spread and the black points are the observations where the home team covered the spread. This means that bookmakers do not have any dead zones in making spreads where a certain team is much more likely to beat the spread at a certain point.

There do not seem to be any biases either making spreads too small or too large , with respect to the spread and the performance. Cash-Ticket Percentage Difference — The red indicates that the team has beat the spread and the black indicates that the team has failed to beat the spread. When there is a significantly higher percentage of cash bet on a team, in comparison to to the number of bets on a team, one of the teams is receiving larger bets.

This is typically an indicator that professional bettors are betting on a team. Those who bet on sports for living tend to bet significantly more than those who bet recreationally, and the professional betters tend to be correct more often than the recreational betters. From Figure 3. This is an indication that the cash-ticket difference may be a useful indicator of performance. Away Win Percentage — The red indicates that the team has beat the spread and the black indicates that the team has failed to beat the spread.

Win Percentage — The red indicates that the team has beat the spread and the black indicates that the team has failed to beat the spread. The data shows that as the win percent rises for a team, its performance against the spread gets worse. For example, if a team is , many bettors will overreact to a small sample size, and in order for the bookmakers to achieve equal amount of money on each team to guarantee themselves a profit, the bookmakers will move the line against the undefeated team.

The opposite phenomena occurs for winless teams. This is likely due to bookmakers shading the lines at such an extreme amount for these extreme win percentages, where they are able to achieve nearly equal action. There is great variation among all the teams, and while certain teams seemed to perform better against the spread, like the New Orleans Saints, treating the team as a random effect in modeling seems to suit the data. There were a few different approaches to modeling that deserved consideration.

Because scores are only in whole units, an ordinal regression model seemed as if it could have been appropriate. However, because there are an unbounded amount of levels, as well as the fact that there are so many levels — many of which have few data points — this approach would not have yielded appropriate results.

A mixed linear model is a good approach to model these data with many different groups the different teams. The downfall to this approach is that it does not give extra weight to the peaks in the score differences between games at 3 and 7, but still the score predictions would be more accurate than an inappropriately used ordinal regression model. Perhaps if there were tens of thousands of data points where each level would be represented numerous times, an ordinal regression would be more appropriate.

To first assess the best mixed linear models, the models were whittled down based on minimizing the BIC on the full dataset. There were a few metrics in this used: error rate between predicted results for the test set and the actual results, and then betting and bankroll performance across each of the simulations.

The k-fold validation used simulations in order to get a large distribution of bankroll amounts. But, if this k-fold validation was performed as usual, this would leave the test data sets with only 4 data points. Instead, the data was randomly shuffled for each of the iterations, and then broken up into 7 folds — with one fold used as a test data set and the rest as a training dataset. For generating the simulated probabilities of beating the spread for each game in the test dataset, I generated draws from its posterior predictive distribution for each model.

The vertical black line represents the median of the draws from the posterior predictive distribution, and the vertical red line represents the actual point spread. The median of the simulated outcomes the vertical black line is placed at The blue represents where the point spread falls in the ECDF. Being either above or below the two redlines means that betting on this game will generate a positive expected value. If the point is below the lower redline, it is advantageous to bet on the away team, and if the point is above the top red line, then it is advantageous to bet on the home team.

The interval of these red lines is 0. If the ECDF is below 0. Because the casino does not give fair odds, and offers odds, where a bettor must stake 1. The edges of the probability provide an expected value of 0.

Expected value is calculated by adding the probability of failure multiplied by Equation 3. Now, to find the probability of success for each game, I found where on the ECDF of the draws from the posterior predictive distribution the current spread falls. The model expects the Broncos to beat the spread with a proportion of 0. Since the spread, in this scenario, is After generating a probability of success, the expected value can be calculated. Since one must bet 1.

To develop a multiple regression system, mining data from an online sports book that can offer accurate historical sports data in a format that is easily accessible and actionable is highly recommended. These sports books also provide step by step rules for implementing regression analysis techniques in sports betting. Note that regression analysis methodology is also employed by most casinos in an effort to generate probabilities that favor the house — for similar reasons, sports books use regression analysis to provide sports betting enthusiasts with the same advantage.

There is one glaring problem in using regression analysis to predict outcomes of sporting events: the differentiation between correlation and causation. Regression analysis is effective at identifying a correlation between events, but cannot properly identify whether one event is caused by another. For example: regression analysis can be used to show that every time Team A loses, player X does not score a goal.

However, regression analysis cannot be used to conclude that Player X not scoring a goal is the cause of Team A losing the match. In other words, regression analysis can be used to determine probable future performance based on defined past outcomes, but is unable to define causes for past outcomes. Ultimately, the effectiveness of any multiple regression system relies entirely on the proper selection and comparison of variables.

In addition to multiple regression analysis, there are two other commonly used wagering methodologies: the arbitrage betting system and the use of statistical anomalies. Naturally, profits are not guaranteed, but arbitrage is a straightforward strategy that can easily be learned by novice bettors.

When implementing a strategy around statistical anomalies, the bettor seeks to gain a competitive advantage by diverging from seemingly sound predictions by introducing variables that are often overlooked by other forms of betting systems. Using this tactic successfully requires a careful study of both teams and players, as well as a variety of incidental variables, such as weather, crowd sizes, health conditions, or injuries.

While regression analyses can help a bettor identify and define the variables that may affect the outcome of any given match, determining which variables to measure and compare is the central challenge in building a winning regression system. Therefore, regression analysis in sports betting is based upon not only a comparison of reliable past data with future events, but in deciding which variables may potentially alter the probabilities of those future events. Margin of victory.

Home Top Sportsbooks Contact Us. Regression Analysis in Sports Betting Systems Sport betting is a form of wagering on the outcomes of traditional probability games such as cards, dice, or roulette as well as on the outcomes of sporting events such as football or baseball.

Traditional gambling and sports betting: Are they same? Logistic regression analysis Logistic regression is a forecasting technique that provides a probability percentage for a given variable. Problem of using regression analysis in sports betting There is one glaring problem in using regression analysis to predict outcomes of sporting events: the differentiation between correlation and causation.

Other betting systems In addition to multiple regression analysis, there are two other commonly used wagering methodologies: the arbitrage betting system and the use of statistical anomalies. Conclusion While regression analyses can help a bettor identify and define the variables that may affect the outcome of any given match, determining which variables to measure and compare is the central challenge in building a winning regression system.

References: 1. Moya F. Top 5 Sportsbooks read review.

With this extra piece of information, which team do you think has a higher chance of winning now? How do we incorporate the home advantage when evaluating the game? To answer the questions above, we build a statistical model using NHL data downloaded from Hockey Reference website.

You can modify for other sports as well. You can read the detailed description of the system here. Or just implement it by following the three steps below. The data has rows, which includes game results between Oct 2nd, , and Jan 3rd, For example, the row below records the game on Dec 6th, The Montreal Canadiens visiting team played against the New York Rangers home team with a final score of 2—1.

It is greater than 0 when the home team wins and less than 0 when the home team loses while being 0 when two teams tie. The data looks like this:. Row 0 has column Vancouver Canucks of value 1 and other columns of value 0. It shows that the visiting team in this particular game is the Vancouver Canucks. Next, we transform these two matrices further to become the final dataset.

For example, row 4 says Anaheim Ducks home team played against Arizona Coyotes visiting team. And Anaheim Ducks home team won the game by one goal. In this way, the final dataset includes information on both goal differences and the home advantage factor. Now we are ready to feed the data into a model!

We use the ridge regression model as a demonstration. It is a linear regression model with an additional term as the penalty. The result is as below:. These coefficients of each team can be considered as the rating for each team. According to this model, Colorado Avalanche is the best team with the highest rating.

My favorite Toronto Maple Leafs is approved as a good team by the model as well! You did it! The statistical method does seem more sophisticated than traditional methods. But how do the performances compare? As we talked about in the earlier section of this article, this is a fundamental statistic that often appears on sports websites.

This is a complicated method that contains information about goal difference and home advantage as well. The method with ridge regression would consider this because it looks at all the teams and all the games together. First, for each particular team , we calculate:. With these statistics, we can predict whether the home or visiting team wins a particular game. Use the example at the beginning again. Team A home team is going to play Team C visiting team.

We use the below statistic to predict the result:. To compare these methods, we use cross-validation for evaluation. Because the result of the model only improves and becomes better than other methods, as the season progresses when more data is available. There is, of course, still room to improve our prediction results. You could add variables considering the recent schedule of the teams. Did the team play games or rest within the last few days? Did the team travel a lot outside the home location?

So the recent games should be more informative compared to the earlier ones. Adding an indicator for that would help. We used the ridge regression model as an example. As an experienced sports fan, you must have valuable knowledge. Combing both the statistical methods and your experience is crucial to making better predictions.

Sports betting is an excellent way of practicing data science skills while having fun. Fit the model before the chip drops! Good luck, everyone! Thank you for reading. Then the bettor analyzes the results of those games to make a determination if one team is favored over the other.

Regression analysis is a type of statistical technique used to determine the important factors that affect the outcome of the event. In the case of sports betting this is usually done with multivariate linear regression. Because sports events are very complicated and there are many factors it is extremely difficult, if not impossible, to be able to accurately identify each variable that affects the outcome of the game.

Also, regression analysis assigns a "weight" to each factors that identifies how much it affects the outcome of the event. Regression analysis has become so sophisticated that some gamblers actually perform it as a full-time job. The results determined that the most important aspect to winning the game was passing efficiency.

One of the problems that results from using linear regression is determining causation vs. Simply put, it is being able to identify the difference between something causing an event and something happening because of an event. Regression analysis also falls short in certain cases which are more difficult to model. For instance, in football, 3 or 7 points are typically scored at a time, so bets involving a final score frequently include combinations of these two numbers.

However, a simple linear regression will not accurately model this. These are deviations from the common rule and give you a competitive advantage. In gridiron American football , the most common margin of difference in the final score is 7 points equal to one touchdown plus extra point or 3 points one field goal. There can be missed extra points, safeties and conversions.

But, they only come into play in a fractional percentage of game outcomes. This point statistical distribution factor opens up the possibility of statistical anomalies. To find anomalies one needs to cautiously review players and team statistics. One should also know significant factors such as: injuries, does the team tend to win more in indoor or outdoor sports stadiums, weather for outdoor games , what atmospheric conditions is the team used to playing in, etc.

You can also look for anomalies based on public opinion and team psyche. Factors that are used into determining betting systems are a mix of psychological, motivational, biological, situational factors that, based on past performances, support one team over another. It is generally believed that more than one factor pointing towards a team is needed to have a successful betting system.

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Various methods can be used to generate a sports betting system, although most experts agree that the most widely used method is regression analysis. Multivariate linear regression, logistic regression, and multiple regression analysis can all be used to calculate the probability of any outcome, and since determining the outcome of a sporting event requires analyzing a high number of variables, regression analysis provides a suitable framework for defining and assigning a value to these variables.

Recent movies and bestseller titles like Moneyball have delved into the world of statistical analysis, driving increased interest in the use of regression analysis for sports betting. Logistic regression is a forecasting technique that provides a probability percentage for a given variable.

Margin of victory is a statistical term which indicates difference between the number of points scored by the winning team and the number of points scored by the losing team. A smaller MV represents a close match, and by using statistical software like SPSS, the following equation can provide the percentage chance that the team will win, based on MV scores:. A percentage chance of winning can also be determined in Microsoft Excel by using this equation:.

Multiple regression systems are widely considered the most reliable modern sports betting system. This means that one must know the past to know the future. To create a multiple regression betting system, one must have reliable data regarding past information of the players and teams, meaning that trustworthy historical data is crucial to building an effective multiple regression system.

Regression 1: Bettor finds that Team A won the regular series against Team B by during the first match of the year. Since both teams have scored a victory, bettor determines that the key variable is the presence of Player X, and decides that Team B will win the match. Thus, by using multiple regression analysis, bettor is able to analyze the events of the past and extrapolate the most probable future. To develop a multiple regression system, mining data from an online sports book that can offer accurate historical sports data in a format that is easily accessible and actionable is highly recommended.

These sports books also provide step by step rules for implementing regression analysis techniques in sports betting. Note that regression analysis methodology is also employed by most casinos in an effort to generate probabilities that favor the house — for similar reasons, sports books use regression analysis to provide sports betting enthusiasts with the same advantage. There is one glaring problem in using regression analysis to predict outcomes of sporting events: the differentiation between correlation and causation.

Regression analysis is effective at identifying a correlation between events, but cannot properly identify whether one event is caused by another. For example: regression analysis can be used to show that every time Team A loses, player X does not score a goal. However, regression analysis cannot be used to conclude that Player X not scoring a goal is the cause of Team A losing the match. In other words, regression analysis can be used to determine probable future performance based on defined past outcomes, but is unable to define causes for past outcomes.

Ultimately, the effectiveness of any multiple regression system relies entirely on the proper selection and comparison of variables. In addition to multiple regression analysis, there are two other commonly used wagering methodologies: the arbitrage betting system and the use of statistical anomalies.

Naturally, profits are not guaranteed, but arbitrage is a straightforward strategy that can easily be learned by novice bettors. When implementing a strategy around statistical anomalies, the bettor seeks to gain a competitive advantage by diverging from seemingly sound predictions by introducing variables that are often overlooked by other forms of betting systems.

Using this tactic successfully requires a careful study of both teams and players, as well as a variety of incidental variables, such as weather, crowd sizes, health conditions, or injuries. Systems can be deceiving. Any sample space can be constrained enough with meaningless criteria to create the illusion of a profitable betting system. For example, a coin can be flipped with heads being home teams and tails being road teams. That, and that sportsbooks adjust their odds according to the systems, makes it difficult to follow systems indefinitely.

The sportsbooks are slower to adjust the odds in some sports versus other sports depending on the number of games played and the amount of money they take in from bettors. Betting systems based on statistical analysis have been around for a while, however they have not always been well known. One group that was known for their accurate predictions was called The Computer Group.

They formed in Las Vegas in and successfully wagered on college football and basketball games for years making millions. Michael Kent , co-founder and one of the lesser-known individuals of the group, would use his computer software to run through massive amounts of data, which then provided the group's network of bettors with useful information. The network of bettors would then bet on games in which they had a statistical advantage as determined by the software. Billy Walters , who was profiled on 60 Minutes , [1] was the most famous member of the group.

Sports betting systems have not always been well trusted or liked by bettors. The stigma is that a sporting event has too many intangibles that a machine can't predict. However, things have begun to change recently as owners of teams have begun to take notice of the value in statistics. Front offices have hired noted statistical analysts such as Jeff Sagarin. Books like Sabermetrics by Bill James, and Basketball on Paper by Dean Oliver , have begun to bring detailed statistical analysis to the forefront of sports betting systems.

Blogs are now being written more frequently about the topic and sports handicapping services have made claims of great success using sports betting systems from advanced statistical research. Determining systems is a matter of using computer analysis tools and extracting all the possible games that meet a bettor's criteria.

Then the bettor analyzes the results of those games to make a determination if one team is favored over the other. Regression analysis is a type of statistical technique used to determine the important factors that affect the outcome of the event.

In the case of sports betting this is usually done with multivariate linear regression. Because sports events are very complicated and there are many factors it is extremely difficult, if not impossible, to be able to accurately identify each variable that affects the outcome of the game.

Also, regression analysis assigns a "weight" to each factors that identifies how much it affects the outcome of the event. Regression analysis has become so sophisticated that some gamblers actually perform it as a full-time job. The results determined that the most important aspect to winning the game was passing efficiency. One of the problems that results from using linear regression is determining causation vs.

Simply put, it is being able to identify the difference between something causing an event and something happening because of an event. Regression analysis also falls short in certain cases which are more difficult to model.

For instance, in football, 3 or 7 points are typically scored at a time, so bets involving a final score frequently include combinations of these two numbers. However, a simple linear regression will not accurately model this.

These are deviations from the common rule and give you a competitive advantage. In gridiron American football , the most common margin of difference in the final score is 7 points equal to one touchdown plus extra point or 3 points one field goal. There can be missed extra points, safeties and conversions.

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