statistical forecasting sports betting

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If this is your first season betting on baseball, well, you picked an interesting one. Unlike football and basketball where the majority of bets are based on the point spreadbaseball is a moneyline sport. This means that bettors need to pick only who wins the game, not who covers.

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Statistical forecasting sports betting

The cash variable is very right-skewed. For modeling and interpretability, it is integral to transform this variable into the log of the cash bet. The number of bets on each side is also right skewed. Here, while the effect is not major, for both the away cash percentage and away cash amount variables, as they increase, the line difference for the away tends to become more negative. This means that when more cash is on the away team, the spread tends to become more favorable to the home team.

For example, a line difference of -2 means that the initial spread could have been the away team is favored by 6 points -6 , but then the spread moved to make the away team favored by 8 points The away team must now win by more than 8 points to cover the spread, opposed to the previous point where the away team only needed to win by more than 6 points.

There are a few outliers where the line difference is greater than 5 points. This sort of extreme movement only can occur due to big player news. For example, if there is news on the Friday leading up to the game that Tom Brady is injured and cannot play, this would cause a massive swing in the line that would not be related to the cash and ticket percentages.

After exploratory data analysis, the next step is finding the best model to forecast the future spread. The model needs to forecast what the spread will be from a certain decision point. This first decision point is the first point when bets will be placed. The chosen decision point is after two-thirds of the observations in each time-series. The data frame containing the observations for each game is cut off at the two-thirds mark, and the model then forecasts the point spread for the final one-third of observations, using only the information up to this two-thirds point.

I consider a Bayesian and frequentist approach to modeling the point spread. After forecasting the point spread for the final one-third observations, I calculate the error for each model by finding the difference between the forecasted point spread and true point spread for each observation. The Bayesian approach to modeling is a time-series random walk plus noise regression model. The process starts by placing a prior for the parameters in my model before updating these parameters with the posterior mean through finding the MLE of the parameters of this regression model.

The full process of creating the dynamic linear model is demonstrated through the example of the Week 2, game between the Minnesota Vikings and the Green Bay Packers. Equations 3. The observation equation Equation?? The evolution equation Equation?? This is the evolution matrix because it allows for the evolution of the state space vector by matching up the dimensions the parameters.

This is the general setup for a dynamic linear regression model. This can be done through a Bayesian method, where the initial parameter start values are set, and then through finding the MLE of the DLM using the dlmMLE , these parameters are updated with the posterior mean. I used a flat prior for the variances of the regression parameters have a flat prior. Table 3. Looking back at equations 3. This is done through the filtering method. The filtering distribution takes in the DLM, and returns a series of one-step forecasts for the observations.

Creating a filtered distribution with the dlmFilter function returns a series of one-step forecasts and variances for the observations, as well as the same information for the state-space vector. The Kalman filtering method extends the time-series with new future predictor values, but does not input future values for the observational values. Once the future predictor values are entered, I create a filtered distribution with this new set — using the filtered values of the extended observational values as my forecast.

There are a few common methods for finding new methods for the predictor values, such as inputting the last known observation, the mean or the median. However, since my predictor values continue to grow, these methods do not apply to this model. I used this approach because for two reasons: it is unrealistic to build a separate Bayesian DLM for each parameter and these parameters simply grow without fluctuation unlike the point spread , so it is not as necessary to build as complex of a model.

There are three parameters that go into that ARIMA method: p is the number of lag observations in the model, d is the degree of differencing and q is the order of the moving average. The auto. While this forecast is certainly not perfect, it generally follows a similar path to the true value.

This is certainly an imperfect method and one area for improvement in this facet of the model. The plots show that this model is a pretty good fit for the data, as the standardized residuals generally look like white noise, though the p-values for autocorrelation become significant when the lag factor reaches high values such as 9. As these models are automatically fitted to best describe the data at hand, they generally fit the data pretty well.

It is important to note that the automatic ARIMA is fit for each different new variable from each time-series opposed to using the same ARIMA model for the cash bet for all series because the trends are not the same across all series. Thus, the automatic ARIMA model will fit the model best to the data for each of the predictor variables. Finally, after generating new values for the predictor variables in my DLM, the Kalman filtering method can be used to find predictions for the spread.

This method follows the exact same approach as above, however, the one-step forecasts for the last third of observations will replace the NAs. In addition, for comparison, the spread is also modeled with the auto. This is a frequentist approach for modeling each time-series. 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.

Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Few people manage to make money from gambling, and fewer still make a living from it. Written for hardened and novice betters alike, Joseph Buchdahl's essential guide examines, through various numerical techniques, how fixed odds punters may learn to beat the bookmaker, protect profits through a sensible approach to risk management, and turn high-risk gambling into a form Few people manage to make money from gambling, and fewer still make a living from it.

Written for hardened and novice betters alike, Joseph Buchdahl's essential guide examines, through various numerical techniques, how fixed odds punters may learn to beat the bookmaker, protect profits through a sensible approach to risk management, and turn high-risk gambling into a form of low-risk investment. Get A Copy. Paperback , pages. More Details Original Title. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Fixed Odds Sports Betting , please sign up.

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KUNDELUNGU MINING BITCOINS

Creating a filtered distribution with the dlmFilter function returns a series of one-step forecasts and variances for the observations, as well as the same information for the state-space vector. The Kalman filtering method extends the time-series with new future predictor values, but does not input future values for the observational values. Once the future predictor values are entered, I create a filtered distribution with this new set — using the filtered values of the extended observational values as my forecast.

There are a few common methods for finding new methods for the predictor values, such as inputting the last known observation, the mean or the median. However, since my predictor values continue to grow, these methods do not apply to this model. I used this approach because for two reasons: it is unrealistic to build a separate Bayesian DLM for each parameter and these parameters simply grow without fluctuation unlike the point spread , so it is not as necessary to build as complex of a model.

There are three parameters that go into that ARIMA method: p is the number of lag observations in the model, d is the degree of differencing and q is the order of the moving average. The auto. While this forecast is certainly not perfect, it generally follows a similar path to the true value. This is certainly an imperfect method and one area for improvement in this facet of the model.

The plots show that this model is a pretty good fit for the data, as the standardized residuals generally look like white noise, though the p-values for autocorrelation become significant when the lag factor reaches high values such as 9. As these models are automatically fitted to best describe the data at hand, they generally fit the data pretty well. It is important to note that the automatic ARIMA is fit for each different new variable from each time-series opposed to using the same ARIMA model for the cash bet for all series because the trends are not the same across all series.

Thus, the automatic ARIMA model will fit the model best to the data for each of the predictor variables. Finally, after generating new values for the predictor variables in my DLM, the Kalman filtering method can be used to find predictions for the spread. This method follows the exact same approach as above, however, the one-step forecasts for the last third of observations will replace the NAs.

In addition, for comparison, the spread is also modeled with the auto. This is a frequentist approach for modeling each time-series. 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. Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book.

Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Few people manage to make money from gambling, and fewer still make a living from it. Written for hardened and novice betters alike, Joseph Buchdahl's essential guide examines, through various numerical techniques, how fixed odds punters may learn to beat the bookmaker, protect profits through a sensible approach to risk management, and turn high-risk gambling into a form Few people manage to make money from gambling, and fewer still make a living from it.

Written for hardened and novice betters alike, Joseph Buchdahl's essential guide examines, through various numerical techniques, how fixed odds punters may learn to beat the bookmaker, protect profits through a sensible approach to risk management, and turn high-risk gambling into a form of low-risk investment.

Get A Copy. Paperback , pages. More Details Original Title. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Fixed Odds Sports Betting , please sign up. Be the first to ask a question about Fixed Odds Sports Betting.

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Knowing the fractional odds allows one to determine how much one must risk in order to achieve a specified reward. Fractional odds simply describe the potential profit that can be won from a unit stake. If the stake is higher than the potential profit, the betting price is said to be odds-on; if lower, then it is termed odds-against.

Where the stake is the same as any potential gain, the odds are known as evens, since there should be roughly an even chance of winning and losing if the odds are fair. In Europe, and increasingly in Britain since the growth of online sports betting, decimal odds are being used instead of fractions. These three pairs of odds may look quite different and yet are equivalent in terms of the size of stake and potential profit. Whereas fractional odds show just the winnable profit for a certain stake, decimal odds describe the total return, including both stake and profit, if the bet wins.

For all decimal odds, a unit stake is assumed. Consequently, odds of 2. Decimal odds less than 2 will be odds-on, whilst prices greater than 2 will be oddsagainst. It is fairly straightforward to convert from fractional odds into decimal odds, because the size of the fractional odds represents the potential profit from a winning bet.

Converting from decimal odds back into fractional notation is a little more problematic. Sometimes the decimal odds quoted do not fit neatly into fractions. Although 2. The simplest way to think of 2. There are advantages to using either presentation of odds. On the one hand, fractional odds help one to visualise the stake and potential profit with simple integer numbers.

On the other hand, decimal odds allow for a much greater range of potential prices, since there are only so many manageable fractions available. Many bookmakers who now quote decimal odds, however, reveal the legacy of fractional odds usage by also constraining the number of betting prices available. Most often, this will be to the advantage of the bookmaker. Perhaps the most significant benefit of decimal odds over their fractional counterparts, however, comes from their obvious suitability to computer analysis for the development of sports prediction and betting systems.

The history of fixed odds dates back to the 19th century and the origins of football gambling. During the s, newspapers started offering fixed prizes for correctly predicting the outcome of games. This is an expensive process and cannot be repeated if mistakes are made or if the bookmaker needs to alter a price in response to customer demand.

Consequently, once the list goes to print, the betting odds become fixed. An Internet bookmaker has more flexibility in this respect, and can change a price to manage his projected liability. Nevertheless, with the exception of the most popular football leagues like the English Premiership, betting odds for the majority of matches remain unchanged up until kick-off.

Prices for other fixed odds football betting, including correct score, double result and total goals rarely change at all. Spread Betting versus Fixed Odds This book is about fixed odds, but there is another field to sports gambling in the form of spread betting, and it is worth devoting a little time to compare and contrast the two forms. Sports spread betting has its origins in the financial markets. Indeed, the majority of spread betting today continues to focus on price movements of company stocks and market indices.

Sport lends itself equally well to spread betting. Unlike in fixed odds 5 where you generally either lose your whole stake or win your fixed profit, the amount you win or lose from a spread bet depends on how right or wrong you are. For example, a spread betting firm may predict that Manchester United will finish the season with 82 points. You must then decide whether the actual total will be higher or lower. If Manchester United finish with more, you will make a loss; if with fewer, a profit.

If they finish with 82 points exactly, you will neither gain nor lose. Spread betting firms will aim to balance their books by having roughly the same number of buyers and sellers for each market that they offer. If a particular event is attracting more buyers than sellers, the firm will simply raise the value of their prediction to attract more sellers into the market.

With the exception of the Internet bookmakers, such price adjustment is 5 6 Returned stakes with no profit or loss are possible with Asian handicap betting. Furthermore, since price changes are easily accommodated, one can continue to both spread bet throughout a 7 sporting event and even choose to close a position before the finish. Test match cricket, for example, which lasts up to 5 days, is particularly suited to spread betting of this nature, with markets available on the number of runs either side may score, or the total number of runs in a game.

Of course the spread betting firms also want to make a profit. If Manchester United finished on 82 points, both buyers and sellers who maintained their position until the end of the season would actually lose. There are three basic categories into which spread bets fall: total number bets; supremacy and match bets; and performance index bets.

These are decided by the totals of certain numbers in sporting events from which winners are declared, for example goals in football, runs in cricket, points in rugby or shots in golf. Where a total points spread is offered for all teams in the league, this is known as the index. Individual football games, with relatively few goals scored per game in comparison to runs hit in a cricket match, are not as well suited to total number spread betting. More usually, supremacy spreads are available, where the spread betting firm offers a price for the number of goals one team will beat another by.

Prices are usually quoted to 1 decimal place because of the low scoring in most games, with a typical spread of 0. The spread for an England v Scotland game might be 0. If the game finishes , buying 1.

In-running odds, however, are only available with a few Internet bookmakers and for only a selected number of televised sporting events, most usually football and tennis. A different number of points are awarded to the winner, runner-up, third place and so on. A performance index may also be used for special markets like bookings in a football game, with 10 points awarded for a yellow card and 25 for a red card, or the performance of a particular player during a Test match, with points awarded for wickets taken, catches made and runs scored.

This is because it is the exact result that determines the make-up of the bet, so one will always maintain an interest in the game. Unfortunately, this is what makes spread betting a far more risky and addictive form of gambling. Additionally, because of its origins in the financial markets, spread betting has tended to attract the more sophisticated type of gambler who is better equipped and more prepared to risk larger sums of money.

With a fixed odd bet, the stake is all that can be lost. A spread bet, however, can win or lose many times more than the unit stake agreed. Fixed Odds Betting Markets There are many types of fixed odds betting markets available and most are suited to the full range of sports that fixed odds betting attracts.

The most popular and common market is match betting, and the earlier discussion on fixed odds was largely made with reference to this type of wager. In standard match bets between two teams or players, winning odds are available for both, and the wager will either win or lose depending on the outcome of the event. Football fixed odds match betting is sometimes 18 known as 1X2 betting.

If the backed team wins or draws, the bet wins; if the team loses, so does the bet. With double chance bets there is no possibility for the draw. Head-to-head betting is similar to match betting, where one backs one team or player. Sometimes, however, and unlike in 1X2 match betting, if a match is tied, half the face value of the wager will be paid or a third if there is a three-way tie , as according to dead heat rules in horse racing.

Head-to-head betting is quite common in golf, where such markets are available over 18 holes 1 round or 72 holes all 4 rounds. For hole betting, they are commonly known as 2-ball or 3-ball bets, depending on the number of players going head-to-head in the bet. Rather confusingly, bookmakers tend to call hole bets match bets. By introducing a decimal, this removes the possibility of a draw, leaving only two possible outcomes.

Some bookmakers like to introduce an extra outcome to the book. William Hill online, for example, offer 3 outcomes: fewer than 2 goals; exactly 2 goals; and more than 2 goals. Other bookmakers introduce even more, although this is with a view to increasing their profit margin on the book.

Correct score betting is popular only with football, where the total number of typical scores is limited. This type of market is not used for the majority of other sports, which have much higher points totals. The chances of correctly predicting the exact score in a cricket match are, of course, very slim. The odds are dependent on the actual match odds between the two teams. Bolton are perceived as having a much smaller chance of winning than Arsenal, and therefore their odds to win , or indeed by any score, are greater.

Very often, correct score books are offered together with the first goal scorer in a game. Some sports are played with two halves, most obviously football, but also rugby as well. For football matches this means a total of 9 betting possibilities is commonly available. This is a popular alternative to simply backing an outright result, which may often be at unattractively short odds.

Obviously the risk is greater since there are more possible outcomes 9 as compared to 3 with standard match betting , but consequently the odds are better. The highest odds are obviously available for the home team to be winning at half-time and the away team to win after 90 minutes. In sporting contests with large fields or competitors, even the shorterpriced competitors may have quite high odds.

To increase the chances of a punter winning something from this bet, it may be offered each way. Each way bets are actually two bets, one for the win and one for a high placing, and are settled as two bets. The place part is calculated at a fraction of the win odds. This fraction will vary by sport and event, and will always be displayed where each way betting is available. For most golf tournaments, the place part is usually settled at one quarter of the full win odds, for st nd rd th th places 1 , 2 , 3 , 4 and sometimes 5.

By contrast, in a football tournament, where there are fewer participants, the each way part may be st nd settled at half odds for 1 and 2 place only. For some sporting contests, there may be an overwhelming favourite, with virtually no possibility of losing. The All Blacks rugby union team would be expected to defeat Holland every time they met, and you would be lucky to 20 find odds of even 1.

By introducing a points handicap, this increases the chances of being able to win the bet by backing Holland. The idea, as with most handicaps, is to give both sides a reasonably even chance of winning by giving the underdog a start. Here, Holland, the outsider, are awarded a head start of 74 points, whilst the All Blacks, the favourites, concede a handicap of points.

If the margin of victory is same as the quoted handicap, all bets on the selected team will lose. There is no possibility for a betting tie or stake refund in standard handicap betting. The magnitude of the handicap, negative for one side and positive for the other, need not necessarily be the same for both sides. Where it is the same, this is sometimes called a line bet, particularly in American sports. For most fixed odds betting, there is no such thing as a betting tie, with the exception of dead heats in head-to-head betting.

To some, this scenario may seem a little too risky. Bets either win or lose — there is no half-way house. Asian handicap betting introduces a number of other scenarios into the betting outcome, where stakes are either returned with no profit or the bet is settled as a split stakes bet, with half winning and half losing. At the same time, it eliminates the possibility of a draw in a football match. Asian handicaps are, as the name suggests, a special type of handicap betting popular in the Far East and commonly used in football betting.

As for standard handicap betting, the underdog will be awarded a head start of a handicap, and the favourite will concede a handicap of the same magnitude. For the purposes of bet settlement, the predetermined number 21 of the handicap will be added to the real number of goals.

Where no handicap is awarded handicap , a drawn game will result in a tied bet and returned stakes. If either side win, bets backing that team will win, whilst bets backing the other will lose. Similar rules apply for 1 goal and 2 goal Asian handicaps, as summarised in Table 2.

The bets are settled as if the punter has backed the away team with the specified handicap. Special bets include odds on the number of corners and bookings a televised match will have, odds for team performance, or the time of first and last goal scorer. These bets have their origins in the spread markets, and it is only through the availability of online gambling that fixed odds bookmakers have been able to break into this market.

All the fixed odds betting markets discussed above are short-term markets, that is, the odds are set only a few days at most in advance of the sporting events. In the case of in-running markets, Internet bookmakers may change match odds during the course of a game usually live football every 10 minutes. It is possible, however, to place bets on sporting contests weeks, months and sometimes years in advance.

Ante post sports bets might include a bet on the next winner of the World Cup, the Premiership champions, the Ashes Series, World snooker champion and so on. Taking a price months in advance can pay dividends, if during the intervening period it becomes clear that the player or team one backed is increasingly favoured to win.

The opposite of course is equally possible, and serious ante post bettors will usually have a deep understanding of their market to reduce the chances of the odds moving against them. The main downside to ante post betting is the return period of any potential win.

Having to wait months or even years to collect on relatively fewer bets, at generally higher stakes or higher odds than for most match or handicap bets, can seem unappealing. Different Types of Fixed Odds Bets Knowing the various fixed odds markets is one thing, but what sort of bet can one actually place? There are all sorts of fixed odds wagers available, although not all of them are suitable or indeed available for every betting market.

With a single bet on a sports event, only one outcome is backed, and the bet can generally either win or lose, although in Asian handicap, there are other possibilities. Singles odds are today generally available for almost any sporting contest one can think of, from home wins, draws and away wins in football matches bets, to ante post wagers on the next Olympic downhill skiing champion. This has not always been the case. Prior to the growth in online gambling, punters were restricted to betting at their local high street bookmaker.

Whilst the fixed odds football coupons printed every week for forthcoming weekend games had every match 1X2 bet available, one was only allowed to bet a minimum of 3 selections as a treble. A treble is one bet involving 3 selections in different events. All must be successful to achieve a return. If any of the selections were home wins, the minimum bet was a fivefold accumulator one bet involving five selections in different games. The only occasion, in football at least, when a single bet was allowed was if the game was televised, an FA Cup match 8 or an international.

Several theories have been proposed as to the reasoning behind this. The plain fact is, however, that the bookmaker's expected profit margin grows with an increase in the number of selections included in a bet. Whilst the potential return from a fivefold accumulator looks much more attractive than from a single, the chances of securing a return are disproportionately smaller for all but a handful of punters.

Multiple bets, as we have seen, involve more than one selection. With the new age of online sports betting, doubles, in addition to singles, have become popular wagers for football match betting. A double is one bet involving two selections in different events, both of which must be successful for the bet to win. The odds for a double are calculated by multiplying together the separate odds for the two single bets. This is obviously easier to do using decimal notation.

Initially, it is not exactly obvious what the odds for the double should be. Instead, it is easier to convert to decimal notation, and use a calculator or computer to determine double odds. The odds for the double are then 4. Despite the relaxation of betting rules, with most Internet bookmakers now allowing singles for the majority of football matches and other sporting events, multiple bets remain fairly popular with the punters.

Some may not be aware of the mathematics working against them with these bets; others may be but remain impulsively attracted to the lure of the bigger returns. Sometimes the only limit to the number of selections included within a multiple bet is the bookmaker's maximum allowable payout on one bet. Stories abound of winning bets containing 15, 18, or even 20 selections in an accumulator.

A few may be true, although many may be put out by the betting industry in an effort to maintain the punters' interest in the multiple bet, a policy clearly advantageous to the bookmakers. There is a way to find 7 bets from only 3 selections, making use of what have incorrectly become known as permutations or "perms". Secondly, there is one treble available at odds of However, there are also 3 doubles available too, by "perming" any 2 games from the 3 selections.

Such a series of bets is commonly known as a "Patent", or a "Trixie" if the singles are left out leaving only 4 bets. Since 1. Whether Bolton or Liverpool is selected first on the betting slip will not affect the outcome of the bet. The greater the number of selections to choose from, the greater the number of combinations available.

Combinations are not, of course, restricted to doubles. If we wish to choose from 4 matches, there are 6 combinations of doubles and 4 combinations of trebles available, in addition to 1 fourfold and 4 singles. Taking the doubles, trebles and the fourfold together as a series of 11 bets is commonly know as a "Yankee", whilst including the singles as well in a bet series is a "Flag". There is really no limit to the number of combinations of bets we can choose, apart from the bookmaker's rules and regulations.

A "Canadian" is a series of 26 bets involving 5 selections in different events, consisting of 10 doubles, 10 trebles, 5 fourfolds plus 1 fivefold. For those who want to link up six selections in 1 six-timer, 6 five-timers, 15 four-timers, 20 trebles and 15 doubles — adding up to 57 bets — they can choose a "Heinz", after the number of Heinz food varieties. A "Goliath" is usually considered to be the ultimate in multiple bets although there is no reason why it need be , with seven selections linked up in 1 seven-timer, 7 six-timers, 21 fivetimers, 35 four-timers, 35 trebles and 21 doubles making bets in total.

For any combination-type bet, a minimum of 2 selections will need to win for the punter to gain a profitable return, although frequently with the larger combination bets, more winners will be required. Whether they perform better or worse than taking the selections merely as singles alone will be explored in more detail in Chapter 6. Any of the bets may be taken each way, effectively doubling the number of bets in the permutation.

Unless a punter is familiar with the types of bets described above, he may sometimes want to know how many ways "r" teams can be permed from "n" selections. For example, how many ways can 3 teams be combined to form trebles from 6 selections?

The simplest method uses a calculator with n an Cr button, where "n" is the total number of selections, i. C is simply shorthand for "Combination". Entering these figures into the calculator returns a result of In other words, there are 20 ways of perming 3 teams from 6 selections, or 20 treble combinations available from 6 selections.

This 26 calculation can also be performed on a computer with a spreadsheet or statistics software application. For those n without a calculator or computer, the Cr formula is given by: n! Alternatively, one can calculate the number of perms using "Pascal's Triangle". For the purpose of betting permutations this is, of course, irrelevant. The values shown in Pascal's triangle, then, determine the number of ways of choosing and combining r selections from an available of total n.

For the purposes of betting, this tells us there are 20 possible trebles available from a total of 6 selections. Using Pascal's Triangle, we can also see that there are 15 possible combinations of both doubles and fourfolds from a selection of 6, 6 fivefolds and 1 sixfold, which make up the Heinz, a total of 57 bets. It is a simple matter of adding further rows to Pascal's Triangle if we want to determine more complex combinations, by inserting a 1 at the left and right of each new row, and then noting that every number in the interior of 27 the Triangle is the sum of the two numbers directly above it.

In Britain, this concerned a few very large betting firms like Ladbrokes, William Hill and Coral, who all had established reputations. If someone wanted to have a wager, this usually involved strolling down to the local betting shop and filling in the coupon.

If successful, a return trip was necessary to collect the winnings. For those betting more regularly this could become a rather tiresome and timeconsuming exercise, although others, particularly those more interested in racing, would and still do treat the visit to the betting shop as integral to the whole gambling experience. Whilst some punters still prefer to deal in cash with their local bookie, there are a number of distinct advantages to sports betting online.

The most obvious advantage of online gambling is one of convenience. Furthermore, with almost all online bookmakers, bets can be placed 24 hours a day, 7 days a week, days a year. It is a simple matter of opening a betting account with an online bookmaker, usually requiring nothing more than a credit or debit card, and occasionally further evidence of identification.

Online accounts can be opened within minutes and used immediately. Winnings are usually credited soon after the events have taken place, and account monies can normally be withdrawn relatively quickly with a simple click of the mouse. Furthermore, online fixed odds betting is free of tax. High street bookmakers do cater for a range of bets, including match bets, correct score and scorecast, and ante post.

However, since online betting coupons are so much more flexible than written or printed ones, they offer a potentially much greater range of events and betting media to choose from. Additionally, singles are available for almost every event with the majority of online bookmakers.

Some high street bookmakers in the UK have finally relaxed their rules concerning minimum trebles on the football long list coupon, but it is likely that this has been in response to the widespread availability of football match bet singles online. Perhaps the most important advantage of online fixed odds betting is the availability of choice in the betting odds.

In a busy high street, there might be two or three firms available from which to choose. Provided you have an available betting account, there are literally dozens online. Each bookmaker, however, will take a slightly different view regarding what he considers the correct price of an event to be, which may vary quite considerably. There may even be rare occasions where prices for an event vary so much that it becomes possible to back all possible outcomes with different bookmakers and still ensure that a small profit is made whatever the outcome of the event.

Such betting opportunities are known as arbitrage, a term again more familiar to spread bettors. It was really the availability of offshore bookmakers operating via the Internet that forced the Government to consider other means of raising tax revenue through gambling. Instead, tax on profits is now paid by the bookmakers. Firstly, there are sometimes currency and transaction costs associated with depositing into and withdrawing from a betting account, depending on the method used.

Debit card deposits in the UK are normally free of charges, but a credit card deposit to a foreign bookmaker may attract a small percentage fee. Withdrawals may also be limited to a minimum amount and may only be free of charge a restricted number of times each month.

Whilst these extra costs are usually low, punters who have a high turnover and movement of betting funds between accounts may find this a rather unattractive aspect of online sports betting. Secondly, most online bookmakers identify the maximum allowable stake or win available with them in their terms and conditions. However, for some events, if the bookmaker is required to manage his liabilities in response to punter demand, the maximum available stake will be much reduced from this.

Such reduced maximum stakes are more commonly found with multiple bets, where the potential wins are much higher. Nevertheless, punters adopting a specific money management plan may be rather put out to find that they are unable to take a betting opportunity at the best odds because their desired stake is larger than the maximum allowable for that event. Sometimes telephone betting, if available, can circumnavigate this difficulty.

Finally, punters need to be aware of depositing with unknown or less reputable online bookmakers. There may be over firms available to choose from, and many offer very attractive odds in comparison to the more established ones. However, there are several incidences of failing bookmakers who have ceased trading and frozen customer accounts.

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Written for hardened and novice betters alike, Joseph Buchdahl's essential guide examines, through various numerical techniques, how fixed odds punters may learn to beat the bookmaker, protect profits through a sensible approach to risk management, and turn high-risk gambling into a form of low-risk investment. Get A Copy. Paperback , pages.

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Creating a Sports Betting Model 101 - Intro to Adjusted Stats (Power Rating Systems!)

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