They may also display race results, payoff amounts, running times, and other information. Increasingly sophisticated equipment has encouraged introduction of a variety of combination bets, such as the daily double picking winners in two specified races, usually the first two , exacta, or perfecta picking the first two finishers in a race in precise order , quinella picking the first two finishers in a race regardless of order , and pick six picking the winners in six consecutive races, usually the second through the seventh.
Pari-mutuel betting is still most practiced in horse racing but has an important place in other sports as well, most notably dog racing and jai alai. Pari-mutuel Article Additional Info. Print Cite verified Cite. While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. Facebook Twitter. Give Feedback External Websites. Let us know if you have suggestions to improve this article requires login.
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See Table 1 for detailed information on the number of matches for each season and competition. Betting odds are widely used to derive forecasts as they are simply transferrable to probabilities and have proven their quality in a large number of different studies. If no bookmaker margin was contained in the betting odds, the inverse betting odds for any possible outcome of a match could be interpreted as its probability of occurring.
To eliminate the bookmaker margin from the odds, i. This approach eliminates the overall bookmaker margin, however it can be criticized as simplifying, as it implicitly assumes that bookmaker margin is distributed proportionately across all possible outcomes of a match e.
For a more detailed discussion on this issue, possible consequences and alternative approaches see [ 25 , 24 ]. Due to the reasonably small margins in our data set average bookmaker overround of 1. See Table 1 and S1 File for more details on the margins.
The ELO rating system is a well-known and widely used rating system that was originally invented to be used in chess, but has successfully been transferred to rate soccer teams cf. The model is based on the idea of calculating an expected result for each match from the current rating of the participating teams.
After the match the actual result is known and the ratings of both participants are adjusted accordingly. A higher difference between actual result and expected result evokes a higher adjustment made to the ratings and vice versa. As a result, for each team a dynamic rating is obtained and is adjusted over time by every new match result that becomes observable. After the match the actual result a H for the home team can be observed. See [ 26 ] and [ 13 , 3 ] for more information on the calculation of a classic ELO rating in chess and soccer.
This modification of the ELO model additionally takes the goals scored by each team into account. Then the parameter k is modified to be. Therefore, the model is able to use more information than the pure result of a match. The calculation has been adopted from [ 16 ] and the model is referred to as ELO-Goals. Note that the well-known World Football Elo Ratings published online [ 13 , 3 ] is also based on a calculation including the goals, however using a slightly different calculation method.
Although betting odds have proven to possess excellent predictive qualities, they have not been used as a basis to create rankings and ratings. Surprisingly it has not been evaluated yet, how valuable betting odds from previous matches are for forecasting future soccer matches. The calculation works similar as shown for ELO-Result, i. The actual result, however, is replaced by the expected result in terms of betting odds.
Let p H , p D and p A be the probabilities for home win, draw and away win obtained from the betting odds. Then the actual result as used in ELO-Result is replaced by:. The model aims at accessing more information than results or goals by indirectly deriving it from the betting odds. At the same time, it is a drastic restriction as throughout the calculation of the ELO-Odds ratings no match result is ever directly used. Moreover, the model uses the betting odds prior to the match as a measure for the actual result, thus only using information that was known prior to the start of the match and fully ignoring the result that is observable after the match.
To make sure this study is based on a solid framework, we make use of previous research and proven statistical methods, that are largely adopted from Hvattum and Arntzen [ 16 ]. As a start value each team is given a rating of 1, points prior to the first match of the first season. To have a useful start value for promoted teams in later seasons, these teams carry on the ratings of the relegated teams.
This procedure has two positive effects: First, it can be assumed that promoted teams are in general weaker than the average team in the league. Thus the ratings of the relegated teams are a more promising estimator of team quality than using an average start value for the promoted teams.
Second, it has the nice side-effect that the sum of ratings stays the same over the full period of time, calculated over all teams that are currently participating in one of the four leagues. These rating differences then are taken as the single covariate of an ordered logit regression model.
As a result from the regression model, logistic functions are obtained that transfer a rating difference into probabilities for home win, draw and away win. Finally, the forecasts are analyzed using the informational loss L i see [ 27 ] for a definition as a measure of predictive quality. Please note that minimizing the informational loss is equivalent to maximizing the likelihood function.
To verify whether differences regarding the loss functions of two models are significant, paired t-tests are used. See Fig 1 for a graphical representation of rating process, forecasting process and testing process. The informational loss for all three models and different parameters is moreover illustrated in Fig 2 , Fig 3 and Fig 4.
Second, the actual results in ELO-Result are subject to strong influence of randomness. A higher adjustment factor does therefore evoke a too strong adaption of the latest results. In general, using the results to choose the parameters i. However, we can see that the results are not highly sensitive to the choice of the parameter s , compared to the sensitivity of the results to the choice of the model see next section.
Table 3 shows the major results of analyzing the predictive quality of the different forecasting methods. Betting odds are shown to have the highest predictive quality, outperforming ELO-Odds on a highly significant level. Therefore, the results of Hvattum and Arntzen [ 16 ] could be reproduced with respect to betting odds, ELO-Result and ELO-Goals, although using a different set of data including four European leagues and two international competitions. The p-value compares each model to the model in the next row.
ELO-Goals being superior to ELO-Result confirms that the goal difference of a match contains more relevant information than its result win, draw, lose. The striking and novel result is the superiority of ELO-Odds to ELO-Goals which confirms that forecasts from previous matches are indeed useful in rating teams and a valuable source of information for forecasting future matches.
The p-value compares each model to ELO-Goals. In fact, this shows that from a predictive perspective the betting odds known prior to a soccer match possess more information than the result known after the match. To put it simple, looking at the betting odds prior to a match gives you more relevant information on team quality and more valuable insights to performance analysis than studying the results afterwards. This result might partly be driven by the fact that the result of a match is a realization of the underlying probability distribution, while the betting odds represent this probability distribution.
Including other match-related quality measures besides results and goals such as expected goals calculated from match statistics after a match could serve as basis for a useful additional ELO rating. Unfortunately, this would either require a publicly available source of expected goals covering the whole database or a database including comprehensive match statistics in order to calculate own measures of expected goals.
By design, we cannot expect the ELO-Odds model to provide better forecasts than the betting odds itself, as these are the only source of information for the model. Nevertheless, it is worth evaluating why there is such a clear gap in predictive qualities.
Note that, although using betting odds as a source of information, the ELO-Odds model by far is exploiting less information than the betting odds. It can only extract team specific information from the betting odds and aggregate them in the ratings. Motivational aspects of a single match or any relevant information like injuries or line-ups that has become available in between two matches will not be reflected in ELO-Odds.
Moreover, the actual result of the preceding match is not reflected in ELO-Odds, while it is surely influencing the betting odds. Finally, the ordered logit regression model using the ELO difference as single covariate might be a limiting factor, thus even an accurate rating does not necessarily lead to an accurate forecast. One important aspect of this study is to shed light on accurate predictive team ratings that are usually used as an intermediate result of forecasting models.
Betting odds for a match can be seen as the market judgement for the quality of both teams participating. However, it is not straight forward to obtain a quantitative rating for each team from the betting odds of various matches. By using the betting odds as an input for the ELO calculation in ELO-Odds, we made the information included in the betting odds visible in terms of a team rating. The results of the previous section have already shown that ELO-Odds in general provides a superior estimation of team quality.
We would like to illustrate this with reference to two remarkable examples. Certainly these examples cannot be seen as a proof for the superiority of ELO-Odds, but they can be useful to illustrate differences in quality estimation and how these can be used to understand the quality development of teams. Before comparing ELO-Odds to ratings based on results or goals, we need to verify that the different ELO measures are comparable at all.
Please note that due to the construction of the ELO calculation, points gained by one team are equally lost by another team. Therefore the sum of points for all teams in our database stays constant over the whole period of investigation.
As a result, the ratings are comparable in terms of size and it is possible to compare the quality estimation of teams in ELO points between different models. In particular it becomes possible to analyze differences between ELO-Odds and ELO-Result on a team level and consequently to gain more detailed insights on the quality and performance development of each soccer team.
Despite small deviations especially at the beginning of the season , the ratings for ELO-Result and ELO-Odds are mainly in line and virtually no difference in ratings exists at the end of the season. In February —after having massively unsuccessful results for half a year—Dortmund was in last position of the league table.
Consequently ELO-Result shows a drastic decrease of almost rating points. Surprisingly ELO-Odds for a long time hardly shows any reaction to the unsuccessful period, proving that the market judgement of the team quality was only weakly modified. The subsequent development might be interpreted as a confirmation of this judgement as Dortmund was playing a successful rest of the season and finished 2 nd and 3 rd in the two following seasons.
Leicester finished 12 th in the following season, which again fits closer to the cautious market judgement than to the rating based on results. In light of the results of this study, these examples show the effective use of a betting odds based rating in order to gain practical insights into the quality of soccer teams. Moreover, they are impressively showing that soccer results seem to be a very one-dimensional and thus an insufficient reflection of team quality. This result is in line with Heuer et al.
This is the major reason for using hardly definable, but valuable criteria like chances for goals to estimate team quality [ 30 ]. Moreover, it gives rise to the idea of calculating advanced key performance indicators using position data from soccer matches [ 31 , 32 ]. Admittedly, the two examples refer to very special situations and were explicitly chosen in order to illustrate differences in ratings. Moreover, both situations were only discussed very briefly not considering events like the coach of Dortmund announcing to leave the club during the season or possible psychological and motivational effects hampering the performance of Leicester after the surprising championship.
The usual perception would be that after 38 matches the teams are fairly well ordered related to their underlying quality throughout the whole season. As a comparison the teams were ordered following the average ELO-Odds rating during the season and presented at the right side of the table. There is a strong similarity between both rankings, but likewise there are a few notable discrepancies.
Atletico Madrid won the title although clearly being ranked in third position by the betting market behind FC Barcelona and Real Madrid. Given the outstanding role of FC Barcelona and Real Madrid, this result might not be surprising and will be in line with the perception of many soccer experts, coaches and officials at that time. Differences concerning less successful teams are more interesting.
According to the market valuation Levante UD was the worst team in the league during this season although finishing 10 th in the league table. In contrast to that, Betis Sevilla was ranked 11 th by the market, but in fact was relegated at the end of the season. This comparison gives valuable insights to the difference between results and market valuation of teams. Certainly, we do not have full knowledge about the exact mechanisms of performance analysis in professional soccer clubs.
From an outside position and following the detailed media coverage, however, it seems that results are by far the most important basis of decision-making. Under the background of this study, club officials should pay more attention to careful performance analysis by assessing various sources of information than solely looking at the results when evaluating the work of players and coaches.
When investigating a quantitative model for forecasting soccer matches, a common approach is to examine the financial benefit of the model by back-testing various betting strategies and calculating the betting returns. For reasons of completeness and comparability to other studies, betting returns for different ELO models were calculated and can be found in S1 File. However, we would like to point out that gaining positive betting returns cannot be equated with a superior predictive quality of the underlying model as measured by statistical measures.
However, it would certainly not be judged as a valuable probabilistic forecasting model. This example illustrates that finding profitable betting strategies and finding accurate forecasting models are slightly different tasks. In addition, ELO-Odds is intended to connect the advantages of betting odds and mathematical models by extracting information from betting odds and using them in mathematical models. Consequently it would—by design—be unreasonable to expect systematically positive betting returns from such a model.
Based on these reasons, the focus of this study is on evaluating the predictive quality of a forecasting model in terms of statistical measures and its benefit in enabling insights to performance analysis. Although the predictive power of betting odds is widely accepted [ 23 , 11 ], betting odds have not been used as a basis to create rankings and ratings.
Lots of effort has been made in developing mathematical models in order to find profitable betting strategies and thus beat the betting market [ 1 , 20 , 16 ]. In contrast, we pursue the strategy of using betting odds as a source of information instead of trying to outperform them.
As the results show, this is a promising approach in an attempt to extract relevant information that would be hardly exploitable otherwise in mathematical models. We could successfully transfer prior results concerning ELO-ratings in association soccer [ 16 ] to a different set of data including both domestic and international matches.
This transferability of results should not be taken for granted as the structure of the data heavily depends on the choice of teams and competitions. The data set used here is characterized by full sets of matches within the leagues and—in relation to this—only a few cross-references i. See Fig 7 for a simplified illustration of the database as a network of teams nodes and matches edges.
Please note that for purposes of the presentation an explaining example is demonstrated, instead of the full database. The aforementioned study was missing international matches and different countries, but including lower leagues. Yet another situation applies for national teams who are playing relatively rarely. Tournaments as the World Cup take place only every four years and are played in a group stage and knockout matches.
Further matches in continental championships or qualifications are lacking matches with opponents from different continents. In other sports or comparable contexts such as social networks the structure again might be completely different. For data sets like the one used within this study, the ELO rating system might not be the optimal approach as it is not designed for indirect comparison. Each match directly influences the rating of both competitors and thus can indirectly influence the future rating of other teams.
However, a match is never directly influencing the rating of a non-involved team. We would expect a notable benefit in treating teams and matches as a network and taking advantage of this structure for future rating approaches. It can be supposed that this will lead to a shortened time period to derive useful initial ratings and more accurate quality estimations, especially for teams not being part of cross-references i. So far, only few attempts to make use of the network structure [ 33 ] or explicitly including indirect comparison [ 34 ] have been made in US College Football.
Other methods like the Massey rating see [ 35 ] for an introduction can be argued to implicitly take advantage of the network structure. However, there is a lack of general theory and a theoretical framework that investigates the best rating methods for different types of network structures. Another aspect contributes to the complexity of evaluating rating and forecasting methods.
The quality of a rating and forecasting model such as ELO-Odds depends both on its ability in estimating team ratings and its ability to forecast the outcomes, given accurate ratings. As match results are affected by random factors, the true quality of a team is never known or directly observable and thus the quality of the rating can only be tested indirectly. Moreover, it can be assumed that the true quality of a team will be subject to changes over time.
In view of this, it is difficult to prove which aspect of the model carries responsibility for achieving or not achieving a certain predictive quality. To gain better insights into the quality of rating models, it will be useful to conduct further studies using a more theoretical framework. This could be achieved by constructing theoretical data sets including known team qualities true ratings and simulated data for the observable results, applying the rating models to this data set and then comparing the calculated ratings with the true ratings.
ELO-Odds provides clear evidence for the usefulness of incorporating expert judgement into quantitative sports forecasting models in order to profit from crowd wisdom. Further evidence for the power of expert judgement can be found in Peeters [ 20 ] where collective judgements on the market value of soccer players from a website are successfully used in forecasting tasks. Moreover, researchers recently have started attempts to extract crowd wisdom from social media data.
An example aiming at soccer forecasting can be found in Brown et al. Within this study we made use of betting odds as a highly valuable tool in processing available information and forecasting sports events. The betting odds themselves are a measure for the expected success in the following match.
Using our approach, we can directly map these expectations of the market to a quantitative rating of each team, i. This measure proves to be superior to results or goals when used within a framework of an ELO forecasting model. We did not evaluate the differences between ELO-Odds and the betting odds themselves in detail. Future studies investigating match related aspects such as motivational aspects, line-up, etc. In contrast to prior research, we emphasized that rating methods and forecasting models can help to gain insights to the underlying processes in sports and that there is a strong link between forecasts and performance analysis.
The present study is further evidence that results and goals are not a sufficient information basis for rating soccer teams and forecasting the outcomes of soccer matches. Expert opinion can possess highly valuable information in forecasting, future rating and forecasting models should become more open to include sources of crowd wisdom into mathematical approaches.
In times of social networks and online communication new possibilities have emerged and will keep emerging. Huge data sets from social media e. Twitter data or search engines e. Google search queries have just been started to be explored in the scientific community and are a challenging, but highly promising approach to be used in rating and forecasting. With respect to the methods and results shown within this study, a measure based on betting odds would be more suitable than the aforementioned measures based on results, goals or league tables.
This could be adapted in future research by taking advantage of the ELO-Odds rating as an improved method to assess team qualities. Appendix including details on calculating probabilities from betting odds Appendix A and the investigation of betting strategies Appendix B. Data set including the minimal data needed to replicate the study as well as main results ratings intended to be usable by other researchers in future research.
Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract Betting odds are frequently found to outperform mathematical models in sports related forecasting tasks, however the factors contributing to betting odds are not fully traceable and in contrast to rating-based forecasts no straightforward measure of team-specific quality is deducible from the betting odds.
Funding: The author s received no specific funding for this work.
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Betsson is an award-winning sports betting website that has been around since and literally grew into a gambling empire. The company provides users from all over the world an option to play poker, casino, bingo games and place their bets on various sports events. Betsson is based in Malta and holds a betting license from the gambling commission in the same country as well as one from the United Kingdom as well. Today, its sports betting option is offered on various markets and more and more consumers choose it as a significant option for sports betting.
BetAmerica made its name in online gambling industry through horse racing, which then branched out into fantasy sports with the launch of FanEx Sports. Today, BetAmerica. Online betting was brought into the sports industry in the late s and has been growing significantly since then. With the emergence and high penetration of the digital platform, punters have the flexibility in placing bets on sports from any part of the world.
Indeed, the digital revolution has given sportsbooks a platform to connect with new customers. Print Cite verified Cite. While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. Facebook Twitter. Give Feedback External Websites. Let us know if you have suggestions to improve this article requires login.
External Websites. The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree See Article History. Get a Britannica Premium subscription and gain access to exclusive content. Subscribe Now. Learn More in these related Britannica articles:. This is a common betting pool in which those who bet horses finishing in the first three places share the total amount bet minus a percentage for the management.
The pari-mutuel was perfected with the introduction in the 20th century of the totalizator, a…. Pari-mutuel pools in horse-race betting, for example, reflect the chances of various horses to win as anticipated by the players.
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Scientific Games Corp. April 30, Baseline Magazine. Ziff-Davis Media. December 1, Retrieved February 18, November 9, New Haven Register. October 7, September 11, March 8, The Hollywood Reporter. Las Vegas Business Press. March 29, December 28, Retrieved December 11, The Guardian. April 27, Retrieved April 27, August 1, July 24, Retrieved December 31, Dagens Nyheter in Swedish.
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