Ett odds inför en fotbollsmatch kan sättas en vecka i förväg men det justeras oftast en eller flera gånger innan matchstart. Anledningen till dessa oddsförändringar varierar men inom spelmarknaden har oddsförändring samma betydelse som riskhantering. Spelbolagen analyserar hur hela marknaden sätter odds och inget bolag vill utsätta sig för större risk än de andra i onödan. Därför fungerar en oddsjustering från ett etablerat bolag som startskottet i en kedjereaktion av oddsjusteringar. Examensarbetets syfte har varit att på uppdrag från Svenska Spel undersöka hur precisa Bolag A, Bolag B och Bolag C är i sina stängningsodds. Med stängningsodds syftas det på oddset företaget erbjuder just före matchstart. Inledningsvis för att kartlägga eventuella oddsintervall där det kan råda bristande riskhantering undersöks utfallet för varje spel (1X2) med det faktiska utfallet. Fortsättningsvis väljs ett Bolag ut för vidare analys. De viktigaste aspekterna i valet av företag är riskhanteringsförmåga samt företagets policy när det kommer till spelare som vinner mycket över en längre tid. För att kunna fastslå eventuella brister i riskhanteringen och för att undersöka huruvida det varit slumpen som varit avgörande så utförs en backtesting på det utvalda företaget. Slutligen utvecklas en matematisk modell för att förutspå utfallet i matcher beroende av målskillnader som kan fungera som ytterligare ett verktyg för Svenska Spel. Resultatet av backtestingen var inte entydigt. I vissa oddsintervall kunde det fastslås att det fanns en brist i riskhanteringen och oddssättningen medan i andra kunde det lika väl ha varit slumpen som varit avgörande. Den matematiska modellen fungerar och beroende på spelstrategi går det att slå marknaden. Likadant kan denna matematiska modell fungera som indikator för spelbolagen att se över sina odds i de utfall där spelarna gör en positiv avkastning. Den matematiska modellen bygger endast på två års data hämtad från engelska Premier League. Resultatet hade kunnat förstärkas med ytterligare två års data. Generellt så kan tillgång till data ses som en begränsning då det endast funnits tillgång till data från de senaste fyra åren. Det som kan argumentera för att använda data från de senaste fyra åren är sportens utveckling. Fotbollen utvecklas i högt takt likaså gör spelmarknaden det. Tillgång till mer data garanterar inte ett bättre resultat. / Odds for a football (soccer) game can be available to place your bets on a week prior to the actual game. From the time that the odds are first available until the referee blows the whistle for kick off the odds will have been adjusted at least once but in some cases multiple times.  In the betting market odds adjustment has the same meaning as risk management and the reasons for these adjustments varies. The betting companies analyze the entire betting market while setting odds because no one wants to expose themselves for a higher risk that others. That is why an odds adjustment from a well-known company sets off a chain reaction of several odds adjustments. The purpose of the master thesis has been to, on behalf of Svenska Spel, analyze how precise Company A, Company B and Company C have been in their closing odds. Closing odds is the odds a company offers right before kick off. To begin with the potential odds intervals where there could have been a potential lack of risk management had to be found. To find these intervals we examine every type of bet (Win, loose and draw) with the actual outcome. The next step in the project was to choose one of these companies’ for further studies. The chosen company had to fit two key aspects. The first aspect was that they had an overall excellent risk management while the second was their legal policy towards gamblers who won repeatedly over time. To be able to establish inadequate risk management there had to be some mathematical ground to ensure the outcome. Thus, a backtesting was performed on the chosen company to further back the conclusion of inadequate risk management or if it was just luck that had been the decisive factor. To conclude the master thesis a tool was developed so that the outcome of future games could be mathematically predicted depending on goal difference. The result of backtesting was not clear. A lack of risk management could be established in some odds intervals while in other odds intervals luck could have been the decisive factor. The mathematical model works and depending on chosen game strategy it is possible to beat the market. At the same time the model can serve as an indicator for betting companies to review their odds in intervals where the player makes a positive return. The mathematical model is based on two years data taken from the English Premier League. The result would have been more conclusive with two additional years of data. A general limitation in this project has been the access of historical data. What may argue against usage of data from beyond the past four years is the rapid ongoing development of the sport. Football is developing rapidly and with it the betting market as well. With this said access to more historical data does not guarantee better results.

The objective of this work is to introduce a new method called the Survivorship Instantaneous Log-odds Ratios (SILOR); to illustrate the creation of SILOR from empirical bivariate survival functions; to also derive standard errors of estimation; to compare results with those derived from logistic regression. Hip fracture, AGE and BMI from the Third National Health and Nutritional Examination Survey (NHANES III) were used to calculate empirical survival functions for the adverse health outcome (AHO) and non-AHO. A stable copula was used to create a parametric bivariate survival function, that was fitted to the empirical bivariate survival function. The bivariate survival function had SILOR contours which are not constant. The proposed method has better advantages than logistic regression by following two reasons. The comparison deals with (i) the shapes of the survival surfaces, S(X1, X2), and (ii) the isobols of the log-odds ratios. When using logistic regression the survival surface is either a hyper plane or at most a conic section. Our approach preserves the shape of the survival surface in two dimensions, and the isobols are observed in every detail instead of being overly smoothed by a regression with no more than a second degree polynomial. The present method is straightforward, and it captures all but random variability of the data.

Wimbledon is one of the most popular annual sports tournament. In the Gentlemen's Single 2009 the top seeded and defending champion Rafael Nadal withdrew from the tournament due to injury days prior to the tournament. Here, we try to analyze the effects of Nadal's withdrawal especially on the ability/strength of the main competitor Roger Federer by using bookmakers expectancies to estimate the unknown abilities of the players and compare them for two different odds sets. The comparison shows that the bookmakers did not incorporate Nadal's withdrawal adequately, assigning too high expected winning probabilities to Federer and Murray. / Series: Research Report Series / Department of Statistics and Mathematics

No description available.

<p>Betting under ordered forms has been around for a long time, but the recent increase in Internet betting and the large sums of money that are now involved makes it even more important for betting companies to have correct odds.</p><p> </p><p>The purpose of the essay is to calculate probabilities for outcomes of football games using a statistical model and to see if you can find better odds than a betting company.</p><p>The data contains the 380 games from the 2004/2005 season and the variables form, head-to-heads, league position, points, home/away, average attendance, promoted team, distance and final league position from previous season.</p><p> </p><p>After performing an ordered probit regression we only find the variable “form of the away team” to be significant at the 5 % level. We suspect the presence of multicollinearity and perform a VIF-test which confirms this. To fix this problem we perform a second ordered probit regression where a number of variables are combined to index variables. In the second regression we once again find only one significant variable. This time it is the variable “difference between home and away teams’ final league position”. A reason for the lack of significant variables could be the size of the data. A new model with five variables is examined and it results in four significant variables.</p><p> </p><p>The calculated odds pick the correct result in 200, 203 and 198 out of 380 games respectively, compared to 197 out of 380 for Unibet. Betting one krona on the lowest calculated odds from the second model will result in a positive yield for season 2004/2005 when using Unibet’s odds.</p> / <p>Vadslagning under ordnade former har funnits under en längre tid, men de senaste årens explosionsartade ökning av Internetspel och de stora summor som då omsätts har gjort det allt viktigare för spelbolagen att sätta korrekta odds.</p><p> </p><p>Syftet med uppsatsen är att med hjälp av en statistisk modell räkna ut sannolikheter för utfall i fotbollsmatcher och att undersöka om man kan hitta bättre odds än ett spelbolag.</p><p>Datamaterialet innefattar de 380 matcherna som spelades säsongen 2004/2005 samt de oberoende variablerna form, inbördes möten, tabellplacering, poängskörd, hemmaplan/bortaplan, publiksnitt, uppflyttat lag, avstånd och slutplacering.</p><p> </p><p>Efter utförd ordered probit regression erhåller vi endast en signifikant variabel vid en signifikansnivå på 5 %, nämligen ”bortalagets form”. Vi misstänker att det kan förekomma multikollinearitet och utför därför ett VIF-test som bekräftar detta. För att råda bot på detta problem genomför vi en andra ordered probit regression där flera variabler slås ihop till indexvariabler. I den andra regressionen får vi åter igen en enda signifikant variabel, men i detta fall är det variabeln ”differensen mellan hemma- och bortalagets slutplaceringar”. Ett skäl till att det inte blir fler signifikanta variabler misstänks vara storleken på datamaterialet. En ny modell med fem variabler undersöks och då blir fyra variabler signifikanta.</p><p> </p><p>De beräknade oddsen väljer rätt utfall i 200, 203 respektive 198 av 380 matcher för de tre modellerna mot Unibets 197 av 380 matcher. I modell 2 ger en spelad krona på utfallet med lägst beräknat odds positiv avkastning under säsongen vid spel hos Unibet.</p>

Betting under ordered forms has been around for a long time, but the recent increase in Internet betting and the large sums of money that are now involved makes it even more important for betting companies to have correct odds.   The purpose of the essay is to calculate probabilities for outcomes of football games using a statistical model and to see if you can find better odds than a betting company. The data contains the 380 games from the 2004/2005 season and the variables form, head-to-heads, league position, points, home/away, average attendance, promoted team, distance and final league position from previous season.   After performing an ordered probit regression we only find the variable “form of the away team” to be significant at the 5 % level. We suspect the presence of multicollinearity and perform a VIF-test which confirms this. To fix this problem we perform a second ordered probit regression where a number of variables are combined to index variables. In the second regression we once again find only one significant variable. This time it is the variable “difference between home and away teams’ final league position”. A reason for the lack of significant variables could be the size of the data. A new model with five variables is examined and it results in four significant variables.   The calculated odds pick the correct result in 200, 203 and 198 out of 380 games respectively, compared to 197 out of 380 for Unibet. Betting one krona on the lowest calculated odds from the second model will result in a positive yield for season 2004/2005 when using Unibet’s odds. / Vadslagning under ordnade former har funnits under en längre tid, men de senaste årens explosionsartade ökning av Internetspel och de stora summor som då omsätts har gjort det allt viktigare för spelbolagen att sätta korrekta odds.   Syftet med uppsatsen är att med hjälp av en statistisk modell räkna ut sannolikheter för utfall i fotbollsmatcher och att undersöka om man kan hitta bättre odds än ett spelbolag. Datamaterialet innefattar de 380 matcherna som spelades säsongen 2004/2005 samt de oberoende variablerna form, inbördes möten, tabellplacering, poängskörd, hemmaplan/bortaplan, publiksnitt, uppflyttat lag, avstånd och slutplacering.   Efter utförd ordered probit regression erhåller vi endast en signifikant variabel vid en signifikansnivå på 5 %, nämligen ”bortalagets form”. Vi misstänker att det kan förekomma multikollinearitet och utför därför ett VIF-test som bekräftar detta. För att råda bot på detta problem genomför vi en andra ordered probit regression där flera variabler slås ihop till indexvariabler. I den andra regressionen får vi åter igen en enda signifikant variabel, men i detta fall är det variabeln ”differensen mellan hemma- och bortalagets slutplaceringar”. Ett skäl till att det inte blir fler signifikanta variabler misstänks vara storleken på datamaterialet. En ny modell med fem variabler undersöks och då blir fyra variabler signifikanta.   De beräknade oddsen väljer rätt utfall i 200, 203 respektive 198 av 380 matcher för de tre modellerna mot Unibets 197 av 380 matcher. I modell 2 ger en spelad krona på utfallet med lägst beräknat odds positiv avkastning under säsongen vid spel hos Unibet.

Der Zusammenhang zwischen den Begriffen "Chance" (odd) und "Wahrscheinlichkeit" (probability) und die Anwendung des Chancenverhältnisses (odds ratio) im Bereich der Biometrie und bei der logistischen Regression werden erläutert. Es wird auf mögliche Fehlinterpretationen der Begriffe Chance und Chancenverhältnis hingewiesen.

Der Zusammenhang zwischen den Begriffen "Chance" (odd) und "Wahrscheinlichkeit" (probability) und die Anwendung des Chancenverhältnisses (odds ratio) im Bereich der Biometrie und bei der logistischen Regression werden erläutert. Es wird auf mögliche Fehlinterpretationen der Begriffe Chance und Chancenverhältnis hingewiesen.

Bookmakers odds are an easily available source of ``prospective" information that is thus often employed for forecasting the outcome of sports events. To investigate the statistical properties of bookmakers odds from a variety of bookmakers for a number of different potential outcomes of a sports event, a class of mixed-effects models is explored, providing information about both consensus and (dis)agreement across bookmakers. In an empirical study for the UEFA Champions League, the most prestigious football club competition in Europe, model selection yields a simple and intuitive model with team-specific means for capturing consensus and team-specific standard deviations reflecting agreement across bookmakers. The resulting consensus forecast performs well in practice, exhibiting high correlation with the actual tournament outcome. Furthermore, the teams' agreement can be shown to be strongly correlated with the predicted consensus and can thus be incorporated in a more parsimonious model for agreement while preserving the same consensus fit. / Series: Research Report Series / Department of Statistics and Mathematics

In June 2008 one of the biggest and most popular sports tournaments took place in Austria and Switzerland, the European football championship 2008 (UEFA EURO 2008). Before the tournament started millions of football supporters throughout the world were asking themselves, just as we did: "Who is going to win the EURO 2008?". We investigate a method for forecasting the tournament outcome, that is not based on historical data (such as scores in previous matches) but on quoted winning odds for each of the 16 teams as provided by 45 international bookmakers. By using a mixed-effects model with a team-specific random effect and fixed effects for the bookmaker and the preliminary group we model the unknown "true" log-odds for winning the championship. The final of the EURO 2008 was played by the teams Germany and Spain. This was exactly the fixture that our method forecasted with a probability of about 20.2%. Furthermore, estimated winning probabilities can be derived from our model, where team Germany, the runner-up of the final had the highest probability (17.6%) to win the title and team Spain the winner of the tournament had the second best chance to win the championship (12.3%). To adjust for effects of the tournament schedule including the group draw, we recovered the latent team strength (underlying the bookmakers' expectations) to answer the question: Will the "best" team win? An ex post analysis of the tournament showed that our method yields good predictions of the tournament outcome and outperforms the FIFA/Coca Cola World rating and the Elo rating. / Series: Research Report Series / Department of Statistics and Mathematics