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Prediction of the 2019 IHF World Men’s Handball Championship – A sparse Gaussian approximation model

Abstract

 In this work, we compare several different modeling approaches for count data applied to the scores of handball matches with regard to their predictive performances based on all matches from the four previous IHF World Men’s Handball Championships 2011 – 2017: (underdispersed) Poisson regression models, Gaussian response models and negative binomial models. All models are based on the teams’ covariate information. Within this comparison, the Gaussian response model turns out to be the best-performing prediction method on the training data and is, therefore, chosen as the final model. Based on its estimates, the IHF World Men’s Handball Championship 2019 is simulated repeatedly and winning probabilities are obtained for all teams. The model clearly favors Denmark before France. Additionally, we provide survival probabilities for all teams and at all tournament stages as well as probabilities for all teams to qualify for the main round.

1Introduction

Handball, a popular sport around the globe, is particularly important in Europe and South America. As there are many different aspects that can be analyzed, in the last years handball had also raised an increasing interest among researchers. For example, in Uhrmeister and Brosig (2018) a group of statisticians and sports scientists selected 59 items from the play-by-play reporting of all games of the 2017 IHF World Men’s Handball Championship and the involved players were compared based on their individual game actions independently of game systems, concepts and tactical tricks. The data were clustered and collected in a matrix, to add up to a “PlayerScore”. In another scientific work, the activity profile of elite adolescent players during regular team handball games was examined and the physical and motor performance of players between the first and second halves of a match were compared (Chelly, Hermassi, Aouadi, Khalifa, Van den Tillaar, Chamari, and Shephard, 2011). A simulation-based comparison of tournament designs for men’s IHF Handball World Cups is presented in Csató (2019).

In this project we elaborate on a statistical model to evaluate the chances for all teams to become champion of the upcoming IHF Handball World Cup 2019 in Denmark and Germany. For this purpose, we launched a collaboration of professional statisticians and handball experts. While this task is rather popular for soccer (see, e.g., Groll, Schauberger, and Tutz, 2015, or Zeileis, Leitner, and Hornik, 2014), to the best of our knowledge this idea is new in handball. In the following, we will compare several (regularized) regression approaches modeling the number of goals the two competing handball teams score in a match regarding their predicitve performances. We start with the classical model for count data, namely the Poisson regression model. Next, we allow for under- or overdispersion, where the latter can be captured by the negative binomial model. Furthermore, as for large values of the Poisson mean λ the corresponding Poisson distribution converges to a Gaussian distribution (with μ = σ2 = λ) due to the central limit theorem, this inspired us to also apply a Gaussian response model. Through this comparison, a best-performing model is chosen using the matches of the IHF World Cups 2011 – 2017 as the training data. Based on its estimates, the IHF World Cup 2019 is simulated repeatedly and winning probabilities are calculated for all teams.

The rest of the manuscript is structured as follows: in Section 2 we describe the underlying (training) data set covering (almost) all matches of the four preceding IHF World Cups 2011 – 2017. Next, in Section 3 we briefly explain four different regression approaches and compare them based on their predictive performance on the training data set. The best-performing model is then fitted to the data and used to simulate and forecast the IHF World Cup 2019 in Section 4. Finally, we conclude in Section 5.

2Data

In this section, we briefly describe the underlying data set covering all matches of the four preceding IHF World Men’s Handball Championships 2011 – 2017 together with several potential influence variables1. Basically, we use a similar set of covariates as Groll et al. (2015) do for their soccer FIFA World Cup analysis, with certain modifications that are necessary for handball. For each participating team, the covariates are observed either for the year of the respective World Cup (e.g., GDP per capita) or shortly before the start of the World Cup (e.g., a team’s IHF ranking), and, therefore, vary from one World Cup to another.

Some of the variables contain information about the recent performance and sportive success of national teams, as the current form of a national team should have an influence on the team’s success in the upcoming tournament. Beside these sportive variables, also certain economic factors as well as variables describing the structure of a team’s squad are collected. We shall now describe in more detail these variables.

Economic Factors:

GDP per capita. To account for the general increase of the gross domestic product (GDP) during 2011 – 2017, a ratio of the GDP per capita of the respective country and the worldwide average GDP per capita is used (source: http://www.imf.org/external/pubs/ft/weo/2018/01/weodata/index.aspx).

Population. The population size is used in relation to the respective global population to account for the general world population growth during 2011 – 2017 (source: https://population.un.org/wpp/Download/Standard/Population/).

Sportive factors:

ODDSET probability. For the four IHF World Cups 2011 – 2017 we got the 24 odds of all possible tournament winners before the start of the corresponding tournament from the German state betting agency ODDSET. These we converted into winning probabilities. The variable hence reflects the probability for each team to win the respective World Cup.

IHF ranking. The IHF ranking is a ranking table of national handball federations published by the IHF (source: http://ihf.info/en-us/thegame/rankingtable). The full ranking includes results of men’s, women’s as well as junior and youth teams and even beach handball. The points a team receives are determined from the final rankings of World Cups of the respective sub-groups and Olympic games and strictly increase over the years, so the ranking system displays an all-time ranking of the national federations. All those results can be regarded totaled or separated for each team’s section. Since this project only examines men’s World Cups, merely the men’s ranking table will be further disposed.

IHF points. In addition to the IHF ranking, we also include the precise number of IHF points the ranking is based on. This provides an even more exact all-time ranking of the national federations’ historic performances.

Home advantage:

Host. It can be assumed that the host of a Word Cup might have a home advantage, since the players’ experience a stronger crowd support in the arena and are more conversant with the host country’s cultural circumstances. Hence, a dummy is included indicating if a national team is a hosting country. Since the World Cup 2019 is jointly hosted by Germany and Denmark, both are treated equally.

Continental federation. The IHF is the parent organization of the different continental federations, the African Handball Confederation (CAHB), the Asian Handball Federation (AHF), the European Handball Federation (EHF), the Oceania Continent Handball Federation (OCHF) and the Pan-American Team Handball Federation (PATHF). The nation’s affiliation to the same continental federation as the host could on the one hand influence the team’s performance similar to the Word Cup’s host by their better habituation with the host’s conventions. Additionally, supporters of those teams have a shorter arrival. On the other hand, handball is not equally prevalent on every continent, especially European club handball is most popular. To capture potential performance differences between the continental federations, two variables are added to the data set. A dummy determining whether a nation is located in Europe, and a dummy seizing whether a nation belongs to the same umbrella organization as the Word Cup host.

Factors describing the team’s structure:

The following variables describe the structure of the teams. They were observed with the 16-player-squad nominated for the respective World Cup.

(Second) maximum number of teammates.

For each squad, both the maximum and second maximum number of teammates playing together in the same national club are counted.

Average age. The average age of each squad is collected. However, very young players might be rather inexperienced at big tournaments and some older players might lack a bit concerning their condition. For this reason we assume an ideal athlete’s age, here represented by the average age of all squads that participated in World Cups throughout the last eight years, so that the absolute divergence between a national team’s average age and that ideal age is surveyed.

Average height. The average height of a team can possibly impact the team’s power. Tall players might have an advantage over short players, as they can release a shot on goal above a defender more easily. Therefore, we include the team’s average height in meters.

Number of EHF Champions League (EHF-]cup) players. As club handball is mainly based on the European continent, the EHF Champions League is viewed as the most attractive competition, as numerous of the best club teams in the world participate and only the best manage to reach the final stages of the competition. Hence, also the best players play for these clubs. For this reason we include the number of players of each country that reached the EHF Champions League semifinals in the previous year of the respective World Cup. The same data is collected for the second biggest European club competition, the EHF-cup.

Number of players abroad/Legionnaires.

For each squad, the number of players playing in clubs abroad is counted.

Factors describing the team’s coach:

The players of course extinguish the most important part of a squad, but every team additionally needs an eligible coach to instruct the players. Therefore, some observable trainer characteristics are gathered, namely Age and Tenure of the coach plus a dummy variable that determines whether he shares the same Nationality as his team.

In total, this adds up to 18 variables which were collected separately for each World Cup and each participating team. As an illustration, Table 1 shows the results (1a) and (parts of) the covariates (1b) of the respective teams, exemplarily for the first four matches of the IHF World Cup 2011. We use this data excerpt to illustrate how the final data set is constructed.

Table 1

Exemplary table showing the results of four matches and parts of the covariates of the involved teams.

jsa-6-jsa200384-g002.jpg

For the modeling techniques that we shall introduce in the following sections, all of the metric covariates are incorporated in the form of differences. For example, the final variable Rank will be the difference between the IHF ranks of both teams. The categorical variables Host, Nationality as well as the two continental federation variables, however, are included as separate variables for both competing teams. For the variable Host, for example, this results in two columns of the corresponding design matrix denoted by Host and Host.Oppo, where Host is indicating whether the first-named team is a World Cup host and Host.Oppo whether its opponent is.

As we use the number of goals of each team directly as the response variable, each match corresponds to two different observations, one per team. For the covariates, we consider differences which are computed from the perspective of the first-named team. For illustration, the resulting final data structure for the exemplary matches from Table 1 is displayed in Table 2.

Table 2

Exemplary table illustrating the data structure.

GoalsTeamOpponentAgeRankOddset...
32FranceTunisia-0.81-12-0.284...
19TunisiaFrance-0.81-12-0.284...
33SpainBahrain1.21-410.129...
22BahrainSpain-1.2141-0.129...
18BahrainGermany0.1047-0.064...
38GermanyBahrain-0.10-470.064...
18TunisiaSpain-0.8110-0.124...
21SpainTunisia0.81-100.124...

Due to some missing covariate values for a few games, altogether the final data set contains 334 out of 354 matches from the four handball World Cups 2011 – 2017. Note that in all the models described in the next section, we incorporate all of the above-mentioned covariates. However, not all of them will be selected by the introduced penalization technique. Instead, rather sparse models will be prefered.

3Methods

In this section, we briefly describe several different regression approaches that generally come into consideration when the goals scored in single handball matches are directly modeled. Actually, most of them (or slight modifications thereof) have already been used in former research on soccer data and, generally, all yielded satisfactory results. However, some adjustments are necessary for handball. All methods described in this section can be directly applied to data in the format of Table 2 from Section 2. Hence, each score is treated as a single observation and one obtains two observations per match. We aim to choose the approach that has the best performance regarding prediction and then use it to predict the IHF World Men’s Handball Championship 2019.

3.1Poisson model

A traditional approach which is often applied, for example, to model soccer results is based on Poisson regression. In this case, the scores of the competing teams are treated as (conditionally) independent variables following a Poisson distribution (conditioned on certain covariates), as introduced in the seminal works of Maher (1982) and Dixon and Coles (1997).

As already stated, each score from a match of two handball teams is treated as a single observation. Accordingly, similar to the regression approach investigated in Groll, Ley,Van Eetvelde and Schauberge (2019), for n teams the respective model has the form

(1)
Yijk|xik,xjkPo(λijk),log(λijk)=ηijk:=β0+(xik-xjk)β+zikγ+zjkδ,
where Yijk denotes the score of handball team i against team j in tournament k with i, j ∈ {1, …, n} ,  i ≠ j and ηijk is the corresponding linear predictor. The metric characteristics of both competing teams are captured in the p-dimensional vectors xik, xjk, while zik and zjk capture dummy variables for the categorical covariates Host, Nationality as well as the two continental federation variables (built, for example, by reference encoding), separately for the considered teams and their respective opponents. For these variables, it is not sensible to build differences between the respective values. Furthermore, β is a parameter vector which captures the linear effects of all metric covariate differences and γ and δ collect the effects of the dummy variables corresponding to the teams and their opponents, respectively. For notational convenience, we collect all covariate effects in the p˜ -dimensional real-valued vector θ = (β, γ, δ).

If, as in our case, several covariates of the competing teams are included into the model it is sensible to use regularization techniques when estimating the models to allow for variable selection and to avoid overfitting. In the following, we will introduce such a basic regularization approach, namely the conventional Lasso (least absolute shrinkage and selection operator; Tibshirani, 1996). For estimation, instead of the regular likelihood l (β0, θ) the penalized likelihood

(2)
lp(β0,θ)=l(β0,θ)-ξP(β0,θ)
is maximized, where P(β0,θ)=v=1p˜|θv| denotes the ordinary Lasso penalty with (positive) tuning parameter ξ ≥ 0. The optimal value for the tuning parameter ξ will be determined by 10-fold cross-validation (CV). The model will be fitted using the function cv.glmnet from the R-package glmnet (Friedman, Hastie, and Tibshirani, 2010). In contrast to the similar ridge penalty (Hoerl and Kennard, 1970), which penalizes squared parameters instead of absolute values, Lasso does not only shrink parameters towards zero, but is able to set them to exactly zero. Therefore, depending on the chosen value of the tuning parameter, Lasso also enforces variable selection.

3.2Overdispersed Poisson model / negative binomial model

The Poisson model introduced in the previous section is built on the rather strong assumption E [Yijk|xik, xjk] = Var (Yijk|xik, xjk) = λijk, i.e. that the expectation of the distribution equates the variance. For the case of World Cup handball matches, the (marginal) average number of goals is around 30 (for example, y¯=27.33 for the matches of the IHF World Cups 2011 – 2017) and supposably the corresponding variance could differ substantially.

A case often treated in the literature is the case when Var (Y) > E [Y], the so-called overdispersion. But for handball matches, also the contrary could be possible, namely that Var (Y) < E [Y] holds. In both cases, one typically assumes that Var (Y) = φ · E [Y] holds, where φ is called dispersion parameter and can be estimated via

(3)
φˆ=1N-dfi=1Nri2,
where N is the number of observations and ri the model’s Pearson residuals.

We will first focus on the (more familiar) case of overdispersion. It is well known that the overdispersed Poisson model can be obtained by using the negative binomial model. To combine this model class with the Lasso penalty from equation (2), the cv.glmregNB function from the R-package mpath (Wang, 2018) can be used (see also, for example, Wang, Ma, and Wang, 2015).

3.3Underdispersed Poisson model

If we fit the (regularized) Poisson model from Section 3.1 to our IHF World Cup data and then estimate the dispersion parameter via equation (3), we obtain a value for φˆ clearly smaller than one ( φˆ=0.74 ), i.e. substantial underdispersion. Hence, the variance of the goals in IHF World Cup matches seems to be smaller than their mean.

To be able to simulate from an underdispersed Poisson distribution (which we would need later on to simulate matches from the IHF World Cup 2019), the rdoublepois function from the rmutil-package (Swihart and Lindsey, 2018) can be used.

3.4The Gaussian response model

It is well-known that for large values of the Poisson mean λ the corresponding Poisson distribution converges to a Gaussian distribution (with μ = σ2 = λ) due to the central limit theorem. In practice, for values λ ≈ 30 (or larger) the approximation of the Poisson via the Gaussian distribution is already quite satisfactory. As we have already seen in Section 3.2 that the average number of goals in handball World Cup matches is close to 30, this inspired us to also apply a Gaussian response model.

However, instead of forcing the mean to equate the variance, we again allow for μ ≠ σ2, i.e. for potential (constant) over- or underdispersion. Note here that the main difference to the over- and underdispersion models from the two preceding sections is that there each observation obtains its own variance via Var(Yijk|xik,xjk)=φˆ·λijk , where in the Gaussian response model all observations have the same variance σˆ2 . On our World Cup 2011 – 2017 data, we obtain σˆ2=20.13 , which compared to the average number of goals y¯=27.33 indicates a certain amount of (constant) underdispersion.

We also want to point out here that in order to be able to simulate a precise match result from the model’s distribution (and then, successively, to calculate probabilities for the three match results win, draw or loss), we round results to the next natural number. In general, the Lasso-regularized Gaussian response model will again be fitted using the function cv.glmnet from the R-package glmnet based on the linear predictor ηijk defined in equation (1).

3.5Increase model sparsity

Note that in addition to the conventional Lasso solution minimizing the 10-fold CV error, a second, sparser solution could be used. Here, the optimal value for the tuning parameter ξ is chosen by a different strategy: instead of choosing the model with the minimal CV error the most restrictive model is chosen which is within one standard error of the minimum of the CV error. While it is directly provided by the cv.glmnet function from the glmnet package, for the cv.glmregNB function it had to be calculated manually. In the following section, where all the different models from above are compared, for each model class also this sparser solution is calculated and included in the comparison.

3.6Comparing methods

The four different approaches introduced in Sections 3.1 - 3.4 are now compared with regard to their predictive performance. For this purpose, we apply the following general procedure to the World Cup 2011 – 2017 data which had already been applied to soccer World Cup data in Groll et al. (2019):

  • 1. Form a training data set containing three out of four World Cups.

  • 2. Fit each of the methods to the training data.

  • 3. Predict the left-out World Cup using each of the prediction methods.

  • 4. Iterate steps 1-3 such that each World Cup is once the left-out one.

  • 5. Compare predicted and real outcomes for all prediction methods.

This procedure ensures that each match from the total data set is once part of the test data and we obtain out-of-sample predictions for all matches. In step 5, several different performance measures for the quality of the predictions are investigated.

Let y˜i{1,2,3} be the true ordinal match outcomes for all i = 1, …, N matches from the four considered World Cups. Additionally, let πˆ1i,πˆ2i,πˆ3i,i=1,,N , be the predicted probabilities for the match outcomes obtained by one of the different methods introduced in Sections 3.1 - 3.4. Further, let G1i and G2i denote the random variables representing the number of goals scored by two competing teams in match i. Then, the probabilities πˆ1i=P(G1i>G2i),πˆ2i=P(G1i=G2i) and πˆ3i=P(G1i<G2i) can be computed/simulated based on the respective underlying (conditionally) independent response distributions F1i, F2i with G1i ∼ F1i and G2i ∼ F2i. The two distributions F1i, F2i depend on the corresponding linear predictors ηijk and ηjik from equation (1).

Based on these predicted probabilities, following Groll et al. (2019) we use three different performance measures to compare the predictive power of the methods:

  • 1 the multinomial likelihood, which for a single match outcome is defined as πˆ1iδ1y˜iπˆ2iδ2y˜iπˆ3iδ3y˜i , with δry˜i denoting Kronecker’s delta. It reflects the probability of a correct prediction. Hence, a large value reflects a good fit.

  • 2 the classification rate, based on the indicator functions 1(y˜i=argmaxr{1,2,3}(πˆri)) , indicating whether match i was correctly classified. Again, a large value of the classification rate reflects a good fit.

  • 3 the rank probability score (RPS) which, in contrast to both measures introduced above, explicitly accounts for the ordinal structure of the responses. For our purpose, it can be defined as 13-1r=13-1(l=1r(πˆli-δly˜i))2 . As the RPS is an error measure, here a low value represents a good fit.

Odds provided by bookmakers serve as a natural benchmark for these predictive performance measures. For this purpose, we collected the so-called “three-way” odds for (almost) all matches of the IHF World Cups 2011 – 20172. By taking the three quantities π˜ri=1/oddsri,r{1,2,3} , of a match i and by normalizing with ci:=r=13π˜ri in order to adjust for the bookmaker’s margins, the odds can be directly transformed into probabilities using πˆri=π˜ri/ci 3.

As we later want to predict both winning probabilities for all teams and the whole tournament course for the IHF World Cup 2019, we are also interested in the performance of the regarded methods with respect to the prediction of the exact number of goals. In order to identify the teams that qualify during both group stages, the precise final group standings need to be determined. To be able to do so, the precise results of the matches in the group stage play a crucial role4.

For this reason, we also evaluate the different regression models’ performances with regard to the quadratic error between the observed and predicted number of goals for each match and each team, as well as between the observed and predicted goal difference. Let now yijk, for i, j = 1, …, n and k ∈ {2011, 2013, 2015, 2017}, denote the observed numbers of goals scored by team i against team j in tournament k and yˆijk a corresponding predicted value, obtained by one of the models from Sections 3.1 - 3.4. Then we calculate the two quadratic errors (yijk-yˆijk)2 and ((yijk-yjik)-(yˆijk-yˆjik))2 for all N matches of the four IHF World Cups 2011 – 2017. Finally, per method we calculate (mean) quadratic errors.

Fig. 1

Left: 10-fold CV deviance for Gaussian response model on IHF World Cup data 2011 - 2017; Right: Coefficient paths vs. (logarithmized) penalty parameter ξ; optimal value of the penalty parameter ξ shown by vertical line.

Left: 10-fold CV deviance for Gaussian response model on IHF World Cup data 2011 - 2017; Right: Coefficient paths vs. (logarithmized) penalty parameter ξ; optimal value of the penalty parameter ξ shown by vertical line.

Table 3 displays the results for these five performance measures for the models introduced in Sections 3.1 - 3.4 as well as for the bookmakers, averaged over 334 matches from the four IHF World Cups 2011 – 2017. While the bookmakers serve as a benchmark and yield the best results with respect to all three-way outcome criteria, the second-best method’s results are highlighted in bold text. It turns out that the Poisson and the underdispersed Poisson model yield very good results with respect to the classification rate, while the Gaussian response model is (in some cases clearly) the best performer regarding all other criteria. As no overdispersion (and, actually, underdispersion) is found in the data, the negative binomial model’s results are almost indistinguishable from those of the (conventional) Poisson model. The more sparse Lasso estimators introduced in Section 3.5 perform substantially worse in terms of prediction accuracy compared to the conventional Lasso solution.

Table 3

Comparison of the different methods for ordinal match outcomes; the second-best method’s results are highlighted in bold text.

MultinomialClass. RateRPSGoalsGoal Difference
Pois0.62710.76650.154622.494439.1713
Pois (λ1se)0.59520.73650.162722.575939.8042
underdis. Pois0.64090.76650.152622.494439.1713
underdis. Pois (λ1se)0.60470.73350.159822.575939.8042
NB0.62850.75750.154622.483639.2347
NB (λ1se)0.60240.74550.159222.332038.6094
Gauss0.64130.75750.151222.060338.0023
Gauss (λ1se)0.60550.73650.159822.589439.7949
Odds0.66880.81140.1256--

Based on these results, we chose the regularized Gaussian response model with constant (and rather low) variance as our final model and shall use it in the next section to simulate the IHF World Cup 2019.

4Prediction of the IHF World Cup 2019

Now we apply the best-performing model from Section 3, namely the regularized Gaussian response model with constant underdispersion, to the full World Cup 2011 – 2017 training data and will then use it to calculate winning probabilities for the World Cup 2019. For this purpose, the covariate information from Section 2 has to be collected for all teams participating at the 2019 World Cup.

It has to be stated that at the time this analysis has been performed, namely at the first tournament day (January 10, 2019) right before the start of the tournament, the teams of Bahrein and Sweden had listed squads consisting of 15 players only and there will probably be one more player moving up soon. Hence, for those two teams the covariates corresponding to natural-numbered team structure variables (such as, e.g., the number of legionnaires) have been normalized to be comparable to 16-player squads by multiplying them with the factor 16/15. Another special case concerns the team of Korea. As this team is formed by a selection of players from both South and North Korea, the federation was given the special approval to nominate 20 players. As it actually might be an advantage to have a larger squad we abstained here from normalizing the covariate values from the Korean team.

The optimal tuning parameter ξ of the L1-penalized Gaussian response model, which minimizes the deviance shown in Fig. 1 (left), leads to a model with 16 (out of possibly 22) regression coefficients different from zero. The paths illustrated in Fig. 1 (right) show that three covariates enter the model rather early. These are the Rank, the Height and the Odds, which seem to be rather important when determining the score in a handball World Cup match. The corresponding fixed effects estimates for the (scaled) covariates are shown in Table 4.

Table 4

Estimates of the covariate effects for the IHF World Cups 2011 – 2017.

VariableEstimate
Age-0.3606
Height0.9542
Rank-1.6366
Trainer.age0.1995
Trainer.tenure0.0000
Legionnairs0.5747
CL.final4-0.0983
EHF.final4-0.2640
max.teammates0.7216
sec.max.teammates0.0000
GDP0.0000
Odds1.1985
Population-0.1607
Age.ma-0.3405
Height.sd-0.6672
Host-0.0801
Host.oppo-0.4673
Trainer.nat-0.2912
Trainer.nat.oppo0.1954
Continent0.0389
Continent.oppo0.0000
Confed0.6293
Confed.oppo0.0000

Based on the estimates from Table 4 and the covariates of all teams for the IHF World Cup 2019, we can now simulate all matches from the preliminary round. Next, we can simulate all resulting matches in the main round and determine those teams that reach the semi-finals and, finally, those two teams that reach the final and the World Champion. We repeat the simulation of the whole tournament 100,000 times. This way, for each of the 24 participating teams probabilities to reach the different tournament stages and, finally, to win the tournament are obtained.

4.1Probabilities for IHF World Cup 2019 Winner

For each match in the World Cup 2019, the model can be used to predict an expected number of goals for both teams. Given the expected number of goals, a real result is drawn by assuming two (conditionally) independent Gaussian distributions for both scores, which are then rounded to the closest natural number. Based on these results, all 60 matches from the preliminary round can be simulated and final group standings can be calculated. Due to the fact that real results are simulated, we can precisely follow the official IHF rules when determining the final group standings (see footnote 4). This enables us to determine the matches in the main round and we can continue by simulating those matches. Again, if the final group standings are calculated, the semi-final is determined. Next, the semi-final can be simulated and the final is determined. In the case of draws in “knockout” matches, we simulate extra-time by a second simulated result. However, here we multiply the expected number of goals by the factor 1/6 to account for the shorter time to score (10 min instead of 60 min). In the case of a further draw in the first extra-time, we repeat this procedure. If the second extra time still ends in a draw we simulate the penalty shootout by a (virtual) coin flip.

Following this strategy, a whole tournament run can be simulated, which we repeat 100,000 times. Based on these simulations, for each of the 24 participating teams probabilities to reach (at least) the main round or the given final rank and, finally, to win the tournament are obtained. These are summarized in Table 5 together with the winning probabilities based on the ODDSET odds for comparison.

Table 5

Estimated probabilities (in %) for reaching (at least) the main round or the given final ranks in the IHF World Cup 2019 for all 24 teams based on 100,000 simulation runs of the IHF World Cup together with winning probabilities based on the ODDSET odds.

Main8th7th6th5th4th3rd2ndChampionOddset
1.jsa-6-jsa200384-g003.jpgDEN99.498.096.893.990.683.575.754.937.225.4
2.jsa-6-jsa200384-g004.jpgFRA89.180.177.970.365.854.747.333.519.423.7
3.jsa-6-jsa200384-g005.jpgGER80.265.661.952.846.936.729.119.39.211.8
4.jsa-6-jsa200384-g006.jpgESP96.075.169.958.450.939.230.219.99.014.2
5.jsa-6-jsa200384-g007.jpgHUN95.583.674.665.652.541.127.517.56.41.8
6.jsa-6-jsa200384-g008.jpgSWE93.878.867.858.344.333.721.313.14.45.1
7.jsa-6-jsa200384-g009.jpgRUS69.050.345.737.131.223.517.010.64.30.7
8.jsa-6-jsa200384-g010.jpgNOR93.578.667.257.943.833.420.712.94.17.9
9.jsa-6-jsa200384-g011.jpgCRO91.858.551.339.632.223.715.99.73.55.1
10.jsa-6-jsa200384-g012.jpgSRB52.832.928.221.917.312.78.14.81.60.5
11.jsa-6-jsa200384-g013.jpgICE80.232.125.017.912.68.94.72.60.70.4
12.jsa-6-jsa200384-g014.jpgAUT53.717.89.47.43.52.60.80.40.00.1
13.jsa-6-jsa200384-g015.jpgTUN50.715.88.26.42.92.20.50.30.00.2
14.jsa-6-jsa200384-g016.jpgEGY46.514.57.66.02.72.10.60.30.00.2
15.jsa-6-jsa200384-g017.jpgARG28.46.52.92.40.90.70.20.10.00.1
16.jsa-6-jsa200384-g018.jpgKAT24.75.02.21.70.70.50.10.00.01.1
17.jsa-6-jsa200384-g019.jpgMAC21.42.51.30.80.40.30.10.00.00.7
18.jsa-6-jsa200384-g020.jpgBRA7.92.01.30.90.50.40.10.00.00.6
19.jsa-6-jsa200384-g021.jpgJPN10.50.70.30.20.10.10.00.00.00.1
20.jsa-6-jsa200384-g022.jpgANG11.01.40.40.40.10.10.00.00.00.1
21.jsa-6-jsa200384-g023.jpgKOR1.10.10.00.00.00.00.00.00.00.1
22.jsa-6-jsa200384-g024.jpgCHI1.30.00.00.00.00.00.00.00.00.1
23.jsa-6-jsa200384-g025.jpgKSA1.40.00.00.00.00.00.00.00.00.1
24.jsa-6-jsa200384-g026.jpgBAH0.20.00.00.00.00.00.00.00.00.1

Apparently, the resulting winning probabilities show some discrepancies from the probabilities based on the bookmaker’s odds. Though the upper and lower half of the teams according to our calculated probabilities seem to coincide quite well with the overall ranking according to the bookmaker’s odds, for single teams from the upper half, in particular, Denmark, Spain and Hungary, the differences between our approach and the bookmaker are substantial. Based on our model, Denmark is the clear favorite for becoming IHF World Champion 2019. These discrepancies could be mostly explained by the fact that the Lasso coefficient estimates from Table 4 include several other covariate effects beside the bookmaker’s odds.

4.2Group rankings

Finally, based on the 100,000 simulations, we also provide for each team the probability to reach the main round. The results together with the corresponding probabilities are presented in Table 6.

Table 6

Probabilities for all teams to reach the main round at the IHF World Cup 2019 based on 100,000 simulation runs.

jsa-6-jsa200384-g027.jpg

Obviously, there are large differences with respect to the groups’ balances. While the model forecasts for example Spain and Croatia in Group B, Denmark and Norway in Group C and Hungary and Sweden in Group D with probabilities clearly larger than 90% to reach the second group stage, in Group A France followed by Germany are the main favorites, but with lower probabilities of 89.05% and 80.16%, respectively. Hence, Group A seems to be more volatile.

5Concluding remarks

In this work, we first compared four different regularized regression models for the scores of handball matches with regard to their predictive performances based on all matches from the four previous IHF World Cups 2011 – 2017, namely (over- and underdispersed) Poisson regression models and Gaussian response models.

We chose the Gaussian response model with constant and rather low variance (indicating a tendency of underdispersion) as our final model as the most promising candidate and fitted it to a training data set containing all matches of the four previous IHF World Cups 2011 – 2017. Based on the corresponding estimates, we repeatedly simulated the IHF World Cup 2019 100,000 times. According to these simulations, the teams from Denmark (37.2%) and France (19.4%) turned out to be the top favorites for winning the title, with a clear advantage for Denmark.

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Notes