Read this Poisson distribution analysis to predict Brazil vs. Croatia

Read this Poisson distribution analysis to predict Brazil vs. Croatia

By Mark Taylor May 13, 2014

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Bettors should read this Poisson distribution analysis of the 2014 World Cup opening game to help them predict the winner between Brazil and Croatia. The article discusses the differences between using Poisson for a World Cup compared to an annual league competition.

Poisson distribution different for a World Cup

The Poisson distribution is ideally suited to modelling correct scores and ultimately individual match odds for soccer matches. By manipulating simple, readily available data, namely the number of goals scored and goals conceded it enables bettors to assign probabilities to every combination of score lines.

These then can be summed to produce odds for each of the three possible 90 minute outcomes, which can be used to help inform bettors World Cup betting predictions. Read this article about how to calculate Poisson distribution for a match involving sides from the same league.

The 2014 World Cup tournament begins with the host country, Brazil playing Croatia in Group A. A Poisson approach can be used to estimate these game odds and subsequent games, but the process is less straightforward when applied to a World Cup rather than a simple league contest.

The Poisson has well documented systematic biases, but the output also depends greatly on the validity of the inputted expected goal rates of each side and international tournaments can present numerous additional challenges when calculating these goal expectations.

Firstly, the quantity of data is naturally an important feature. Typically a season’s worth of domestic league scoring data, 38 games, will give a more reliable set of odds than simply using a handful of games where streaks can occur. Witness Sunderland’s recent winless and winning sequences that saw them producing results consistent with both title contenders and relegation certainties, separated by barely a month.

To gather an equivalent amount of international data requires that you look back over several years, during which the lineups may have changed markedly. The emergence of a “golden generation” may not be fully reflected in earlier contests.

Next, international matches also range from full bloodied World Cup finals games down to friendly matches, which may involve a degree of squad rotation.

Croatia have played around 40 matches over the last four years, comprising a mixture of European Championship games, World Cup qualifiers and occasional friendlies. Brazil has had a larger diet of friendlies as they qualified directly as the host nation in the 2014 World Cup.

Finally, goal expectation values are also dependent upon venue and Brazil will be the home side in the opening game. However, there is some evidence that the home/away dynamic in international football in South America differs from that in Europe.

World Cup European qualifying games have traditionally seen the home side win around 45% of the matches, with a home field advantage in the region of 0.4 goals. However these figures slipped to below 42% for home wins and below 0.2 goals respectively in the current campaign.

By contrast, home winning percentage in the Conmebol qualifiers has been consistently higher at 57%. Even if we remove the three high altitude countries which play their home fixtures in excess of 2,500 metres above sea level, Bolivia, Ecuador and Columbia, home field still shows elevated levels compared to their counterparts in Europe. 54% of home sides won in the recent qualifying tournament in South American, even without matches involving the high altitude trio.

Therefore, Croatia may have attained their away record in a confed where away sides prosper relative to South America, while Brazil host in a continent where home sides appear to do better than in Europe.

In producing a goal expectation for both Croatia and Brazil in the opening game of World Cup 2014, we should be aware that all of the above will affect our calculations.

Eliminating friendly matches isn’t really an option for the hosts because they have played such little tournament football outside of the Confederations Cup. We should probably also include friendlies in Croatia’s estimate.

Croatia’s presence in Brazil indicates that they had a relatively successful qualifying campaign. They also qualified for Euro 2012 and if we stack their statistics with only these results, we may be modelling talent and good luck, especially against a team in Brazil that didn’t have the opportunity to inherit guaranteed positive results by a need to qualify.

Influence of HFA on Poisson analysis for the World Cup

The uncertainty surrounding the balance of home field advantage in South America can be partly addressed by taking the average goals scored and conceded by both teams at home and away over their last say 40 matches and adjusting those figures more in line with the venue related ratios seen in the host continent.

For ease of calculation, we won’t weight more recent games more heavily.

Of the previous 40 matches Croatia has played, a third were friendlies and the remainder were played as qualifiers for Euros or World Cups. Three were on neutral venues in Euro 2012. Overall, they have scored 1.575 goals per game (gpg) and conceded 0.925 gpg.

Home and away matches are virtually equal in number and opponents range from Spain down to Malta. So these figures may be considered as representative of Croatia’s performance on broadly neutral ground against average opponents, expressed in goals.

Brazil scored 2.55 and allowed 0.725 gpg home, away and occasionally on neutral soil over their previous 40 matches.

A typical international contest in South America, excluding games involving countries at altitude would see the home team scoring 1.65 goals per game and 1.06 gpg conceded, so a contest between average teams at a neutral ground would see each side, on average claim 1.355 goals per game.

Putting these figures together, Croatia scored 1.575/1.355 or 116% of an average South American matchup. Brazil conceded 0.725/1.355 or 54% of average and finally, visiting sides, which Croatia will be, score, 1.06/1.355 or 78% of average.

Multiplying 1.16 by 0.54 by 0.78 and finally by the average goals per game for an average side at a neutral venue, or 1.355, gives an estimate that Croatia might be expected to score 0.66 goals against Brazil on opening night.

A similar calculation for hosts, Brazil makes them likely to score an average of 2.12 goals in return.

Match Outcome

Poisson Probability

Odds Implied Probability

Brazil Win

0.72

75.53%

Draw

0.18

18.59%

Croatia Win

0.10

8.26%

If we put these figures into a Poisson calculator from the earlier link, the win/draw and loss figures shown in the table above are generated.

Brazil is currently 1.324* to win the game, with an implied probability of 75.53% and Croatia at 12.110* or implied probability of 8.26%. Therefore, the European side offer marginal value to spoil the opening day for the host country.

However, it shouldn’t be a surprise that there is one final twist.

European sides win around half of their matches against countries from the remainder of the globe when the World Cup is contested in Europe, but this falls to below 40% in similar contests when the finals are in the Americas. The implication being that a continental advantage also exists in addition to normal home advantage. However looking more recently this data may vary, so read this article on how relevant trends are to predicting the World Cup winner.

Therefore, Brazil, despite only four of their squad currently playing their domestic football at home, could also benefit from this advantage in addition to the benefit of being the host country.

However, it is clear that estimating odds for games that occur once every four years is both a science and an art.

Mark Taylor is a freelance soccer and NFL writer who, along with producing expert content for Pinnacle Sports, also runs his own soccer analytics blog, the Power of Goals.

*Odds subject to change

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