The 2018 edition of the FIFA world cup is scheduled to begin next Thursday June 14, with the host nation Russia taking on Saudi Arabia. With some very high profile teams like Brazil, Argentina, Germany, France, Spain, England, and Portugal all contending for the gold medal, just how likely can the host nation Russia win the gold medal?
Just under a week before the kickoff of the 2018 world cup, the host nation Russia is currently ranked 70th, based on the FIFA/Coca-Cola world ranking: https://www.fifa.com/fifa-world-ranking/ranking-table/men/index.html. Based on this very low ranking, it seems very unlikely that the host nation Russia can win the tournament. But just how unlikely? To answer this question, let’s allow previous world cup data to tell us the story.
World cup data for the previous 20 editions was obtained from this website: https://gist.github.com/knwin/ea1fffcda6c95375268c. Code was written in python to analyze the data. For the previous 20 editions of the world cup, the host nation has won the gold medal 6 out of 20 times as shown on this table:
The last time the host country won the tournament was in 1998, which is 20 years ago. In the history of the FIFA world cup, only in 6 out of the 20 editions has the host nation won the tournament. This translates to a 30% chance of the host nation winning the tournament. The 30% probability of the host nation winning the gold medal, can be treated approximately as a random variable. Using the Binomial probability distribution with a success probability of p = 0.3 and a sample size of N = 20, the calculated standard deviation is 0.1 or 10%. The 95% confidence interval for the expected 30% probability is accordingly 30% plus and minus 20%. Such a large sample variability is expected for a small sample with size N = 20.
Based on this simple analysis, we can conclude with 95% confidence that the probability of Russia winning the world cup is in the range 10% to 50%. A Bayesian hierarchical probability model could be constructed, that takes into account not only the results of previous world cup data, but also the current ranking of the host nation. With a current ranking of 70, we could conclude that the chance of Russia to win the world cup should be towards the minimum of the 95% confidence interval, which is approximately 10% chance.
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