Just how surprising are the 2018 Russia World Cup’s first-round group-stage games? I collected betting market odds prior to the start of the games and calculated that we would have obtained a 52% profit had we placed a bet on the least likely scenario of each game.
Below is the game-by-game breakdown of our return: ($1 bet on each game)
For a more scientific treatment, let us calculate the forecasting error. Here, I use the Rank Probability Score to take into account the fact that three possible scenarios have ranked order. In other words, the scenario “draw” is closer to the scenario “Country 1 wins” than the scenario “Country 2 wins” is.
For example, betting markets assigned only a probability of 20%-30% to the actual outcomes in both the Peru vs Denmark and the Germany vs Mexico games (respectively “Denmark wins” and “Mexico wins”). But the forecasting errors for the two games are different, because betting markets assigned greater odds to “draws” in the Peru vs Denmark game (40%) than in the Germany vs Mexico game (13%). Thus, the forecasting error for the Germany vs Mexico game is larger.
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