Decisiveness of matches in the WC group stage
Watching the world cup is a complex business. There are too many games at too many odd hours to watch everything and remain gainfully employed, but it can be hard to decide whether to stay up late to watch an obscure CONCACAF side play a European superpower, or crawl out of bed for a showdown between a pair of star strikers and their traffic cones come team-mates.
If quality is all you're after then the answer is obvious, but the most interesting games are those both teams need to win. In a previous post I defined match meaning as
the total change in probability that each team will qualify for the next round based on the result of a single game.
For a knockout match between two evenly matches teams this will be 1: 2x(0.5x0.5 + 0.5x0.5). A knockout where one team is 70% likely to win will be 0.84: 2(0.7x0.3 + 0.3x0.7). For a group stage, the calculation is more complex, so a monte-carlo method was employed:
Meaning = | P(Qual) - (P(Win)xP(Qual|Win) + P(Draw)xP(Qual|Draw) + P(Loss)xP(Qual|Loss)) |
Total meaning being calculated for all four teams in the group, for each game.
Match probabilities were calculated using the Elo Ratings. Historically, draws are normally distributed around the rating difference: ~40% for evenly matched teams, with a standard deviation of 200. The win/loss probabilities are taken from the Elo formula on the site.
The results indicate that the least interesting match will be Brazil vs Cameroon, the home side being near-certainties to qualify, and the latter unlikely to overcome Croatia and Mexico. The most: Croatia vs. Mexico, being a virtual knock-out, followed by Bosnia-Herzegovina vs Nigeria, the two middle sides in a group containing Argentina and Iran. A full list of qualifying probabilities, and predicted match meaning follows:
|Ivory Coast||Japan||14 June||0.431|
|Colombia||Ivory Coast||19 June||0.388|
|Greece||Ivory Coast||24 June||0.402|
|Uruguay||Costa Rica||14 June||0.383|
|Costa Rica||Italy||20 June||0.421|
|Costa Rica||England||24 June||0.402|
|Argentina||Bosnia and Herzegovina||Iran||Nigeria|
|Argentina||Bosnia and Herzegovina||15 June||0.330|
|Bosnia and Herzegovina||Nigeria||21 June||0.440|
|Bosnia and Herzegovina||Iran||25 June||0.407|
|Ghana||United States||16 June||0.333|
|Portugal||United States||22 June||0.378|
|Germany||United States||26 June||0.358|
|Russia||South Korea||17 June||0.390|
|Algeria||South Korea||22 June||0.330|
|Belgium||South Korea||26 June||0.418|
12th June, 2014 22:48:18