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#### How were your predictions?

By Vince Ruscello

A few weeks ago, I made some predictions about the World Cup scores based on an analysis of past tournaments.

I thought it only appropriate to report on the accuracy of my prognostications.

(The following analyses were conducted prior to the final weekend’s matches due to publication deadlines.)

“*In the last six World Cup tournaments, from Italy in 1990 to South Africa in 2010, the goals/match has followed a near-perfect Poisson distribution – the average goals/match is 2.4*.”

This year in Brazil, the average goals/match is less than 2.6. A 1-sample Poisson rate test shows that this is well within the confidence interval around a true rate of 2.4.

*“(T)he probability of 90-minutes of play ending in a 0-0 tie is around 9%.”*

In Brazil, 10 games ended in a 0-0 tie versus the 6 predicted. A 1-proportion test again shows this is within the margin of error.

*“(T)he probability of five or more goals scored in regulation play is also less than 10%, giving credence to some soccer critics’ complaints about the lack of action.”*

Eight games ended with 5 or more goals in this year’s World Cup – very close to the predicted value.

*“The mean [time between goals] is estimated by dividing the game time, 90 minutes, by the average goals/game, 2.4. Result: 37.5 minutes.” *

*and*

* “Goodness-of-Fit tests confirm that the Exponential distribution is a good model of the shape of the inter-goal times.”*

The average inter-goal time for the 2014 World Cup is 35.0 minutes, very close to the prediction, and the exponential distribution does, in fact, model the distribution of inter-goal times in this year’s event. (See the Probability Plot Below)

*“(T)he probability of the final score remaining the same as the half-time score is only 30%.”*

So far, 15/61 matches have remained unchanged after halftime, and my prediction reputation is still untarnished.

*“(T)here is still a 25% chance that the score will change in the last ten minutes. But with five minutes to go, there is only a little more than 10% chance of a score change.” *

I missed these two completely! An astounding twenty-eight out of sixty-one matches, more than 45%, had a score in the last ten minutes – twelve of those changed the outcome of the match. Fifteen matches, almost 25%, had a score in the last five minutes of regulation time, nine of which changed the outcome.

My predictions assumed equal probabilities of scoring throughout the full time of play. This result shows that scoring probability is not uniform throughout the 90-minute match, that is, the intensity of play probably increases as the end approaches, much like the NBA.

So, I analyzed all of the goal times from all 424 matches since 1990 (Italy) with Binary Logistic Regression. The result shows that scoring probability does, indeed, increase as the game progresses. The graph below shows the results of the analysis. The spots are the actual counts of goals that occurred in the corresponding minutes of each match. The Red line is the regression fit. The scoring probability in the 90^{th} minute is almost double the probability in the first minute. There is, therefore, good reason to watch all the way to the end, especially if the game is close.

So, as the World Cup 2014 ends, we can reasonably conclude that, though the participants & winners may change, the average scoring pattern of the matches has remained consistent for more than 20 years. I also learned this week that scoring rate is not constant throughout the 90 minutes of play, and that exciting changes can occur very quickly towards the end of the match.

Extrapolations into the future are risky, but I’ll go out on a limb and say that in 2018, the results will be about the same. And, even though it is early, I will predict a 50% chance of higher than average scoring in Russia…

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