The 2014 World Cup has gotten off to a high-scoring start. Through the first week of the tournament, an average of 2.9 goals have been scored per game, the highest since 1970. And if that average climbs to over 3 goals per game, this’ll be the highest scoring World Cup since 1958!
So is this year’s World Cup actually bucking a trend of the low scoring tournaments that came before it, or can we simply attribute it to random variation? Let’s use a data analysis to find out!
Determining a Trend
I went to FIFA’s website and collected the goals per game in every world cup. Now that we have the data, let’s start by looking at a time series plot.
The time series plot shows that this year isn’t too much of an outlier. Sure, it’s the most goals per game since 1970, but it’s hardly blowing the other years out of the water. The 1982 World Cup had 2.8 goals per game, and both 1994 and 1998 had 2.7 goals per game. When compared to those years, 2.9 goals per game in this year’s World Cup doesn’t sound all that incredible.
Now, if the average returned to pre-1962 levels, that would be a lot of goals. The first six World Cups were significantly higher scoring than the game today. Because there was a clear shift in the mean before 1962, I’ll to make another time series plot looking at only the more recent World Cups that have had a similar amount of goals scored per game.
Now that we’ve removed the first six World Cups, we’re able to look at the plot on a smaller scale. And it does appear that goals per game was decreasing throughout the years before 2014. We can use Minitab’s Trend Analysis to see if this is, in fact, true.
There is a downward trend in the number of goals per game from 1962 to 2010. Instead of including 2014, I used the model to forecast what we could expect for this year using the data from the previous years. It gave us a forecast of about 2.3 goals per game, which is the same as the previous two years.
So now we’ve established that the 2.9 goals per game is bucking a downward trend. But is the difference between the forecast (2.3) and the observation (2.9) just random noise, or is there some factor in this year’s World Cup that is causing more goals to be scored?
Determining a prediction interval
The trend analysis above simply uses a regression analysis with the average number of goals per game as the response and the order of the observations (1, 2, 3, etc….) as the predictor. That means we’d get the same result if we did a fitted line plot using the order of the data instead of the year for the X axis.
And now we can use this regression model to give us a prediction interval for the 14th observation, which would correspond to the year 2014 in our trend analysis above.
Just like the trend analysis, we see that we would expect there to be 2.3 goals per game. And the prediction interval indicates that we can be 95% confident that the average number of goals for 2014 will be between 1.86 and 2.75 goals per game. Hey wait...2.9 goals per game is outside this interval. Could 2014 be special after all?
NOTE: I used the prediction interval instead of the confidence interval because we’re dealing with a single observation (2014) as opposed the average of multiple years. If you want more information about the difference between a confidence and prediction interval, I suggest reading this blog post.
Considering the Sample Size
Before we go concluding that scoring is on an upward trend in the World Cup, we need to remember the sample size. Our observation for 2014 is only for a eight days' worth of games, whereas the other data values come from the entire tournament. Through the first 4 days of this year's World Cup, the average goals per game was 3.5. For the next 4 the average was 2.4. The abundance of high-scoring games could have been simply random variation in a small sample of the first few games, and unlikely to continue.
But we won’t know for sure until we get some more data! So let’s wait two weeks and come back to see how the tournament is going. Until then, I leave you with this...