Ok, I admit it – I’m a stats nerd. I love nothing better than perusing the league tables in the back pages of the Sunday papers, so imagine my delight when Prozone offered me the chance to analyse their data from the 48 games of the Group Stages of the 2010 World Cup.

In a previous article in the New Scientist prior to the start of the World Cup (Haake and Choppin (2010), June 5, 35-37) and on this site (“*Does altitude affect football tactics*“) we suggested that altitude might have an effect on tactics, and in particular on shots from inside and outside the box. The only data available at that time however was for the 8 World Cup qualifying games for Mexico – including those at Mexico City at 2,200 m.

*The results showed that the number of shots from outside the box increased with altitude at the expense of those from inside the box. The question is, has the same happened at the World Cup?*

Well, let’s first consider the total number of shots; in the group stages there were (surprisingly) a total of 1302 shots of which 624 were on target and 678 were off target. There were also more shots in general from outside the box from inside (718 compared to 584). While the number of on- or off-target shots inside the box were the same, there were slightly more shots off target from outside the box. This is as might be expected with longer shots being less likely to hit the goal.

So far so good. But what about the effect of altitude? Figure 2 shows the total number of shots per game (i.e. both teams together) versus the altitude of the venue in which the game was played. What do we conclude from this diagram? That there are around 27 to 28 shots per game, of which 14-16 shots per game from outside the area compared to around 12 shots per game from inside the area. Another thing that is self-evident is that there is a lot of scatter and that there isn’t really much of an altitude effect.

Figure 3 shows a similar graph for the shots on target and there is now just possibly a trend for more shots per game at higher altitudes, particularly from outside the box. Of course, this could just be due to scatter in the data, but we will press on and see if there is an effect on the most important parameter of all – the number of goals.

### The effect of altitude

The trend line in Figure 4 implies that the number of goals per game increases from around 1.75 per game at sea level to around 2.25 at 1,700 m. The number of goals from inside the area is, on average, around 1.75 per game at all altitudes so the increase appears to be largely due to goals from outside the box.

Let’s think about what we’re saying here – there are more goals from inside the area; this makes sense (to me at least) that the success from close range should be higher. What about more goals from outside the area? The main effect of altitude is the reduction in air density – this leads in turn to reduced aerodynamic forces including those due to spin which makes the ball curve in flight. At altitude, therefore, the ball tends to fly straighter so that if your aim is true, then you are more likely to get a shot on target. Also, since the drag on the ball is lower, the ball tends to fly marginally faster than at sea level and the ball might be more likely to deceive the goalkeeper.

Am I convinced by this? Not absolutely – for a start if I run the data through complex statistical packages they say that there isn’t enough data to be sure of its significance. Secondly, there are so many other things that could affect the data – the random allocation of high shooting teams at a particular venue, individuals with a penchant for shots outside the box etc.. One thing I have noticed is the appalling state of some of the pitches which could have influenced where the players shoot from.

For now though, I’ll make a prediction for the World Cup final: since the game is being played in Johannesburg at around 1,700 m I would expect around 14 shots on target, and around 2 to 3 goals. This doesn’t tell you the score of course and with gut instinct I’m going for 2-1. But neither analysis nor gut instinct will tell me who will win.

Perhaps I’d better just ask Paul the octopus.