Height (dis)advantage

There has been a lot of talk about how Liverpool can't play against a tall striker. The perfect example would be in the game against Aston Villa, where Christian Benteke made a wonderful performance. But, is this true? Can Liverpool really not win against a tall striker?

I decided to investigate this, this time thanking the Reddit Match Threads and Squawka. After searching the height, in metres, of the tallest forward we played against, I had to see if Liverpool won/drew/loss the game and put this information in a chart.

Disclaimer: Liverpool's home game against Stoke City on October 7th 2012 is not in the chart for aesthetic reasons. Because of Peter Crouch immense height (2.01 m) it would make the chart less readable; the game ended a 0-0 draw.

As you can see in this chart Liverpool has a win and a draw, against almost all opponent sizes. The only result that are not greatly distributed are the losses, the majority of them being against opponent whose size is 1.86 m (Dempsey & van Persie twice).

The results against the smallest heights are 1 win, 1 draw and 1 loss. The results against the tallest heights (not including Stoke's draw) are 1 win and 1 draw.

A good way to measure if their is a significant difference in height between the results is the average.
The average of all the losses is 1.873 m, which is very close to the wins, 1.877 m. Then we have the average of all the draws, 1.894 m, but if we don't include Peter Crouch's outlier it would go down to 1.880 m.

Impossible

Then this means that on average we draw against the tallest attackers, and we (on average) lose against the smallest ones. Leaving all the winning against the middle teams.

Another way of measuring their significance is using a t-test. After analysing the data, it showed that the means of all three results are the same, with a p-value of 0.36 between the loss-draw, a 0.41 between win-draw and a 0.81 between win-loss.

What does this mean?

It's actually saying that there is statistically no difference between the results. Refuting the idea posted on the start of this article. Meaning Liverpool has no type of disadvantage and they could win all the games regardless of the opponent's height.

**Update**

If the same forwards start in the upcoming 13 league games (except Ba for Chelsea), we're going to play 4 teams that have attackers smaller that 1.86 m, 4 teams whose forwards are between 1.86-1.88 m and 5 teams with strikers taller than 1.88 m.