Simple one this – firstly let’s take the last twelve Premiership seasons and look at the how the number of goals scored and allowed by a team are distributed.
So the distribution of goals conceded somewhat resembles a normal distribution – with an equal mean and median (50). The distribution of goals scored is more interesting though. For one thing it really doesn’t look all that ‘normal’ in shape – there’s a lot more weighting to the low side of the mean than the high. In fact the median of the group is 47 goals, ~6% fewer than the mean. The second thing to notice is that the spread appears naturally wider for goals scored than allowed – and if we look at the most ‘extreme’ seasons in terms of goals scored and allowed then it appears this observation may be true:
The real way to measure the distribution though is via standard deviation. So lets take that group of 240 teams and calculate the standard deviation for the number of goals, shots on target, and total shots that they score and concede.
So the observations from the plot are correct – the spread is wider in terms of attacking events than defensive ones. One thing that sticks out here is that the gap between STDEV of goals F/A is ~10% of their mean value, as opposed to ~5% and ~4% for ST and TS – it’d be great if someone who knows statistics better than I could explain whether that tells us something about the game or its because STDEV, by its nature, takes square roots. I think it’s the former but I’m not going to comment on it until I’m sure.
Anyway this, I think, is the conclusion we’d draw solely by looking at the transfer market where, in general, strikers cost more money than defenders. It seems intuitive to me that you’d spend more money on players who can have the largest effect on your team and, if there’s a larger variation in the number of goals scored, then that’s where your resources should be being directed.