Mohamed Salah, winner of the Golden Boot, holds the record for ‘Most goals scored in a 38-game Premier League season for 2017/18’ at 32 goals. This is just 2 goals away from the all-time record.

With 36 games and 32 goals, this gives Salah a very impressive goal-to-game ratio of 0.89, the highest ratio of the 50 top scorers. So his record clearly sets him apart as the the best scorer, right?

 

 

 

 

Here are the top 10 Premier League goal-scorers that season:

Rank	Last Name	First Name	Team	Games Played	Games Started	Minutes Played	Goals	Assists	Shots on Goal	Total Shots
1	Salah	Mohamed	LIV	36	34	2921	32	10	67	143
2	Kane	Harry	TOT	37	35	3083	30	2	76	184
3	Aguero	Sergio	MCI	25	22	1969	21	6	42	95
4	Vardy	Jamie	LEI	37	37	3255	20	1	35	69
5	Sterling	Raheem	MCI	33	29	2592	18	11	36	89
6	Lukaku	Romelu	MUN	34	33	2869	16	7	43	86
7	Firmino	Roberto	LIV	37	32	2777	15	7	38	84
8	Lacazette	A	ARS	32	26	2212	14	4	35	68
9	Gabriel	Jesus	MCI	29	19	1671	13	3	31	53
10	Hazard	Eden	CHE	34	28	2433	12	4	37	71

In this analysis, I took raw data from the top 50 goal scorers of that season taken from  Fox Sports. I cleaned the data and it is available in a notepad file here. I then imported this into SPSS to analyse.

 

Salah primarily plays on the right wing, this position allows him to cut into the centre where he can shoot on goal with his speed and dribbling skills or play quick passes to his capable teammates. Salah has praised his manager Jürgen Klopp for letting him in more central positions, saying “I play closer to the goal than any club before.” He has even been nicknamed the “Egyptian Messi” by Italian media.

Salah’s accolades include:

• PFA Players’ Player of the Year: 2017–18
• FWA Footballer of the Year: 2017–18
• Premier League Golden Boot: 2017–18
• Premier League Player of the Season: 2017–18
• PFA Team of the Year: 2017–18 Premier League
• Liverpool F.C. Player of the Season: 2017–18
• Liverpool F.C. Players’ Player of the Season: 2017–18

These are all great achievements and qualities and I don’t deny any of them. However I don’t feel that the data show a player as consistently remarkable as the headlines would suggest.

 

Simple Stats

For instance, when looking at his total shots in the top 50 list, that number is considerably larger than most other players. And when you take his goal to shot ratio you get 0.22, meaning he scores 0.22 goals per shot taken on average. This puts him at #9 in this list of the top 50 goal scorers.

Then taking his ratio for goals to shots on goal, this gives 0.48, so nearly half of his on-target shots end up as a goal. This might seem impressive, but this paces him as #12 on the list when this is the deciding variable. Even when dividing shots on goal by total shots puts him at #13 for his shot accuracy.

 

Pearson’s
Correlation = 0.776

 

 

 

 

 

Pearson’s
Correlation = 0.856

 

 

 

We can see from the scatter plots that the records by Kane and Salah, the extreme cases in these graphs, are simply a continuation of this trend.

It’s still hard to break through and make the opportunity to take these shots, but other players seem to be more precise in their use of their shots. I think this shows that there are many players that display a more consistent ability to turn opportunities into goals.

It’s possible that Salah has this accolade of top scorer more due to the amount of scoring opportunities his team have allowed for him rather than because of his superior talent.

I would argue that Salah is not an outlier, but rather an extreme value of a predictable trend.

 

 

 

A Deeper Look

I then used the data for ‘Goals to Shots-on-Goal’ data to model a linear regression.

This gave the formula for expected number of goals scored from our independent variable, SOG (Shots-on-Goal).

exp(Goals) = −0.239 + 0.389 ∗ SOG

When layered on our graph we get this:

We can hold this to be appropriate given our regression test assumptions are valid:

• Normality – the residuals should be normally distributed.
• Homogeneity of variance (homoscedasticity) – the error variance should be constant.
• Independence – the errors associated with one observation are not correlated with the errors of any other observation.

 

Regression residuals (the
difference between the
predicted and observed
values) are normally
distributed above and
below the line.

 

 

 

Variance of errors
remain constant, does
not grow or shrink.

 

 

  

 

Independent as errors
show a random patter
about the zero line.

 

 

When we look back at the graph with the regression line; Salah, with 32 goals, is above the line. Therefore, he has scored more goals than the model has predicted given the amount of shots-on-goal he has taken. However, he is not the furthest above the line given his position.

Salah, having taken 67 SOG (Shots-on-Goal), should have scored 25.824 goals by this prediction. This means he scored 23.9% more goals than expected.

Sergio Aguero, with 21 goals and 42 SOG, was expected to score 16.1 goals, outperforming this model by 30.4%.

Wayne Rooney took only 17 shots-on-goal and amassed 10 goals, scoring 56.9% more than the expected number of only 6.37 goals. Almost double what Salah beat the model by. This may seem like a sample with too few goals to be significant. So I give you:

Jamie Vardy, with 20 goals to his name, taking 35 SOG out-scored his expected value by a very impressive 53.8%.

 

 

I wanted to show you that the raw number of goals a player scores in a season is just one very small measure of overall performance. It is a much more accessible, and easier to understand statistic, but there are so many ways to quantify every little aspect of how a player or team have played. And what I have done here is only a small subset of this.

I would urge you to do your own research and investigate statistical claims, because there is always much more beneath the surface headlines.