Shooting the breeze

Who will win the Premier League title this season? While Leicester City and Tottenham Hotspur have their merits, the bookmakers and public analytics models point to a two-horse race between Manchester City and Arsenal.

From an analytics perspective, this is where things get interesting, as depending on your metric of choice, the picture painted of each team is quite different.

As discussed on the recent StatsBomb podcast, Manchester City are heavily favoured by ‘traditional’ shot metrics, as well as by combined team ratings composed of multiple shooting statistics (a method pioneered by James Grayson). Of particular concern for Arsenal are their poor shot-on-target numbers.

However, if we look at expected goals based on all shots taken and conceded, then Arsenal lead the way: Michael Caley has them with an expected goal difference per game of 0.98, while City lie second on 0.83. My own figures in open-play have Arsenal ahead but by a narrower margin (0.69 vs 0.65); Arsenal have a significant edge in terms of ‘big chances’, which I don’t include in my model, whereas Michael does include them. Turning to my non-shots based expected goal model, Arsenal’s edge is extended (0.66 vs 0.53). Finally, Paul Riley’s expected goal model favours City over Arsenal (0.88 vs 0.69), although Spurs are actually rated higher than both. Paul’s model considers shots on target only, which largely explains the contrast with other expected goal models.

Overall, City are rated quite strongly across the board, while Arsenal’s level is more mixed. The above isn’t an exhaustive list of models and metrics but the differences between how they rate the two main title contenders is apparent. All of these metrics have demonstrated utility at making in-season predictions but clearly assumptions about the relative strength of these two teams differs between them.

The question is why? If we look at the two extremes in terms of these methods, you would have total shots difference (or ratio, TSR) at one end and non-shots expected goals at the other i.e. one values all shots equally, while the other doesn’t ‘care’ whether a shot is taken or not.

There likely exists a range of happy mediums in terms of emphasising the taking of shots versus maximising the likelihood of scoring from a given attack. Such a trade-off likely depends on individual players in a team, tactical setup and a whole other host of factors including the current score line and incentives during a match.

However, a team could be accused of shooting too readily, which might mean spurning a better scoring opportunity in favour of a shot from long-range. Perhaps data can pick out those ‘trigger-happy’ teams versus those who adopt a more patient approach.

My non-shots based expected goal model evaluates the likelihood of a goal being scored from an individual chain of possession. If I switch goals for shots in the maths, then I can calculate the probability that a possession will end with a shot. We’ll refer to this as ‘expected shots’.

I’ve done this for the 2012/13 to 2014/15 Premier League seasons. Below is the data for the actual versus expected number of shots per game that each team attempted.


Actual shots per game compared with expected shots per game. Black line is the 1:1 line. Data via Opta.

We can see that the model does a reasonable job of capturing shot expectation (r-squared is at 0.77, while the mean absolute error is 0.91 shots per game). There is some bias in the relationship though, with lower shot volume teams being estimated more accurately, while higher shot volume sides typically shoot less than expected (the slope of the linear regression line is 0.79).

If we take the model at face value and assume that it is telling a reasonable approximation of the truth, then one interpretation would be that teams with higher expected shot volumes are more patient in their approach. Historically these have been teams that tend to dominate territory and possession such as Manchester City, Arsenal and Chelsea; are these teams maintaining possession in the final third in order to take a higher value shot? It could also be due to defenses denying these teams shooting opportunities but looking at the figures for expected and actual shots conceded, the data doesn’t support that notion.

What is also clear from the graph is that it appears to match our expectations in terms of a team being ‘trigger-happy’ – by far the largest outlier in terms of actual shots minus expected shots is Tottenham Hotspurs’ full season under André Villas-Boas, a team that was well known for taking a lot of shots from long-range. We also see a decline as we move into the 2013/14 season when AVB was fired after 16 matches (42% of the full season) and then the 2014/15 season under Pochettino. Observations such as these that pass the ‘sniff-test’ can give us a little more confidence in the metric/method.

If we move back to the season at hand, then we see some interesting trends emerge. Below I’ve added the data points for this current season and highlighted Arsenal, Manchester City, Liverpool and Tottenham (the solid black outlines are for this season). Throughout the dataset, we see that Arsenal have been consistently below expectations in terms of the number of shots they attempt and that this is particularly true this season. City have also fallen below expectations but to a smaller extent than Arsenal and are almost in line with expectations this year. Liverpool and Tottenham have taken a similar number of shots but with quite different levels of expectation.


Actual shots per game compared with expected shots per game. Black line is the 1:1 line. Markers with solid black outline are for the current season. Data via Opta.

None of the above indicates that there is a better way of attempting to score but I think it does illustrate that team style and tactics are important factors in how we build and assess metrics. Arsenal’s ‘pass it in the net’ approach has been known (and often derided) ever since they last won the league and it is quite possible that models that are more focused on quality in possession will over-rate their chances in the same way that focusing on just shots would over-rate AVB’s Spurs. Manchester City have run the best attack in the league over the past few seasons by combining the intricate passing skills of their attackers with the odd thunder-bastard from Yaya Touré.

The question remains though: who will win the Premier League title this season? Will Manchester City prevail due to their mixed-approach or will Arsenal prove that patience really is a virtue? The boring answer is that time will tell. The obvious answer is Leicester City.

Win, lose or draw

The dynamics of a football match are often dictated by the scoreline and teams will often try to influence this via their approach; a fast start in search of an early goal, keeping it tight with an eye on counter-attacking or digging a moat around the penalty area.

With this in mind, I’m going to examine the repeatability of the amount of time a team spends winning, losing and drawing from year to year. I’m basically copying the approach of James Grayson here who has looked at the repeatability of several statistical metrics. This is meant to be a broad first look; there are lots of potential avenues for further study here.

I’ve collected data from (tip of the hat to Andrew Beasley for alerting me to the data via his blog) for the past 15 English Premier League seasons and then compared each teams performance from one season (year zero) to the next (year one). Promoted or relegated teams are excluded as they don’t spend two consecutive seasons in the top flight.


Below is a plot showing how the time spent losing varies in consecutive seasons. Broadly speaking, there is a reasonable correlation from one season to the next but with a degree of variation also (R^2=0.41). The data suggests that 64% of time spent winning is repeatable, leaving 36% in terms of variation from one season to the next. This variation could result due to many factors such as pure randomness/luck, systemic or tactical influences, injury, managerial and/or player changes etc.


Relationship between time spent losing per game from one season to the next.

As might be expected, title winning teams and relegated sides tend towards the extreme ends in terms of time spent losing. Generally, teams at these extreme ends in terms of success over and under perform respectively compared to the previous season.


Below is the equivalent plot for time spent winning. Again there is a reasonable correlation from one season to the next, with the relationship for time spent winning (R^2=0.47) being stronger than for time spent losing. The data suggests that 67% of time spent winning is repeatable, leaving 33% in terms of variation from one season to the next.


Relationship between time spent winning per game from one season to the next.

As might be expected, title winning teams spend a lot of time winning. The opposite is true for relegated teams. Title winners generally improve their time spent winning compared to the previous season. Interestingly, they often then see a drop off in the following season.

Manchester City and Liverpool really stick out here in terms of their improvement relative to 2012/13. Liverpool spent 19 minutes more per game in a winning position in 2013/14 than they did the previous season; I have this as the second biggest improvement in the past 15 seasons. They were narrowly pipped into second place (sounds familiar) by Manchester City this season, who improved by close to 22 minutes. They spent 51 and 48 minutes in a winning position per game respectively. They occupy the top two slots for time spent winning in the past 15 seasons.

According to, Manchester City and Liverpool scored their first goals of the match in the 26th and 27th minutes respectively. Chelsea were the next closest in the 38th minute. They were also in the top four for how late they conceded their first goal on average, with Liverpool conceding in the 55th minute and City in the 57th. Add in their ability to rack up the goals when leading and you have a recipe for spending a lot of time winning.


The final plot below is for time spent drawing. Football-lineups doesn’t report the figures for drawing directly so I just estimated it by subtracting the winning and losing figures from 90. There will be some error here as this doesn’t account for injury time but I doubt it would hugely alter the general picture. The relationship here from season to season is almost non-existent (R^2=0.013), which implies that time spent drawing regresses to the mean by 89% from season to season.


Relationship between time spent drawing per game from one season to the next.

Teams seemingly have limited control on the amount of time they spend drawing. I suspect this is a combination of team quality and incentives. Good teams have a reasonable control on the amount of time they spend winning and losing (as seen above) and it is in their interests to push for a win. Bad teams will face a (literally) losing battle against better teams in general, leading to them spending a lot of time losing (and not winning). It should be noted that teams do spend a large proportion of their time drawing though (obviously this is the default setting for a football match given the scoreline starts at 0-0), so it is an important period.

We can also see the shift in Liverpool and Manchester City’s numbers; they replaced fairly average numbers for time spent drawing in 2012/13 with much lower numbers in 2013/14. Liverpool’s time spent drawing figure of 29.8 minutes this season was the lowest value in the past 15 seasons according to this data!


There we have it then. In broad terms, time spent winning and losing exhibit a reasonable degree of repeatability but with significant variation superimposed. In particular, it seems that title winners require a boost in their time spent winning and a drop in their time spent losing to claim their prize. Perhaps unsurprisingly, things have to go right for you to win the title.

As far as this season goes, Manchester City and Liverpool both improved their time spent winning dramatically. If history is anything to go by, both will likely regress next season and not have the scoreboard so heavily stacked in their favour. It will be interesting to see how they adapt to such potential challenges next year.