Thinking Outside the Box

What if Manchester City decided to “shoot-on-sight”?

There has been a revolution of sorts in the NBA over the past few years. The improved skill and tactical awareness of modern NBA players like Steph Curry has led to a strategy of teams taking more of their shots from 3-point range.

“Live by the three, die by the three” is the common refrain heard on the asphalt of Brooklyn. Or so I’m told. I really wouldn’t know.

Anyway, looking at some of the statistics behind this change in approach had me wondering, could we see a similar renaissance of thought in the Premier League? What if teams started taking pot shots from distance more frequently… or taking it to its rather more extreme conclusion, what if teams only took shots from range? Take Manchester City, who are faced most weeks by connoisseurs of double-decker passenger transportation. Surely one option is simply to ignore the defence entirely and slam shots in whenever it is feasible you might score.

Often, we’ll refer to teams having a ‘shoot-on-sight policy’, but let’s face it, this is rarely actually the case. In actuality, it describes a team that is more willing to shoot whenever they get in-or-around the penalty area. But what if a team like Manchester City woke up one day and chose violence?

Imagine the scene. Erling Haaland takes the kick-off and knocks it back to Kevin De Bruyne. The match takes shape immediately, with their opponents quickly settling into a de facto low block. After a few passes, Rodri has the ball centrally, he has time and space. Guardiola watches on from the sidelines expecting him to shift it out wide to Jeremy Doku, but unexpectedly Rodri takes a single step and sends a rocket straight at the keeper. Pep is waving his hands furiously, conducting an invisible orchestra. The keeper punts and the ball lands at the feet of Akanji. Again under little pressure, he progresses up the pitch, feeding it into John Stones who has a madness in his eyes. He’s had enough of this tiki-taka nonsense. The Yorkshireman looks up, about 35 yards from goal, and unleashes a true centre back’s effort that goes sailing over the bar, probably landing somewhere near the Dales from whence he came. The Catalonian on the sidelines looks like he is about to spontaneously combust.

This is fun to think about but let’s take a look at whether this kind of strategy could actually ever work. The first thing we need to understand is what does the probability of scoring look like at different ranges? Well, we can use xG statistics to give us some idea. And I can guarantee that some 50-something traditionalist Burnley supporter has had a minor aneurysm at the mention of xG. It’s fine Derrick, stick with it, this will be fun. xG is very simply the chance of a given shot being scored and depends on a range of factors, with distance from goal being one of the most important.

A health warning for those of you out there with a data background who are looking for robust six-sigma results: I would temper your expectations. I’m just like… a guy. A guy using data in ways it was simply never meant to be used.

Using a bunch of data on xG from Premier League matches, we can roughly ascertain how the probability of scoring tends to decrease with range.

Data source: StatsBomb

We can see on the above heatmap that the probability of scoring drops off quite quickly, going from 10-11% at the edge of the box, down to 1-2% at 35-yard range. The eagle-eyed readers among you might be wondering about the 26% outlier near the middle of the box. Well spotted. I haven’t bothered excluding penalties because I’m lazy and that’s where they’re bucketed. For those that didn’t spot that, you need to up your game, no room for passengers here.

This visualisation is enough to give us a ‘reasonable’ range under which a shoot-on-sight strategy might be successful. People often talk about the ‘second penalty box’, i.e. the 36-yard range. If your average shot distance goes beyond that your chances of scoring are pretty minimal. We can see this relationship more explicitly with this second chart:

Data source: StatsBomb

As might be expected, a shot's chances of going in takes the form of an exponential decay. Penalties, which are much more likely to be scored, cause a bump at 12 yards, but then your odds keep getting worse. At the edge of that ‘second penalty box’ range, your chances of scoring are down to 1.1% - roughly a 1 in 100 chance.

But let’s not give up hope just yet. After all, if there’s one thing my hypothetical scenario above demonstrated, it’s that this shoot-on-sight strategy would likely vastly increase the volume of shots. Sure, your chances of scoring are less, but if you’re shooting often enough, that wouldn’t matter… would it?

Well first, we need to figure out how the average distance at which a team tends to shoot might impact the number of shots it has in a game. We’re talking about Manchester City here, so let’s focus on their data. I tried to answer this by gathering all data points from City matches in the 2023/24 season across all competitions. The scenario we’re looking at here means we need to narrow the data down to those games that were less jogo bonito and more jogo autocarro. In other words, eliminate data from games that were in any way close, where the opponent wasn’t defending for their lives. To do this I removed data points where the xG of the opponent was greater than 0.7. Why 0.7? Well that usually translates into at least five decent half-chances, which feels about right in distinguishing teams that are actually trying to attack. Don’t think too hard about it, this is for entertainment purposes only.

I also excluded teams who were just woefully bad, and therefore outliers, giving City 30+ shots in a game. Because if the opponents defensive shape is that bad, then this tactical shift isn’t really needed anyway (I’m looking at you Crvena Zvezda).

This left me with what I would consider to be a decent ‘core’ of City games where the opponent was sat in defending. We can now take a look at the number of shots in these games versus the average shot distance and lo and behold, there is a trend…

Data source: FBref

… okay it’s not a great trend. Data scientists can prize the R-squared value from my cold dead hands. But it does feel like there is a general upward slope. Taking shots from further out on average = more shots. That does seem to be a sensible conclusion even if we’ve made some quite bold assumptions.

And we can take this sensible conclusion and extrapolate it beyond all common sense. We’re going where no man has gone before. The line on the chart shows that if a team’s average shot distance wasn’t 18 yards (like City’s) but instead 36 yards, we can expect that the number of shots would also roughly double. From 18-27 shots per game, up to 43-52 shots per game. The mid-point of the projection is at 47.6 shots. That’s roughly one shot every 75 seconds that the ball is in play, which feels just about feasible.

Now, a word of warning here, some of you may be saying “well there’s no way any good opposition would sit there like lemmings and not change up their approach when faced with this ridiculous strategy”. And to that I say, you are correct, but we can only play what’s in front of us. Stop ruining my fun.

So now we have everything we need to know if this strategy could work. We know how shot success varies with distance, and we know roughly how many more shots per game we can expect to see if we shoot-on-sight. Combining these two will give us how many goals we can expect per game. Our new footballing paradigm, destined to…

Data source: StatsBomb, FBRef

… oh.

The wonderful thing about data is that sometimes you stumble upon the reason why things are the way they are. Even with nearly double the number of shots, the number of goals scored per 90 minutes craters. Remember I said that City’s average shot distance per game is about 17-18 yards? Well direct your eyes to the peak of this chart. Well done statisticians, you win again.

I am not, however, so easily deterred. Not willing to give up my dream because of some mere inconvenience like reality. Let’s change our approach and ask: How can we reverse these fortunes? Under what scenario could we make this work?

I ask you again to imagine the scene.

It’s a wet and windy night at the Etihad, the ball is skipping across the surface of the pitch. Swirling gale-force winds are making it incredibly difficult to track the trajectory of the ball. In the opening minute of the match Grealish is through on goal, West Ham keeper Areola comes charging out of his box and gives ol’ Jack the Nigel De Jong treatment. Cutting him in half from chest height. The referee takes a dim view of it and instantly sends Areola off. But there’s horror on the sidelines as West Ham realise they don’t have Fabiański or Foderingham on the bench, they’re both injured. They have no choice. Tomáš Souček dons the gloves. He’s played as goalkeeper in training, and he’s got pretty good close-range reactions but he really struggles to get down into the corners when making saves.

Pep, seeing this farce play out in front of him, strokes his chin with contemplative delight. He immediately orders Erling Haaland to drop deep to play alongside Rodri in a double pivot. Haaland so far this season is operating at twice his xG, scoring nine goals when the stattos would suggest he should only have four. The Man City fans, despite a decade of exposure to tactical innovation, shift uncomfortably in their seats. Some start to wonder if Guardiola has finally cracked. Perhaps his recent visit to the Stockport Hat Museum as part of a charitable initiative with City in the Community has left him with a bad case of mercury poisoning?

What the City fans don’t know is that the laws of probability are shifting like sand beneath their feet.

Data source: StatsBomb, FBRef. Absurd Modelling: Me.

Between the weather, an outfield player being put in as keeper, and having a robot Viking sending howitzers from afar, the xG curve has lifted. Shots from distance are now 14 times more likely to be scored.

Fortunately for City, this is the exact boost they need to get the law of averages to work in their favour. This is what it takes to make a shoot-on-sight strategy work, the bald genius has done the maths in his head like Rain Man, and he knows this to be true.

As Haaland completes his hat-trick of 35-yard screamers in the 80th minute and wheels away to celebrate, Pep doesn’t react. He simply looks on and quietly whispers under his breath…

“Live by the three, die by the three.”

All data used in this article is courtesy of FBRef and StatsBomb, charts and visualisations made using python and matplotlib.