Tottenham got a lucky break in their Premier League win over Manchester City

How often does this happen? One team have lots of shots and do not score, the other team have hardly any shots and do score. Last Sunday in the Premier League Manchester City had 19 shots and none of them went in, Tottenham had three shots and two of them went in.

Jermaine Jenas, a television pundit who once played for Tottenham, shared his experiences. He said: “I have been involved in games like that before, where my team have ended up winning despite being outplayed for long periods. You come off thinking "Yes, we worked hard, dug deep and we really deserved something." Then, after the dust settles and you watch it back, you realise you got away with one, like Spurs did here.”

Spurs got away with another one earlier in the season against City. In that game too they had three shots and scored twice. City had 30 shots and scored twice. City manager Pep Guardiola said: “Football is the only sport you can have 30 shots to the other team’s three and draw, and even lose. In other sports when you do what we’ve done – in basketball, tennis, golf – you win. That’s why football is fascinating.”

How fascinating is football?

I studied every Premier League game in the seven seasons 2012-13 to 2018-19. Half of the teams who had more shots than their opponents won. Having one more shot than your opponents obviously is not the same as having 40 more shots, as City did in 2014-15 at home to West Bromwich. The greater the difference in the number of shots the more likely it became that the team with most would win.

Teams who took between one and five shots more than their opponents won 45 per cent of the time. Teams who took between six and ten shots more than their opponents won 50 per cent of the time. Teams who took between 11 and 20 shots more than their opponents won about 60 per cent of the time. And teams who out-shot their opponents by more than 20 won 70 per cent of the time.

So far all this makes sense. You score with shots, so if you have more shots than your opponents you should be more likely to win. You are. But you are not sure to win. This is where football can seem like it has stopped making sense.

Teams who out-shot their opponents by more than 20 won 70 per cent of the time. Which means 30 per cent of the time they did not win.

Suppose there were ten of these games in one round of Premier League fixtures. We should expect seven of the teams with most shots to win. But we should expect three not to win – two to draw and one to lose. One loss and two draws is a lot for ten teams who have taken so many more shots than their opponents.

Not all pundits are as understanding as Jenas. Others would come up with explanations for the draws and loss. Some would say that in those games the team with most shots had been wasteful and the team with fewest shots had been clinical, unless they were talking about a 0-0 draw.

They would be right if they meant one team had missed a lot of chances and the other had not, but we knew that already. They would be wrong if they meant one team consciously had done something the other had not.

They might say that this season Tottenham have been clinical against City and City have been wasteful against Tottenham. In other games Tottenham scored from a smaller proportion of their shots than City. Did Tottenham deliberately do against City something they did not do against other opponents? Did City deliberately not do against Tottenham something they did do against other opponents?

No. These things just happen. This is the only sense we can make out of the bits of football that do not seem to make sense. They will happen one time out of every so many, but we cannot tell which time.

City in other games this season scored one goal for every seven shots, as they did over the previous three seasons. Suppose a team who average one goal every seven shots play a game in which they have 19 shots. How likely is it that they will not score? There is a one-in-18 chance.

Tottenham in other games this season scored one goal for every eight shots, as they did over the previous three seasons. Suppose a team who average one goal every eight shots play a game in which they have three shots. How likely is it that they will score two goals? There is a one-in-25 chance.

A single Tottenham shot going in the goal (a one-in-eight chance) is a bit less likely than a single City shot going in the goal (a one-in-seven chance), which is a bit less likely than rolling a dice and getting the number you want (a one-in-six chance).

Imagine you are watching two children playing Snakes and Ladders. One throws a six to overtake the other and win. You do not say: “What a clinical throw, what great skill you showed when shaking that tumbler”. You congratulate the winner and console the loser. But you know the winner got away with one. Football teams can too.

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