First-leg goals tally offers only a small clue to what happens next

What next? There were eight goals when Manchester City played Monaco in a Champions League round of 16 first leg. That was the highest number ever in a round of 16 first leg.

There were six goals this season when Bayern Munich played Arsenal and also when Leverkusen played Atletico Madrid. Altogether there were 34 goals across the eight games. That was the highest aggregate for round of 16 first legs. The previous highest was 26 in season 2013-14. In the other 12 seasons the aggregate was always between 16 and 22.

The 2016-17 second legs start tomorrow. How much do the first legs tell us of what might happen in the second legs?

One-seventh. There is some correspondence between scores in the first and second legs of knockout ties, but not much.

The round of 16 started only in season 2003-04. I looked at scores in all two-legged ties in the Champions League and European Cup from the last 30 seasons, 1986-87 to 2015-16. The Champions League evolved from the European Cup.

The higher the score in the first leg, generally speaking, the higher the score in the second leg. But the differences were much smaller in the second legs than they had been in the first legs.

After a first leg without goals the average number of goals in the second leg (excluding extra time, as all these figures will) was 2.5. After a first leg with seven goals the average number scored in the second leg was 3.5. The difference in the first leg had been seven goals; in the second leg on average it was only one goal.

Playing with the data I found that the best estimate of the number of goals in a second leg would have been a calculation in which one-seventh of the weight was given to the number of goals in the first leg and six-sevenths of the weight was given to the average number of goals in all second legs.

Thirty years is a long time, but during it there were fewer than 200 two-legged knockout ties in the Champions League and European Cup. So I went back all the way to the start of the European Cup in season 1955-56. That gave me a sample of more than 1,200 home and away ties.

And what I found was the same. The best estimate of the number of goals in a second leg would have been a calculation in which one-seventh of the weight was given to the number in the first leg and six-sevenths of the weight was given to the average for all second legs.

A game between Manchester City and Monaco we might have expected to be high scoring. Both teams like to attack, and their opponents like attacking them. But few of us would expect the average number of goals in meetings between Manchester City and Monaco to be as high as eight. Even for them what happened at the Etihad two weeks ago was unusual.

Using only the eight goals scored in the first leg and my simple formula, my expectation for the number of goals scored in the second leg at the Stade Louis II next Wednesday is 3.5. The calculation is (8 x 1/7) + (2.75 x 6/7) = 3.5, where 2.75 represents the average number of goals scored in second legs. That implies a 68 per cent chance of over 2.5 goals and a 32 per cent chance of under.

My expectation for Arsenal v Bayern Munich tomorrow is 3.2, implying a 62 per cent chance of over 2.5 goals and a 38 per cent chance of under.

Refs do well not to make more errors

Stewart Downing stuck out a foot and tripped James McArthur. It happened during Middlesbrough’s Premier League game at Crystal Palace. Instead of pointing to the penalty spot referee Bobby Madley reached for his yellow card and booked McArthur for diving.

It was the sort of mistake that gets ridiculed. On Match of the Day even the polite Jermaine Jenas could not help himself.

“I don’t know how Bobby Madley did not see this one,” he chuckled. “It was a poor decision… McArthur clearly gets to the ball first. You can see Bobby Madley’s position, with his assistant on the other side, they get a clear view of the incident, how none of them have managed to give it, but not only not give the right decision… they’ve booked McArthur on top of that for diving. It’s a poor decision.”

Quite so. I am surprised there are so few of them.

Our eyes deceive us. Often. Not only now and again.

On May 13, 2015, police shot a man on a street in Manhattan, New York. One eyewitness told the New York Times: “I saw a man who was handcuffed being shot”. Another said: “He looked like he was trying to get away from the officers.”

Such things can and do happen, but they did not happen that morning in Manhattan.

Surveillance video showed that the man was not handcuffed when he was shot. Nor was he running away. Somebody else was. A policewoman was fleeing down the street, chased by the man, who was swinging a hammer.

The witnesses were good, honest people. They were not lying. They described what they believed they had seen. But what they believed they had seen did not happen.

When they realised that they were wrong they were deeply upset.”I feel totally embarrassed,” said the lady who had believed that the man was handcuffed when he was shot. “It makes me think about everything in life.”

Scientist Neil deGrasse Tyson says: “Our senses are quite feeble when it comes to recording objective reality.” Hardly anyone accepts this but it is true. Eyewitness evidence is frighteningly unreliable.

I am amazed by how rarely referees see things that did not happen. There are one or two incidents most weeks to poke fun at on Match of the Day. We should be astonished there are not a lot more.