What's the maths behind a fantastic FA Cup final?

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1. Are you ready?

The FA Cup final - the biggest day of the national footballing calendar.

The pitch is prepared, the pies are hot, 90,000 fans are seated and 10 million people around the country are tuned in, waiting for kick-off.

What’s the maths behind making this moment happen?

2. Matchday in a minute

Dan Walker introduces timelapse video of a Wembley matchday in under a minute.

3. The wonder of Wembley

Infographic showing stats and data about the FA Cup final at Wembley

4. Pitch puzzles, tickets and legroom

The Wembley pitch is 68 metres wide x 105 metres long = 7,140 square metres, the same as both Arsenal’s and Aston Villa’s. This is now the Uefa standard size for pitches hoping to host Champions League or European Championship matches.

7,140 square metres divided by 22 gives each player 325 square metres of space, or a strip almost 5 metres wide. If you divided up the pitch among 90,000 fans, each would get a divot of 800 square centimetres, around the size of a vinyl LP cover.

Stadium seating is divided in half for the fans of the two teams, with Aston Villa on the west and Arsenal on the east.

25,000 tickets are allocated to each of the clubs, 17,000 to Club Wembley, and 20,000 to the FA’s Football Family – which includes volunteers and tickets for all League clubs, plus any non-League clubs who reached the third round.

The legroom of the seats at Wembley is more than a typical London theatre or budget short-haul plane. However a business class seat on the Channel tunnel train gives you significantly more legroom.

Train image: tipsfortravellers

Wembley stadium's footprint is 103,000 square metres – more than twice the old stadium footprint of 40,500 square metres. It took 250,000 tonnes of concrete and steel to build – 10 times the amount used in the previous stadium.

Image: Foster and Partners

5. Live to the world

Facts and figures about the FA Cup final 2015

6. When 300,000 went to Wembley

No one knows exactly how many people attended the first Cup final to be held at the newly built Wembley Stadium in 1923.

The official capacity was 126,000, but an estimated 300,000 managed to get into the ground. The crowd surged onto the pitch and famously had to be encouraged back to the touchlines by PC George Scorey, mounted on a white horse called Billie, before the match could start.

Given the numbers inside Wembley there were remarkably few serious injuries, but the events triggered a Parliamentary inquiry – the Shortt Report. It was one of the first times maths was used to model crowd safety at football stadiums.

Many features that are now commonplace at matches were first proposed in this report, such as all-ticketed matches, stewards, a minimum number of turnstiles per thousand capacity, and regularly spaced vertical and horizontal gangways.

The White Horse bridge leading to the new Wembley Stadium was named in Billie’s honour.

PC Scorey was awarded tickets to subsequent Cup finals in gratitude, however he was reportedly not interested in football and chose not to attend!

7. Safely home

Win, lose or draw – how maths helps everyone to get home safely

Dr G Keith Still, professor of crowd science at Manchester Metropolitan University, who spent three years studying crowds at Wembley stadium, talks through some of the basics.