This task was test-driven at the recent AMSP Core Maths days (as
part of ‘Quibans Live’). Thanks to those
who made suggestions for improvements.
The story appeared in a number of places before the 2019 FIFA
Women’s World Cup and there were discussions about whether women should play
with smaller goals because women are, on average, shorter than men. This version is taken from the Daily Telegraph.
'Reducing
size of women's goals would not help fight for equality,' says England
goalkeeper Karen Bardsley
England goalkeeper Karen Bardsley believes reducing
the size of goals in the women's game would jeopardise the fight for equality
in football.
Chelsea manager Emma Hayes has suggested the
women’s game could be adapted to bridge the ‘physical differences’ between
women and their male counterparts.
She suggested smaller goals could stem criticism
often directed at female goalkeepers, who are generally of a smaller stature to
their male counterparts.
Manchester City goalkeeper Bardsley, about to play
in her third World Cup when she will add
to her 77 international caps, does not believe
narrowing the width between two posts is the way forward.
“My big thing is we need to change how people feel
about goalkeeping, I don’t think there is enough respect for the position in
the game, whether male or female.
“There is a stigma, that you have to be a certain
size, or not very good with your feet, or you have had to go in goal as a last
resort.”
How could we explore, using some Core Maths knowledge,
whether the goals should be made smaller?
On one level it doesn’t matter. Football is a relatively low-scoring game
(compare it with American Football, basketball, rugby, cricket, etc, where the
numbers of points (etc) are very much bigger).
If the goals are bigger than necessary and this results in more goals
being scored then this isn’t a big deal.
The goals are the same size for both teams after all.
We could find data for the heights of male and of female
goalkeepers and compare them.
In fact, I think the size of the goal was set in the 1866
version of the laws of the game and according to the BBC the “average height of
men has risen by almost 11cm since the mid-19th century”.
Wikipedia has the current average height of UK men at 175cm
and women at 162cm, so if both have increased by about 11cm since the size of
the goals was fixed then women are now roughly the same height as men were back
then.
Here’s my favourite way to explore this issue: If the goalposts are too big for women then
that presumably means more goals are being scored by women. Let’s use the number of goals per game from
the last two World Cups (Russia 2018 for men and France 2019 for women) and
compare the data.
The Google Sheets file has the full data, but here are the relevant
parts. You might want to give the
summary data to the class and ask them to work out averages and interpret them.
Before giving it out you might want to ask whether the
average number of goals per game will be different in the group stage or the
knock-out part of the tournament.
Is this a reasonable set of calculations to do? Are there ways to improve this?
Those who followed the women’s competition will know that
the eventual winners, the USA, beat Thailand 13-0. This is clearly an outlier, so perhaps we
should remove it from the women’s data?
At Quibans Live several people pointed out that if there was
extra time in a match then there was more opportunity to score goals (the
penalties that follow extra time have not been included here, though that is
another avenue that could be explored).
A normal-length match is 90 mins, so extra-time of 30 mins is equivalent
to another third of a match.
Here are the results with the 5 extra-time men’s matches and
the three extra-time women’s matches included:
Very close indeed!
This data doesn’t suggest the goals should be smaller in the women’s
game.
Final thought:
This is clearly relevant to the elite athletes at the last
two world cups. Does it still work for
those playing at lower levels?
