Quibans 91: SPOTY and the Christmas Number 1

'SPOTY' is the annual BBC 'Sports Personality of the Year'. 

This Quibans takes an article from a year ago.  It appears that it is updated each year (and is nonsense every time!).  The versionfor 2019 has been done as a video (but includes the same graphics as in 2018).

Here I present the article a section at a time, with a question after each.  My thoughts and comments appear together at the end.  You may want to give students the address of the webpage and ask them to go through it for themselves.

BBC Sports Personality of the Year: How do you win the main award?

14 December 2018
The BBC Sports Personality of the Year 2018 will be crowned on Sunday but what are the key factors in the make-up of previous winners? From birthplace to facial attributes, we've been analysing the ideal candidate...
The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.

Question 1: This image appears at the end of the article.  It suggests that to win SPOTY you ideally need to do athletics, to have been born in London, to have blue eyes, to be 29 years old and to have had your achievement in August.  Any comments at this stage?

Here is the first image:

Q2)  Why might it not be surprising that there are more Athletics winners than there are from other sports?

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Q3)  Why is this unsurprising?

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Q4)  Any comments?

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Recall the line of text near the start of the article:

The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.

Q6)  Looking at the previous image, what can we work out?

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Q7)  Why is this not a surprise?

Q8) So let’s look back at the diagram we started with.  Any further comments?

Here are my answers:

Q2)  There are lots more athletes than there are motor racing drivers and there are lots of sports included under the heading ‘Athletics’.  There are really only 11 England cricketers who might be in with a chance and footballers suffer because people will only vote for national team players and not those from clubs they don’t support, 

Q3)  London is bigger than anywhere else, so it has a larger proportion of the population.

Q4)  What has this got to do with success in sport or with popularity?  Does having green eyes make you less popular?  No.  Does it make you less successful?  No.  And the facial hair is presumably partly to do with fashion.

Q5) If you have blonde hair you are more likely to have blue eyes!  So these two things are linked.

Q6)  There are 65 winners here, so some people have won it twice.

Q7)  Many awards will have been because of events that take place in the summer, such as the Olympic Games (July/August) or Wimbledon (June).  There are most winners from athletics and that is overwhelmingly a summer sport.  Is it also likely that those who win things in Jan/Feb/March are forgotten by the time you get to December and the voting for SPOTY?

Q8) We have said already that athletics and August are likely to be linked and that London is the biggest city in the UK, so is likely to have more people who are born there.  The blue eye colour is interesting: for the men it was equal, but by including the female winners you get blue being the mode.  Clearly, if you are male then this isn’t relevant!  But hold on: vastly more men have won than women, so should that be mentioned here?

Here is a list of the Athletics winners of SPOTY (from Wikipedia):

Of the Athletes, 5 were born in London (Christopher Chataway, Seb Coe, Daley Thompson, Fatima Whitbread and Jonathan Edwards). 

The final four of those appear to have brown eyes, leaving only Christopher Chataway.  He was 23  years old when he won and his big achievement (breaking the 5000m world record) took place in October. 

Chataway meets only the first 3 of the 5 criteria.  Are there any who meet 4 of them?  Jonathan Edwards is the only one of the athletes who makes 4 out of 5.  He was a Triple-Jumper, born in London, was 29 and his world championships win was in August. 

None of the other winners (from any sport) get 4 of the 5. 

So this is an example of where appealing to the averages at every stage doesn’t help us in predicting the winner.

Extension:  Number 1 song at Christmas

This used to be one of the biggest songs of the year.  Many different newspapers carried exactly the same story.  This version comes from the Independent:

Music experts find formula for ‘perfect’ Christmas number one

Music researchers have crunched the numbers on Christmas songs to find the perfect formula for a festive hit.

Experts at a UK music label looked at every Christmas number one from the last 50 years to see what they have in common and determined that the Pet Shop Boys’ 'Always On My Mind' came closest to being the quintessential tune for the holidays.

“I think we’re a long way from an algorithmically-generated Christmas number one,” said Howard Murphy, founder of Ostereo which conducted the research, in a press release accompanying the data.

“But certain characteristics do make a song more likely to resonate with audiences at Christmas,” he added.

For a song to hit the top spot on Christmas Day it needs to be three minutes and 57 seconds, in the key of G major, played at 114 beats-per-minute and performed by a 27-year-old solo artist, according to the research.

Other key trends among the songs analysed were that the majority were ballads, nearly half were cover versions and nearly all were about something other than Christmas.

'Always On My Mind' hits the ideal length and key exactly, as well as being a cover of Elvis’ 1972 hit, but is slightly faster than the formula suggests at 125 bpm and performed by a duo who had an average age of 31.5 when the song hit number one at Christmas 1988.

'Mary’s Boy' by Boney M came a close second, researchers said, with a tempo of 113 bpm, length of four minutes two seconds and a key of F, two semitones lower than G.

Clearly this isn’t a ‘formula’ – they have just averaged the attributes of all the Christmas number one songs over the years.  What types of average have they used for each attribute?  How is this story related to the SPOTY one?

Sources:

https://www.bbc.co.uk/sport/sports-personality/42367914

https://www.bbc.co.uk/sport/av/sports-personality/50752816

https://en.wikipedia.org/wiki/BBC_Sports_Personality_of_the_Year_Award

https://www.indy100.com/article/christmas-number-one-how-to-guide-perfect-formula-pet-shop-boys-boney-m-elvis-8674946

Quibans 90: Goal sizes

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?   

Sources: https://www.telegraph.co.uk/football/2019/05/29/reducing-size-womens-goals-would-not-help-fight-equality-says/

https://en.wikipedia.org/wiki/Laws_of_the_Game_(association_football)#1863_rules

https://www.bbc.co.uk/news/health-23896855

https://en.wikipedia.org/wiki/List_of_average_human_height_worldwide

https://docs.google.com/spreadsheets/d/1PupE-_c8zGfNsRBROBa8urFv48HQqk8oz42qu_lczUc/edit?usp=sharing

Quibans 89 – Men vs Women in the European elections 2019

I voted by post earlier in the week.  Some parties had more female candidates than others.  I wondered whether it was the case that across the country certain types of party have more male or female candidates.  Here’s what I did with my Year 12 Core Maths class.

Some background to the electoral system:

Each country in the EU has its own voting system for the European elections.  England is divided into 9 regions and Wales and Scotland are each a region (Northern Ireland has a different system, so I didn’t involve them).  In each region there are a number of seats, ranging from 10 seat for the South East region to 3 seats in the North East.

You don’t vote for an individual but for a party.  Each party has a ‘list’ of candidates for each region.  Last time around in the 7-seat East of England region most parties had seven candidates.  Having worked out that UKIP should get 3 seats, the Conservatives 3 seats and Labour 1 seat (using the D’Hondt method – but that’s not relevant here), the top three candidates from the UKIP list were elected as MEPs, the top three from the Conservative list and top Labour candidate.

What we did:

On a shared Excel file, I had each region on a separate sheet.  I divided these up around the class (some students had a sheet each, others worked as a pair).  First they sorted out whether each candidate was male or female.  This wasn’t always obvious, so they Googled if they weren’t sure.

Then they typed into another sheet the number of female and male candidates for each party.

They had to deal with some issues.  For example, some candidates are standing as ‘independents’, meaning they are not part of a party.  We decided to ignore them.  Some candidates have withdrawn from the election; we removed the ones we knew about.

These are the results, for the parties that are standing in every region:

11% of the UKIP candidates are female, through to Change UK, for whom 57% of the candidates are female.

Is it interesting that the more pro-Brexit parties tend to have more male candidates, while the more pro-Remain parties have roughly equal numbers of men and women?

Better methodology?

But hold on: maybe this doesn’t tell the whole story.  What if the LibDems have the same number of male and female candidates but the top few in each region are all men?  It is extremely unlikely that those further down each list will be elected, so this is important. 

Here is how I intend to deal with that.

The students recorded a list of Male and Female candidates for each party.  Here’s part of that list:

Since the lesson (we will talk about this next week) I have turned that into a set of binary numbers, where F becomes 1 and M becomes 0.

I then turned the binary into a decimal.  This means the first-ranked candidate in each list is worth double the one that follows, which is worth double the one after that, etc.  If there are 5 candidates in a list, the 5th one is worth 1 point, the 4th is worth 2 points, the 3rd gets 4 points, the second gets 8 points and the first is 16 points.  Add up the number of points for the female candidates and then divide by the total (which is 1 + 2 + 4 + 8 + 16 = 31).  That gives a fractional weighted-score for the female candidates in each region.

Then I found the average of these. 

The second column shows this new figure (with the first column showing the previous data):

Not much difference (apart from the Green Party)! 

Final thoughts:

It was good for the students to see a way to carry out this sort of analysis.  

It was good to divide up the work.  I couldn't find an easy way of getting hold of the gender of each candidate, so sharing the workload was a good thing.

We had to decide how to deal with problems (withdrawn candidates).

We had to think about how to do the analysis.

Here are links to my original spreadsheet and the one my class filled in.

If you want your class to use the original version then you will need to save it and share it with them (your IT people in College will be able to help if you haven't done this before).

Source:  https://inews.co.uk/news/politics/european-elections-2019-candidates-mep-who-standing-eu-vote-full-list/

Quibans 88: Bottled water

I started by giving out just this paragraph from the Guardian article that follows:

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit ### bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year [in the UK], you would end up with a ###-metre skyscraper.

There are some nice Fermi estimations required here.

What are the dimensions of a football pitch? What are the dimensions of a water bottle? How many bottles are used in this country in a year?

Then we need to convert some units and carry out the calculations, not forgetting to round off sensibly.

The students worked in groups. A typical estimate for the size of a football pitch was 110m by 60m. Some measured their water bottles (!) and found a diameter of about 6cm and a height of 20cm.

If working out the area covered by the pitch and by a bottle we need to be careful when converting units (10,000 cm² = 1m²). We also need to decide what “packed into a tight grid means” (we took it to mean a rectangular grid). The easiest way is to work out how many bottles fit along each side of the pitch and then to multiply these. These figures gave us 1.8 million (pleasingly close to the 1.7 million in the article). Other estimates in the room varied between 1.6 million and 2.8 million.

Working out the height is more difficult. If everyone in the country has one bottle per week then that would give us about 1.7 billion bottles per year. That would need to be stacked 1000 rows high, which means a height of about 200m. In fact the article says it’s 2.2 billion _litres_ per year (each bottle holds 500ml), so we have underestimated the answer.

I then gave out a fuller version of the article (below) and asked what things they could work out.

If we care about plastic waste, why won’t we stop drinking bottled water?

Sun 28 Apr 2019

For all the innovation and choice that define the food and drink industries, if you want to make money, you could do a lot worse than bung some water in a bottle and flog it. A litre of tap water, the stuff we have ingeniously piped into our homes, costs less than half a penny. A litre of bottled water can cost well over a pound, especially for something fancy that has been sucked through a mountain.

Yet the bottled water market is more buoyant than ever, defying the plastics backlash inspired by stricken albatrosses on the BBC’s Blue Planet, and a broader, growing sense that something has to change.

Sales in the UK were worth a record £558.4m in the year to last November, an increase of 7%, according to the latest figures from the market analyst Kantar. Separate data from the analysts Nielsen show that last year we guzzled more than 2.2bn litres of bottled water, including “take-home” and “on-the-go” products. That’s an annual rise in volume of 8.5%.

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit 1.7m bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year, you would end up with a 514-metre skyscraper – 200 metres taller than the Shard.
Hope is not entirely out of reach. That plastic skyscraper conceals attempts in the bottled water industry to change. If nothing else, the rate of growth has begun to ease (sales were up 7% in the year to November 2018, compared with 8% the previous year).

But even if large numbers of us are quitting bottled water because of care for the environment, others are taking it up. The introduction of the “sugar tax” on juices and fizzy drinks has pushed more people to bottled water, while health awareness has boosted its desirability. Kantar says tap water consumption is growing at roughly the same pace (we still drink almost three times as much tap water as bottled water).

So the plastic tide only creeps higher. The industry is quick to point out that all its bottles are recyclable. “But collection rates are, at the most generous estimates, 56%, so the actual recycling rate will be lower than that,” Chetan-Walsh says. And while bottles may be recyclable, very few are made of recycled plastic. Highland Spring launched recycled half-litre “eco” bottles alongside its standard bottles in January; Evian has vowed to use only recycled plastic across its range by 2025.

Kinvara Carey, general manager of the Natural Hydration Council, an association of the biggest bottled water manufacturers, cites a survey in which people were asked what they would do if bottled water were not available. “Forty-four per cent would buy another drink, which is not great, 14% would go without and 4.5% said they would find a fountain,” she says. “The choice is important.”

We can work out things like:

1) The cost of a litre of bottled water
2) How the price has changed in the past year
3) What the amounts were last year
4) How many bottles are recycled
5) The volume of landfill taken up by bottles
6) Why the percentages in the final paragraph don’t add up to 100%
7) How much water each person drinks each day

Source: https://www.theguardian.com/environment/2019/apr/28/if-we-care-about-plastic-waste-why-wont-we-stop-drinking-bottled-water

Quibans 87: McDonald’s straws

I gave the article below (from the BBC website) to my Yr 12 class and asked them what they could work out.  They had some great ideas (which are shown below the article), largely because we have been working on this sort of thing throughout the year.  If you wanted to use this with a class that isn’t used to working in this way then the ideas my class came up with could be turned into questions to ask.

McDonald's plastic straw petition: Call to ditch paper straws

24 April 2019

McDonald's is being called on to stop its roll out of paper straws in the UK and Ireland, amid claims that they "dissolve" in drinks.

The fast food giant is switching from plastic to paper straws at their 1,361 restaurants after customer pressure. An online petition calling for a return to plastic straws has so far garnered more than 35,000 signatures.

McDonald's say they are "doing the right thing" while a supplier said customers need to "compromise". The restaurant chain supplies 1.8 million straws to its four million UK customers each day.

Things my class worked out:

• 35,000 people have signed the petition.  That’s less than 1% of the people who visit McDonald’s in one day.
• About 6% of the population of the country go to McDonald’s each day.
• On average each restaurant uses 1323 straws per day.  [We talked about rounding this off more appropriately – and decided that 1300 is probably better.]
• Just under half (45%) of customers use a straw.  This might be because some people don’t have a drink, or have a hot drink, or have juice without a straw.
• There are 1.46 billion visits to McDonald’s in the UK and Ireland each year.  [Better as 1.5 billion?]  We know this can’t be 1.5 billion different people because that would be about a fifth of the population of the planet!  On average, that’s 22 visits per year per person, which is equivalent to about two visits per month.  Maybe half the population go once a week and the other half never go? 
• A straw weighs about 0.42g.  That means 756kg of straws per day.  Over the course of a year that’s the weight of 3600 adults.

Source: https://www.bbc.co.uk/news/uk-wales-48038130