Quibans 76: Away matches

During the Christmas period (the weekend before Christmas, up until just into the New Year) the Premier League football teams play four games.  BBC Sport website had this as a headline:

Premier League festive fixtures: Which clubs have toughest schedule?

As part of this they looked at how far supporters of each club would travel if they attended all four games.  (Distances are measured by road from the stadium of their own club.) 

Q1) Across the whole season, which team's supporters would you expect to travel the furthest?  Which would travel the least?

Here are the teams and a rough indication of where they are
Arsenal   (London)
Bournemouth   (South coast)
Brighton and Hove Albion   (South coast)
Burnley   (North west)
Chelsea   (London)
Crystal Palace   (London)
Everton   (North west)
Huddersfield Town   (North west)
Leicester City   (Midlands)
Liverpool   (North west)
Manchester City   (North west)
Manchester United   (North west)
Newcastle United   (North east)
Southampton   (South coast)
Stoke City   (Midlands)
Swansea City   (South Wales)
Tottenham Hotspur   (London)
Watford   (London)
West Bromwich Albion   (Midlands)
West Ham United   (London)

Here is a map of the teams (taken from awaydayplanner.com, with the teams highlighted in blue). 

Q2)  Do you want to change your answers?  (NB: Liverpool and Everton are so close together that they appear as a single dot here.)

In the article this graph was included:

Q3)  What sort of correlation do you think there is between the distance travelled during the Christmas period and that travelled during the whole season?  Can you predict the pmcc?

Here are the figures (taken from a Talksport article, from awadayplanner and from the BBC).  The spreadsheet can be downloaded here.

Answers/thoughts

It might initially appear that all teams will travel the same distance to play each other, but further reflection suggests that teams that are closer to the middle of the country are likely to travel the least.
There are several ways to think about this.  There are six teams in London.  Their journeys to play each other will be quite short, but for Newcastle to play each of the six London teams they will need to make six long journeys.

One way to convince yourself that clubs on the periphery are likely to travel furthest (Eg Newcastle, Swansea, Burnley, Brighton) is to go to ridiculous extremes.  If Pluto United joined the premier league then for one game each season the other 19 clubs would travel once to Pluto.  But the fans of Pluto United would have to travel to Earth 19 times to play each of their away games.

In all of this we are making the assumption that each match is a self-contained trip.  It might be possible for Newcastle fans to make a single trip to London and to stay there for all of the London matches, but in practice this will mean living in London for the season, because football teams rarely play two matches in three days and usually (roughly) alternate between playing a match at home and then one away.

The table for Q3 shows the clubs in order.  I had predicted that Newcastle and Swansea would be the two clubs with the furthest journeys and that a north London club would have the shortest journey in total.

Burnley were particularly fortunate with their festive travel distances.  Tottenham Hotspur were a bit hard done by. 
The pmcc is 0.52 - indicating a weak positive correlation.


Sources:
http://www.bbc.co.uk/sport/football/41812290
http://awaydayplanner.com/
https://talksport.com/football/how-far-fans-every-premier-league-club-must-travel-next-season-least-most-distance

Quibans 75: Don't Panic!

This story appeared in most newspapers.  The Sun put it like this:

200 litres every hour!  Clearly letting in water isn't ideal for a ship, but is 200 litres a lot?

How long before it will sink?

Some data here (from the Daily Telegraph) might help:

Some thoughts/answers:
I googled the capacity of a standard bath-tub.  It appears that 120 litres or 150 litres are fairly common capacities.
To put this into perspective: it's letting in about one and a third bath-tubs of water per hour.  That doesn't seem very much!

A length of 920 feet, beam of 230 feet and draught of 36 feet are given in the Daily Telegraph graphic.  I assume that 'beam' means the width of the ship and that the 'draught' is the amount of ship under the waterline.  There is a lot of aircraft carrier above the waterline, but if we find the rough volume of ship underwater (treating it a cuboid) then we would get 920*0.3 * 230*0.3 * 36*0.3, which is about 200,000 cubic metres.  That's 200 million litres.

At 200 litres per hour that is a nice round million hours before the part currently below the waterline to fill with water.  It will take just over 100 years for this to happen.  So if left untreated, if it still exists in a hundred years, if no-one uses a pump, and if the navy runs out of buckets for bailing purposes, then the ship will probably be in trouble early in the 22nd century.


Sources:
https://www.thesun.co.uk/news/5168494/hms-elizabeth-leak-navy-repairs-millions/
http://www.telegraph.co.uk/news/2017/12/18/hms-queen-elizabeth-britains-new-31bn-aircraft-carrier-has-leak/

Quibans 74: Parking fines

The article below is excerpted from the Cambridge News website (link at the foot of the page).

Read the article, carry out some calculations and comment on the substance of the article.  Some of my ideas follow the article (after a jump).

Where you are most likely to get a parking ticket in Cambridge

One Cambridge road has seen more drivers slapped with parking tickets than any other, new data has revealed.  If you park regularly on Chesterton Road, to the north of the city centre, you may well have seen parking wardens issuing yellow tickets as it is the number one place to get a ticket in Cambridge.

The fining hotspot was revealed after a Freedom of Information Request by insurance comparison website comparethemarket.com, which has detailed an interactive map with its findings.

The data also shows Cambridge was the top city in the East of England for parking fines, with twice as many handed out in the city over three months compared to the next ranking area.

Cambridgeshire County Council issued a total of 12,234 penalty charge notices between July and September 2017, making £281,025 of revenue.

But the region's second parking fine hotspot - East Hertfordshire - lagged behind with 6,950 fines on motorist's vehicles generating a revenue of £191,878.

Simon McCulloch, director at comparethemarket.com said: "Our parking fines hotspots have revealed that motorists need to be extra vigilant when it comes to something as simple as parking their vehicle correctly if they want to avoid a hefty fine.  If you do find yourself with a PCN, it’s worth checking your ticket, as you can often reduce the fee by half, simply by paying it within 7 or 14 days, depending on your local council."

The top 10 parking fine areas in East of England

1. Cambridge (12,234) - £281,025

2. East Hertfordshire (6,950) - £191,878

3. Watford (6,428) - £136,818.69

4. Norwich (5,719) - £171,570

5. St Albans (4,963) - £132,570

6. Colchester (4,791) - £91,220

7. Ipswich (4,551) - £107,044

8. Welwyn Hatfield (3,599) - £79,650

9. Dacorum (2,800) - £90,459

10. Basildon (2,365) - £74,746

Write down comments about the article above before scrolling down to see what I have written.

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Here are a few ideas.  These are not necessarily complete - there are likely to be other things that can be worked out too.

First of all, it doesn't seem sensible to draw a pie chart (the whole pie would refer to the number of fines or the amount of money from only the top 10 places).  A bar chart might show this well.  A scatter graph would show the relationship between the number of fines (given in brackets) and the amount of money collected.

It is clear that the ranking has been carried out on the number of fines rather than the amount of money, because the former goes down in order whereas the latter jumps around a bit.

We could work out the correlation coefficient and finding that this is 0.95 we could comment that there is a very strong positive correlation between the number of fines and the amount of money paid in fines.  This is perhaps unsurprising.

The 69 pence involved in the Watford total looks a little strange!

The spreadsheet below shows the amount of money per fine.  Presumably the 'money per fine' is not a round number in most cases because fines are different in car parks and on the side of the road and because you get a discount if you pay quickly.  

This makes the Norwich figure of exactly £30 per fine look a little odd.

I followed the link in the article and found the original data.  Here is the section for the East of England:

First of all, this is in alphabetical order of location!  Surely actually ranking them would be more sensible?

Then we have the 'location' which, as per the article, is presumably the location with the most fines.

Finally - have a look at the Norwich revenue!  This wasn't disclosed for some reason.  

The author of the Cambridge News article appears to have decided to assume all of the Norwich fines were £30.  I find it a bit galling that they didn't disclose that in the article.

Maybe a better way to do this would be to use the average of the fines in other places, or to look at the highest and lowest and to give an upper/lower bound?

Final problem with this article and this research is that not all the places listed are the same size!  It would make sense to factor in the population or the number of cars or the number of visitors rather than using the raw figures.

Oh - and last thought: the first sentence is surely trivially true?  Unless there is a tie then it will always be the case that "One Cambridge road has seen more drivers slapped with parking tickets than any other" !

Source: http://www.cambridge-news.co.uk/news/cambridge-news/cambridgeshire-parking-fines-east-anglia-13994628