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21.10.2014 Brain Teasers
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FOOTBALLIn an average week, do more people play football, or watch a football match?
More people play football than watch a football match.
The key to approaching market sizing type questions is: to start by clarifying the question; then to identify any assumptions you can make to simplifythe problem; next to break down the problem logically, before finally getting into the detail of the numbers. Interviewers will be impressed with peoplewho can approach a problem conceptually, and also who can find ways of getting to a roughly right or "80/20" version of the truth quickly, which can
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be refined later.
Start by raising any questions you have to clarify the parameters of the analysis. In this case, you might want to confirm that "watching a match"means watching a match in person, not on TV; and that "playing in a match" means playing in an organized manner with 2 full teams and a definedpitch, rather than a kickabout with friends in the local park, or with your children in the garden. Football could include 5aside as well as full XIs, butdoes not include nonstandard football, e.g. Eton Fives or other variants.
There are normally some simplifying assumptions to make up front â and you should always lay these out to the interviewer and confirm s/he ishappy with them, before proceeding. The assumptions in this example could be:
Assume we are talking about people in England â and that the conclusion for England will be the same as for the rest of the U.K, as there is nostructural reason to believe the other nations behave differently
Assume we are talking about distinct individuals rather > than played occasions â so people playing > once a week > or watching > once a weekdoes not count
Assume you only need to prove that the number playing is greater / less than the number watching â rather than the absolute numbers involvedin each.
Once you've clarified the scope and agreed your simplifying assumptions, you can start laying out a logical structure to breaking down the problem.
For this question, one approach would be to start by listing out all the different playing and watching "occasions". This allows you to show yourinterviewer that you've considered the problem as a whole, rather than diving down a particular line of argument â and also allows them to alert youto anything you've missed. Don't be afraid to use a piece of paper to write these down.
For example, an occasion list might look like:
ChildrenSchool PE lessons
Interschool matches
Other children's matches (county or other local leagues)
AdultsAdult amateur: 5aside, local Sunday leagues, company teams etc
Adult professional: Premier League etc.
Once you laid out the occasions, you should then prioritise which ones to analyse, in this case, based on:
a). Do you believe the numbers of players vs spectators will be asymmetric, or do the players and spectators cancel each other out? If canceling out,you can ignore the occasion, for the purposes of the analysis (remember, you don't need to know how many, just more or less)
b). Which occasions contribute the most to total player or spectator numbers: you should always focus your efforts on the "big ticket" items which willhave the most impact on the final solution.
A "prioritization matrix" might look like:
The logic behind this prioritization is as follows:Most children (especially boys) will play football at school, but there are rarely any nonplaying spectators other than the PE teacher
A child playing in a match (school or other league) will on average bring 1 parent or other friend to watch â so the number playing and the numberwatching will cancel out
Practically noone watches adults play amateur football on a regular basis
Professional, i.e. League, football players are a small proportion of all adults playing football â and certainly in proportion to the number ofspectators
This leaves us with two occasions in favour of players â School PE (significant) and Adult Amateur (unknown); and one occasion in favour ofspectators â Adult Professional (significant). Therefore, if you can prove that School PE is greater than Adult Professional, you can answer thequestion, without needing to work out the number of Adult Amateur players (currently unknown). First, start by working out how many children playfootball in school
a) How many schoolage children are there in England?
English population = 50m (you would be expected to know this / know that the total UK population is around 60m, and most of this is in England)
Years of school playing regular matches = 9
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(Ages 7 â 16, as most don't start PE in their first few years at school, and tend to stop playing in Sixth Form, or leave school)
Therefore, total children = 2m / 3 * 9 = 2m *3 = 6m
There are actually 7.5m children in school in the UK, so 6m of matchplaying age in England seems sensible.
b) Of schoolage children, how many play football?
Remember, you are looking for the minimum likely number, to prove it is more than people watching football, rather than the actual.
You should also bear in mind that the proportion of children playing is very different for girls than boys. A cautious minimum estimate could be
Proportion of girls = 0%
Proportion of boys = 25%
Therefore, total players = 0%*(6m/2) + 25%*(6m/3)
= 25%*(6m/2)
= 750,000
Therefore, the minimum likely number of people playing football in an average week is 750,000.
Next, work out how many people watch professional football.
There are two dimensions to the total number of spectators:
number of matches * number of spectators per match.
a) How many professional matches are there per week?
Assume that each professional team plays each week.
Number of matches = number of professional teams / 2
= 92 / 2
= 46
You may know the number of professional teams already â but don't worry if you don't. The best approach is to break it down further â into numberof leagues * teams per league. If you assume there are 4 leagues, and 20 â 25 teams per league, this gives you a range of 80 â 100 teams, or anaverage of 90 teams therefore 45 matches.
The interviewer will let you know if you are completely wrong on the number: the key thing is to show a logical approach to estimation.
b) What is the attendance at each match?
The first think to bear in mind is that attendance will vary significantly between the different leagues â so the Premier League would have muchhigher attendance than Division 2. You could start by assuming that each League has half the attendance per match than the previous league. Thismeans you only need to estimate the average attendance at a Premier League match.
Premier League total = 30k (this is an estimate)
Other Leagues total = 30/2 + 30/4 + 30/8
= 15k + 8k + 4k (round up)
All Leagues total = 30k + 15k + 8k + 4k
= 57k
All Leagues average = 57k / 4
= approx 15k
The actual number for average attendance is 15.4k, so very close to this number.
c) What is the total average attendance?
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Total attendance = matches * spectators per match
= 45 * 15k
= 675k (you can multiply this out longhand)
Therefore, the likely number of people watching professional football is 675k.
675k is less than the 750k minimum estimate for children playing football, which does not include the number of adults playing amateur football.
Therefore, more people play football than watch football in an average week.
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