Following up on my reviews of the Official Tournament magazine and the MATCH brand kid’s diary for recording results, and of the Panini Guide to the 2018 FIFA World Cup trading cards, here is my article on how scoring in the 2018 FIFA World Cup works.

As you know by now there are 32 teams in 8 groups, or 4 teams in each group, and 8 x 4 = 32 if you know your maths. The teams go through the Group stage where in each Group, each Team from one country plays against all the others in that Group which they have been allocated to. See this link * here* for information on how the draw for the groups works.

**The 8 Groups are labelled with letters from A to H, and this year are:**

**Group A**

Russia, Saudi Arabia, Egypt, Uruguay

**Group B**

Morocco, Iran, Portugal, Spain

**Group C**

France, Australia, Peru, Denmark

**Group D**

Argentina, Iceland, Croatia, Nigeria

**Group E**

Costa Rica, Serbia, Brazil, Switzerland

**Group F**

Germany, Mexico, Sweden, South Korea

**Group G**

Belgium, Panama, Tunisia, England

**Group H**

Colombia, Japan, Poland, Senegal

The team representing Australia, the country I live in, is in Group C and plays each of the other 3 teams in Group C. In other words Australia plays 3 other country teams in the group Australia is in, and all other 31 teams also play 3 other teams / matches in their Groups.

So, a total of 48 matches are played in what is called the Group Stage. 6 matches are played in each Group and 6 matches x 8 groups = 48 games or matches.

Now if you are a maths student looking at combinations and permutations, you could ask

“if there are 4 teams in 1 group and each team has to play or be matched against each of the other teams, how many matches would there be?”

Or put it this way: **how many unique pairs can be made from 4 items where order is not taken into account?**

It doesn’t matter if you write “France versus Australia” OR “Australia versus France.”

This “problem” mathematically speaking is a Combination Formula (at its simplest), written as:

## n C r

This actually means:

“What is the number of possible combinations of r items from a total of n items”.

In the FIFA World Cup example, we say “what is the number of possible combinations of 2 teams from a total of 4 teams?”

**The solution is: n! / r! (n – r)!**

Alas, we now encounter the** !** sign which is not just an exclamation of exasperation, but in mathematics, means FACTORIAL. When you see the special ! Factorial symbol, it means to multiply from the starting number denoted by a letter ( in this case by either n or r) by numbers descending by one, all the way down to one.

In our soccer example, we have n = 4 because a group is made up of 4 teams. r = 2 because we want to take pairs or 2 at a time from the total of 4.

n – r is 4 – 2 which equals 2 so we have in the divisor

4! / 2! x (4 -2)! or 4! / 2! x 2!

4! is 4 x 3 x 2 x 1 = 24

2! is 2 x 1 = 2

So we have 24 / 2 x 2

24 / 4

24 / 4 = 6

Like I said, 6 Matches are played in each Group !! The MATHS doesn’t lie, woohoo.

** So what, some of you may be saying at this point.** Well, I love mathematics and statistics and information, and the Combination Formula can actually come quite in handy in some real-life situations. What’s more, once you get into the maths of Permutations where the order of things matter, things can really heat up!

A

permutation, also called an “arrangement number” or “order,” is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself. The number ofpermutationson a set of elements is given by n! (n factorial; according to Uspensky 1937, p. 18).

If you can understand the above, give yourself a gold medal. A pictorial representation may make things easier to understand though.

You could say imaginatively that the above describes 3 kids going for a vaccination shot but none of them wants to go first (or even second or third, for that matter). Their exasperated parent wonders how many arrangements of all 3 recalcitrant kids there are, and using nous and pencil and paper scribbles out the possibilities, which of course are 6 as shown in the 3rd line in the sketch above. If I were the parent I would put each of the 6 permutations in a hat and randomly draw one of them, and the kids would have to go into the doctor’s room in that order. So there.

Now here is a nice looking JPG showing the formulas for both –

**C COMBINATIONS (where order doesn’t matter) and**

**P PERMUTATIONS (where order does matter)**

At the end of the Group Stage (consisting of 48 matches) comes the “Round of 16” (which I am really keen to watch) which as the name implies, consists of 16 teams. The SBS TV Guide shows how these talented 16 teams are matched in Matches 49 to 56 i.e. 8 matches.

You can see that the best 2 teams in each Group go through to the “Round of 16”, i.e. the outright Winner of each of the 8 Teams, A to H, plus the second highest scoring team, called the “Runner Up” of each of the 8 Teams.

Now you may wonder *“how does a team from a Group win their Group?*” and please note that I think that there is no such thing as a dumb question. In fact I think “good on a person for asking questions, as long as she learns from it”. Sometimes society thinks some things are common-sense or well known, but there are things which are neither. Take the movie “**Nell**” for example, starring the amazing Jodie Foster. Nell was raised by non-humans and had no sense of the common world of human beings, and no knowledge of or interest in things like mobile phones.

I have rather cleverly drawn up a hypothetical Table with made up Team Names and Results in a **Group Stage Group Results Table**. The Table below is for one of the 8 Groups. The kid’s MATCH diary for the FIFA World Cup includes this type of Table for each Group results. See this post HERE for information about the diary. Of course, to fill in a Table like the one below, you need to know the scores / results for the individual matches played by each of the 4 teams in a Group.

**Hypothetical “raw data” for the table above is shown below.**

**Teams Win/Draw**

A v B A 6 goals v 2 goals

A v C A 5 goals v 0 goals

A v D D 2 goals v 3 goals

B v A A 2 goals v 6 goals

B v C draw 1 goal v 1 goal

B v D B 4 goals v 0 goals

C x A A 0 goals vs 5 goals

C x B draw 1 goal vs 1 goal

C x D C 1 goal v 0 goals

D x A D 3 goals vs 2 goals

D x B B 0 goals vs 4 goals

D x C C 0 goals vs 1 goal

**Points are allocated as follows.**

**Win ** 3 points

**Loss ** 0 points

**Draw** 1 point

**GF** = Goals For **GA** = Goals Against

In this example, Australia is the outright winner with the most Points, 6, but after Australia, going by Points alone, both the Bahamas and the Caribbean have an equal number of Points, being 4.

The **Goal Difference** (GD) is looked at when more than 1 team has equal points.

**GD = GF – GA**

In our example, the Caribbean team had 2 Goals For (or they scored 2 goals overall) and had 6 Goals Against them (meaning overall the Teams they played against in their group scored a total of 6 goals).

**GD = 2 – 6 = – 4**

The **BAHAMAS** are the** Runner-ups** having 4 points but having the lowest Goal Difference, in this case, zero. GD = 7 – 7 = 0 for the Bahamas, in this example.

Y**ou can read more about the FIFA World Cup scoring** at my other blog * HERE* if you like, as beyond Goal Differences (i.e. if 2 teams have the same GD) other measures are used to ascertain the top 2 teams in a Group..

**Results Sheets**

I find the best hard copy Results sheet to fill in is actually the one in the * Guide to the Panini Adrenalyn XL FIFA 2018 trading cards*! It is set out on one A4 page and allows one to fill in the Goals won for each of the 48 games of the 8 groups, then of course for each Match in the Round of 16 onward. You can see the Results sheet, if you want, by scrolling to about half-way down the Post

*here .*The Round of 16 involves the Winner of each Group playing against the Runner-up of the other Group in the pairs AB, CD, EF, and GH. For example, the Winner of Group A plays against the Runner-up of Group B, and the Winner of Group B plays against the Runner-up of Group A. See the picture of the SBS Guide above, in this Post. The Round of 16 is made up of Matches 49 to 56.

As its name implies, the **Quarter-finals** **(QF)** consists of 4 matches, the **Semi-finals** **(SF)** of 2 matches, and the **Final** is one Match, with the 2018 FIFA World Cup grand final winner coming out victorious.

As by now you may have worked out, the **QF** comprises 4 matches, Match 57 to 60, being the winner of Match 49 against the winner of Match 50 and so on ( 51 v 52, 53 v 54 and 55 v 56) – but not playing or broadcast on television in this order.

The **SF** consists of the Winner of Match 57 against the Winner of Match 58, and the Winner of Match 59 against the Winner of Match 60. These are Matches 61 and 62.

The Winners of these latter 2 Semi-final matches, go into the Grand Final. The Final is Match 64. The Losers of Matches 61 and 62 go into the 3rd place play-off, which is Match 63.

So there you have it, unless I have got anything wrong (in which case, please let me know nicely). Because I love data and the FIFA World Cup and scoring, I have typed out a Results Sheet for all the 48 initial matches of the Group Stage and for the full Group Stage Results and Round of 16 onward. I am providing them as Word Documents in both DOCX format and DOC format below.

2018 FIFA WORLD CUP RESULTS – docx

2018 FIFA WORLD CUP RESULTS – doc

Neither the SBS TV Guide or the Official FIFA World Cup Tournament Programme include score / results sheets, or have a large pull-out Sheet for recording Results. So I decided to produce my own.

**UPDATE**: I have added a post to my other blog “Our Lovely World” explaining penalties, yellow & red cards, and how the teams get through to the Final. **Click here to go there.**

**I hope someone reading this truly appreciates this post, and shares it with others.**

### Thank you.

Categories: Mathematics, Self-help, Sport