How fair is the World Cup?

With England through to FIFA World Cup semi-finals, I am wondering: how fair is the knockout system that determines the first, second and third-place winners?

To simplify things, let us assume that the teams can be ranked in order of their relative strengths, and that each team plays consistently to its ranking, so that a higher-ranked team will always beat a lower-ranked one. (Yes, I know this is a gross oversimplification.) Let us also assume that the seeding system used by the organizers is fair, so that the eight seeded teams (which include the host nation) are the top ranking eight teams (another big assumption).

These 8 seeded teams were then assigned randomly to 8 groups and based on our assumptions, each seeded team could be expected to win its group. It would then meet a different group’s (unseeded) second-place team in the round of 16, which it could also be expected to beat. So, based on our assumptions, the quarter-finalists should be the top-ranking eight teams.

In the knockout competition, the winning finalist is awarded first place, the losing finalist second place, and the losing semifinalists compete in a playoff for third place. So using this system, the #1 ranked entrant will always get first place.  But, based on the random way the teams have been bracketed together, what are the chances of a team winning second or third place?

Well, I did the math, and here are the chances for each team’s possible outcomes:

Team rank 1st place 2nd place 3rd place Playoff loser Eliminated in quarter-finals
#1 1 0 0 0 0
#2 0 4/7 2/7 0 1/7
#3 0 2/7 3/7 0 2/7
#4 0 4/35 8/35 8/35 3/7
#5 0 1/35 2/35 12/35 4/7
#6 0 0 0 2/7 5/7
#7 0 0 0 1/7 6/7
#8 0 0 0 0 1

As you can see, the knockout system is only accurate for determining the first-place winner and there is a very good chance that the second and third places won’t go to the “right” teams.  There’s even a chance that the second-place winner could be the #5 ranked team!

In fact, there’s only an 8-in-21 chance that the #2 and #3 teams will both be placed correctly, a 4-in-21 chance that their places will be reversed, and a 3-in-7 chance that one or other of them won’t get placed at all.  The only certainty is that at least one of these two teams will get second or third place.

Note that this analysis doesn’t take account of the random factors that affect every team’s match-day performance: it only reflects the advantages and disadvantages that can arise from the “luck of the draw.”

Conclusion: the World Cup’s knockout system is not very fair at all when it comes to allocating second and third places.

DISCLAIMER: I’m posting this before England’s semi-final game is played, so don’t consider this to be sour grapes!

The Cryptolaundry

Below is a blog entry that I posted back in 2010. Although I was talking about the money markets at the time, what I said back then is even more applicable today to the cryptocurrency ecosystem.

Sometimes I like to think of the banking system and the financial markets as a gigantic Magic Money Machine. They create money out of nothing and spread it around. Most of the time this magic works very well, and everybody has money, and the shops are full of things they can buy, and everyone is happy.

But every once in a while something goes wrong with the machinery, and the magic starts working backwards. Instead of money being made, it starts disappearing. And suddenly nobody has any money, the shops start closing, and everybody is sad. Yet no-one has taken the money, and nobody even knows where it went. It has just vanished, like fairy dust.

Because money, like fairy dust, only works if you believe in it. And when people stop believing, the magic dies, and their money turns back into the worthless paper (or more commonly these days, the worthless bits of information) from which it was made.

Today it seems to me that the whole alt-coin infrastructure is like a gigantic laundry business that depends on a bunch of guys who (in the words of the old saying) have been earning a precarious living by taking in one another’s washing. But when the going gets tough and their operation becomes unprofitable, they will simply turn off their machines and walk away. And then alt-coins will be seen as the worthless bits of information that they always were. And their price won’t just go to zero–there won’t even be a price.

The First Lord’s Song

When I was a lad I served a term
In Father’s real estate construction firm.
I cleaned the windows and I swept the floor,
And I polished up the handle of the big front door.
I polished up that handle so carefullee
That now I am the ruler of Amerikee!

As Apprentice I made such a mark
I built two skating rinks in Central Park;
I made those skating rinks so very slick,
That I learned the art of double-dealing double quick.
I wheeled and dealed so artfully,
That now I am the ruler of Amerikee!

As a dealer I made such a name
That I went to play in the casino game;
My funds went up and up by leaps and jumps
For in every hand I dealt myself the cards were trumps.
The casinos filed for bankruptcy,
But I became the ruler of Amerikee!

From royal flushes I earned so much
That to pageantry I turned my touch
I carefully inspected every beauty queen
As the only reigning monarchs I had ever seen.
But that kind of reign so attracted me,
That now I am the ruler of Amerikee!

I grew so proud at last I went
On a ego-trip to run for President.
I raved and ranted for a border wall,
And I never thought of checking any facts at all.
I thought so little, they rewarded me
By making me the ruler of Amerikee!

Now, billionaires all, whoever you may be,
If you want to rise to the top of the tree,
If you’re not ashamed to play the fool
Be careful to be guided by this golden rule –
Ignore all the facts, and tweet outrageously,
And you all may be rulers of Amerikee!

The Little Drummer Boy

Christmas makes me sore, parumpumpumpum
It’s only half past four, parumpumpumpum
But I can sleep no more, parumpumpumpum
The little boy next door, parumpumpumpum rumpumpumpum rumpumpumpum,
Has a new drum.

Why did Santa bring, parumpumpumpum
Such a confounded thing, parumpumpumpum
His neck I’d like to wring, parumpumpumpum
Can’t hear the angels sing, parumpumpumpum rumpumpumpum rumpumpumpum,
Over that drum.

Isn’t this a bore, parumpumpumpum
Can’t take it any more, parumpumpumpum
This is a state of war, parumpumpumpum
I’m going to go next door, parumpumpumpum rumpumpumpum rumpumpumpum,
With my gun.

Wet Christmas

The sun is shining, the grass is brown
The water has gone away
There’s never been such a day in Beverly Hills, L.A.
This drought has lasted for far too long,   and so we’re going to sing this song….

We’re dreaming of a wet Christmas
Just like in Portland, Oregon
Where the skies are foggy, the ground is soggy
And all the sprinkler bans are gone

We’re dreaming of a wet Christmas
With every Christmas card we get
May it be the rainiest yet
And may all your Christmases be wet.

Airline food

 

 

Fly Chicken and Leek casserole

I don’t know whether to be disappointed or relieved: I couldn’t find a single fly in my casserole.

Roadtrip, anyone?

Here’s the solution to last week’s traveling pea soup salesman problem.

The shortest possible round-trip route visiting all 35 towns is 3198 miles, as follows (of course you can start at any point on the circuit and proceed in either direction):

Eureka; Redding; Chico; Susanville; Truckee; Sacramento; Stockton; Modesto; Santa Nella; Merced; Sequoia Park; Selma; Fresno; Yosemite; Bishop; Barstow; Needles; El Centro; San Diego; Palm Springs; San Bernardino; Riverside; Long Beach; Los Angeles; Bakersfield; Ventura; Santa Barbara; Buellton; San Luis Obispo; Monterey; Santa Cruz; San Jose; Oakland; San Francisco; Santa Rosa; Eureka.