|The curse of the knock-out
system - How likely does a favorite team become World Cup winner
A first investigation...
(In the following all matches
that were decided by the penalty lottery are counted as ties).
It is more difficult
for the best team to win the World Cup as many believe. This is caused
by the way the Cup is played. A knock-out system does not forgive a mistake
in the wrong moment, a bad day, or even just bad luck. Remember Brasil
1990. Maybe they were a team about to lose only one of twenty matches,
but they had this match in the first knock-out round. So they did not have
anymore matches to prove how strong they were and went home as a failure.
It is almost impossible
a team to win 7 consecutive matches. Most teams who reach the finals
of such big tournaments, have to sneak through somehow at some point, or
at least had a low point in the first round. The only team that
could win all their matches since the second world war has been the
of 1970. But since then football has changed, the matches have become
closer, more and more decided by single moments. Germany 1982, 1986, and
1990, needed a won penalty shoot-out along their way to reach finals,
in 1982 and 1986 they had lost first round matches to Algeria and Danmark.
Italy 1982 and 1994 had struggeled in the first round and somehow got through,
while the strong 1990 squadra had their problem suddenly in the semis.
Belgium made the semi-finals 1986 despite
winning only two matches,
Sweden did not win any more 1994 (apart from the 3rd place play off). And
Brasil 1994 had the necessary luck of most of the recent World Champions:
with Netherlands they had only to beat one single top team
to reach the finals in which they then could not defeat the Italians in
120 minutes - they needed a penalty shoot-out.
The same can be said of
France 1998: only two of the superpowers crossed their way: Brasil
in the final and Italy in the quarter final, again a penalty shoot-out
Imagine your machine
is runnung well right from the start. This can be a cloud to sail on but
it can be a psychological problem as well. There is not much room for improvement
but for doubt. Suddenly there occur problems. Many teams which played
above their average potential for some matches then were bitterly punished.
Think of USSR and Denmark 1986, even Spain. Romania could not keep the
same level for all matches in 1994. Among teams that struggeled in the
first round and then pulled together were Germany 1982, 1986, Italy 1982
and 1994, Bulgaria 1994, Argentina and England 1990, or Germany 1974. Sometimes
it is very good to have a bad moment in the first round and then see yourself
improving. It is only very difficult to plan such a moment.
Now we come to the
chances for the favorites to win it. First one has to define what percentage
means here. Let us create a 'best team of the world'. Let us call it
Brasil. If you say this Brasil wins the next match by 85%, despite the
high value, this does not mean at all that indeed Brasil will win. It only
means, was the match played 100 times, our Brasil might win round about
85 times. But which match you will see, one of the 85 or one of the other
15, this value does not tell you at all. Another way to look at it: Winning
6 of 7 matches is a terrible high value. It means anyway that you do
win one of those seven matches. If you think of the World Cup, which
one will it be? A first round match? A knock-out match?
Anyway this value is much
to high. Brasil might win its 6 of 7 matches against minnows but think
of the matches against Argentina, France & co. In those matches the
odds should be almost down to 50:50. The way teams have to go in their
World Cup adventures is hard to predict. It has showed in the past that
not all favorites who make it through to the second round win their groups,
usually some of them, qualify as runners-up. This could mean, and now we
turn to the World Cup 2002, that instead of a considered relatively easy
2nd round match match against Senegal, Uruguay, or Danmark, the World Cup
co-favorites Argentina could face World Champions France.
It is possible that
France has to beat England, Brazil, and Argentina to reach a final while
someone else might to have to put off 'only' South Africa, Mexico, and
Let us pick France
as our superteam and let us consider an average value of 75% (made of a
90 % against Nigeria and a 60 % against Argentina), what is very, very
high, for France to advance in any play-off match. As shown before,
this value means, if looked at from the other side, France would lose one
of four matches (or at least draw and go out on penalties). So it is obvious,
France, as any other team, to win the World Cup have to be above-average
lucky: They have to win all four knock-out matches in a row! This requirement
of luck is caused by the number of four play-off rounds and the high number
of participating teams, this is not because France are not strong enough.
Now you can calculate the
probability of France winning: It is 75% of 75% of 75% of 75%. Or easier:
Only in 31,6% of the
cases this superteam team wins the World Cup.
This is less than every third World Cup. And this value even neglects
the slim possibility of an early first round failure and does not take
the qualification into account as well.
That even this value is too
high, you can easily imagine, if you consider the following: The 100% have
to be distributed on all the 32 participating teams. OK, you might be able
to neglect some teams now, but if France has 30%, there are only 70% left
for Argentina, Italy, Cameroon, England, Germany, Spain, Japan,
and Portugal (plus all the rest). This means less than 10% in
average for each of those giants. Now you might start to develop a
feeling for how much luck is involved in winning such a tournament.
If you played out the
championship on a league basis, this all would become different. But
the effect we can watch here in the play-off system is caused by the fact
that a team that has lost, cannot play on anymore to recorrect their result.
In a league you can lose the first match and win the rest, in knock-out
football you are out. Also teams might face a schedule of different
Remember that Brasil has
had brilliant teams at each World Cup since 1982 but anyway not reached
the semi-finals between 1982 and 1990!
(About all single evaluations
you could argue, but you should try to see there is a general tendency
that is not much affected by changing the values by some percent).
Anyway, single results
of such stochastic processes are not predictable and somebody has to
Why not France?
That this is not a fantasy
of The Shot That Passed Right Throught The Net you can see when you analyse
the odds of the bookmakers. For those real experts (they risk their existence
if they evaluate wrong) the hottest favorites are rated only at about 20
% or lower to lift the Cup.