[MD-sorular] Matematik ve futbol_2

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24 Haz 2008 Sal 12:06:19 EEST


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http://goal.blogs.nytimes.com/2008/06/14/a-draw-is-a-draw-is-a-draw-or-maybe-not/#more-548

June 14, 2008,  1:16 pm
A Draw Is a Draw Is a Draw - Or Maybe Not

By Peter Berlin <http://goal.blogs.nytimes.com/author/pberlin/>

Tags: Euro 2008 <http://goal.blogs.nytimes.com/tag/euro-2008>

ZURICH — Euro 2008 lurches into its final octet of group games Sunday night
with several places in the quarterfinals deliciously in the balance.

Turkey plays the Czech Republic in Geneva for the one remaining berth from
Group A. The two teams are level on points, goals scored and goals conceded.
What happens if they draw?

The position in Group C is even more tantalizing. On Tuesday, Italy and
France will stage their third World Cup final rematch in less than two
years, also level on points and goals. But the battle for second place
behind the Dutch could end in a absolute three-way tie if France and Italy
draw and the Netherlands beats Romania by three goals. What happens then?

It is enough to send any soccer nerd searching online for the competition
rules and leafing through the record books, with all their tempting
side-alleys, for precedents.

The Euro 2008 tie-breaking rules start off clearly enough. If two teams are
level on points, the first tiebreaker is the result of the match between
them. If more than two are tied it is the goal difference in matches between
the teams involved. Then it is the overall goal difference in group games.
After that comes total goals scored in group games. It is quite possible
that Groups A and C will end with a tie which none of these rules will
break. That is a pity, because at this point the rules grow a little
confused. There is an answer, however, and I shall get back to that later.

The four-team group format with two teams advancing may seem natural to us
now, but it was only arrived at by a long process of trial and error in the
World Cups.

The first World Cup, in 1930, had a four-team, first-round group, but also
three three-team groups. Only the top team advanced. After that, the World
Cup abandoned groups until 1950 when it was meant to start with four
four-team groups but, because three nations withdrew (the Scots in a fit of
pride), one group had three teams and another just two. Again only the top
team advanced.

In 1954 in Switzerland, the top two teams advanced but, bizarrely, each team
only played two other teams in its group. Germany was thrashed, 8-3, by a
Hungarian team in the process of reinventing soccer. Germany beat Turkey,
4-1, and ended up tied with the Turks, who beat South Korea, 7-0, in their
other game. The Turks, of course had a massively better goal difference, but
the two teams played off. Germany won, 7-2. It advanced to the final where
it met the ''Magical Magyars'' again, fell two goals down after eight
minutes, then fought back in the Bern mud to win, 3-2. Even 54 years later,
it is a result that must fill any non-German soccer fan with sadness.

In 1990, Ireland and Netherlands drew the last game in their group to finish
exactly tied on points, goals scored and goals conceded. Second place was
decided by the drawing of lots. The catch? Both advanced anyway under the
24-team format. Nevertheless, the Irish undoubtedly benefited. They faced
Romania in the second round, and advanced after a penalty
shootout. The Dutch had to face West Germany and went out.

The World Cup has stuck with four-team groups ever since, but had a period
from 1982 to 1994 when, because of the 24-team format, the top 2.66 teams in
each group advanced. In 1994, Bulgaria and Argentina and Ireland and Italy
tied exactly in their groups. The Bulgarians and Irish took second place
because they had won the head-to-head games, but it did not matter. The
Argentines and Italians still advanced, and Italy went on to reach the
final.

The European championship only started in 1960 and only got round to
dividing its teams — eight at the time — into groups in 1980.

The closest finish in a Euro group came just four years ago. Spain and
Greece drew in their second group game then both lost their final games, to
end up tied on points and goal difference. But, and this is something of a
surprise to those of us who think of the Greeks as the most goal-shy of
European champions, the Greeks advanced because they had scored four goals,
compared to two by the Spaniards.

Only once in either the Euros and the World Cup have two teams ended up tied
on points, goals scored and goals conceded, having drawn their head-to-head
game. That happened to Argentina and England in the 1958 World Cup. But
those were more leisurely days. There was time for a playoff and they met
again. Indeed there seem to have been no tiebreaker rules. Wales and Hungary
also tied on points in their group and played off, even though Hungary had
scored six goals and conceded three, while the Welsh scored and conceded
just two. Wales and Argentina won and advanced.

The most infamous tied group in World Cup history was in Spain in 1982.
Germany and Austria kicked off after Algeria had beaten Chile, 3-2, in its
last game. They therefore knew that a German victory would leave the three
teams tied but if the Germans won by two goals or less, Algeria would be
eliminated on goal difference.

Horst Hrubesch scored for Germany after 10 minutes. Nothing else happened.
Both teams advanced. The game was dubbed the ''Anschluss match'' and led to
a change in the tournament format. Now the final pairs of games in every
group are simultaneous.

It is relevant here, first, because it will be brought up again before
Germany and Austria meet again Monday in the tightly balanced Group B.
Second, because the simultaneous kick-offs could lead to a truly bizarre
situation in Group C on Tuesday.

That brings us back to how the ties will be broken. In the UEFA rules, after
goals scored the next tiebreaker is: ''coefficient from the qualifying
competitions for the 2006 World Cup and for the 2006/8 UEFA European
Football Championship (points obtained divided by the number of matches
played).'' Note that this excludes the World Cup itself. The reason is that
European qualifying is played under UEFA auspices, the finals are run by the
world governing body, FIFA.

But, these are clearly old rules, and since they were drafted for some Euro
tournament lost in the mists of time, it has occurred to some bright spark
that there was a flashier way to resolve things. (Nobody could be bothered
to stick that idea into the right place in the rules; it is appended in the
next section.)

What is that bright idea? A penalty shoot-out of course! If two teams draw
in the final round of games and then end up tied on points and goals, UEFA
can bring us a made-for-TV moment. It has never happened before, but it
could happened twice in three days.

If the Turks and Czechs draw, the referees will immediately ask for lists of
five names from each team and plonk the ball on one penalty spot while the
players embrace and link arms in the center circle.

But if the French and Italians finish their game level, they will have to
stand around and wait for the result of the Romania-Netherlands game. If the
Romanians get a result better than a three goal defeat, both the World Cup
finalists can troop off the field and head for the airport. If the Romanians
lose by more than three goals, Italy and France start blasting away on the
spot.

Things get really interesting if the Dutch beat the Romanians by exactly
three goals, as they did the French and Italians. Should the Romanians score
more goals in defeat than the Italians and French do in drawing, the
Romanians advance. If they score fewer, we're back to penalties. And if the
Romanians, French and Italians end up in an unbreakable three-way tie? Then
its those coefficients.

My math, and it isn't official UEFA math, suggests Italy will go through
with a coefficient of 2.36 points a game in two qualifying competitions,
edging Romania (2.25) and way ahead of France (2.09).

Of course, France or Italy can avoid such a situation by actually winning a
game. But so can Romania. If it beats the Dutch, it cannot hep but finish
second.

And that brings us back to the Anschluss match. The Netherlands has won the
group. It would no doubt like to keeps its considerable momentum going, but
that doesn't mean its coach, Marco van Basten, won't rest his key players.
Furthermore, there is a chance that the Dutch, if they reach the semifinal,
could again face the second-place team in its group. Who wouldn't rather
face Romania with the trophy on the line and nerves on edge, than those
veteran finalists, Italy or France?
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