championship system. How to identify the best two out of three teams? To be honest?

Xintrea2012-07-29 23:44:18

Algorithms

Xintrea, 2012-07-29 23:44:18

We have three teams A, B and C. We play, for example, hockey. It is necessary to choose the two strongest from three teams.
We arrange the championship according to the scheme "each with each" (not discussed). Then it turns out that three games will be played:
A with B
A with C
C with B
Let the goals be scored in this way:
A with B -> 100:105 -> Team B won
A with C -> 1:2 -> Team won C
C with B -> 2:1 -> Team C won
Now, if we choose by the results of the games (win/lose), it turns out that the best teams are B and C.
But this is somehow unfair to the A team, because they scored 101 goals, and the C team only 4 goals. On the other hand, if you choose by pucks, then A and B are the strongest. But this is unfair to Team C, because they won two games.
Question: how to organize a championship for three teams to be fair?

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10 answer(s)

la0, 2012-07-30
@la0

maybe in the AB match, all goalkeepers on both sides were sent off for behavior. Here is the result.
Outcome. Washers are not taken into account.
With equality, you can take into account not the absolute number of goals (scored-missed), but relative. (blanked/omitted), because 107/106 2/1
In any case, the word "honesty" will have to be replaced by the word "regulation", which may include a random definition as a last resort. (see the regulations of the last football championship).

NeverFoldAQ, 2012-07-30
@NeverFoldAQ

What difference does it make how many goals a team scores in one single match?
Team A scores 0 points and there is nothing unfair about that. She lost to all opponents. Distance is what it is.
Is it fair to consider a novice poker player who sits down at the table and wins N-amount in 2 hours, if he loses it by the end of the month, more skillful than some Phil Ivey who has consistently won the same N-amount for a month? :)
With an equal number of points, I consider the following algorithm to be fair:
Points -> personal meetings -> difference between goals scored / missed.

winbackgo, 2012-07-30
@winbackgo

Wins are counted in championships. And who scored there and how much is a completely different statistic.

LeoCcoder, 2012-07-30
@LeoCcoder

First you need to decide what is the strongest? Who wins or who scores more goals? This problem cannot be solved exactly.
Suppose we have 3 identical teams, what should we do then?
Or, for example, 1 strong and 2 equally weak? how to choose 2 strong ones?
In your example, when out of 3, when you need to choose 2, you need to play 2 games: A with B, whoever wins is included in the strongest. The loser plays with C, whoever wins is in the strongest. Total 2 strong teams selected.

65520, 2012-07-30
@65520

0. Determine the criterion of fairness;)

Alexander Zelenin, 2012-07-30
@zelenin

you do not want to determine the most scored team, but the strongest. Obviously, the teams that scored and conceded 100 goals each, firstly, failed the match, which means they are weak, and secondly, they are practically equal in strength according to the results of the match between themselves.

kamiram, 2012-07-30
@kamiram

traditionally there are 2 approaches.
I tend to be more honest (10 down 20 out == 1 down 2 out)

ShadowMaster, 2012-07-30
@ShadowMaster

Hockey? What difference does it make how many goals they scored? The rules of the game say that the one who scores more goals than the opponent wins.
Won the Russian national football team in the last European Championship scored more than missed, but lost the tournament.

mithraen, 2012-07-30
@mithraen

If you consider the ratio, then there will be a problem with division by zero.
It is more logical then to consider the difference between the account divided by the amount of the bill.
Then the loser will have a negative result.
The disadvantage of this system will be only that the score 0:1 and 0:100 will lead to an identical result in the ranking.

MiXei4, 2012-07-30
@MiXei4

Why it is wrong to count the number of goals instead of wins
1. Anything can happen in any given match. Injuries to leaders, removal of a couple of players, rain on the field, sun in the eyes, and so on. Therefore, you can only compare indicators from other matches with this one in extreme case
2. In your example, you can see that the weak teams A and B stupidly played an agreement so that under no outcome team C would go further. (if you count the goals).