SOCCER AND COIN TOSSING

Under 20 COSAFA semis going on today: South Africa vs. Zimbabwe and Angola vs. Mozambique. However, that’s not the main story. The main story is that Zimbabwe won the right to play South Africa with the toss of the coin as both Zimbabwe and Malawi were tied on seven points. Are you kidding me? Why did they have to toss the coin? Looking at the standings Zimbabwe had a better goal aggregate than Malawi so why even bother to do the coin tossing? What if the coin tossing was in favor (American) of Malawi? Throwing subjectivity away, it’s good that the coin toss was in favor of Zimbabwe. The coin tossing rule was “thrown in” a day before their “final” matches played yesterday: Malawi 3 Botswana 2; Zimbabwe 2, Mauritius 1. Had Malawi beaten Botswana 7-2, Malawi and Zimbabwe would have been equal on everything. In that case, yes, coin tossing would have made a little bit of sense considering that the Semis are being played today. Since they were not playing against each other penalties and extra time were out of the equation.

Coin flipping or coin tossing is the practice of throwing a coin in the air to resolve a dispute between two parties or otherwise choose between two alternatives. It is a form of sortition that by nature has only two possible outcomes: Head and tails; ship and head; cross and pile; etc.

In soccer, coin flipping is used to decide which end of the field the teams will play to and/or which team gets first use of the ball, or similar questions in soccer matches. I think coin flipping should be restricted to that. It shouldn’t be used to decide who wins if the game ends in a draw or who goes to the next round in case the teams are tied on points. To my knowledge thus far, the team that scores the most goals by the end of the match wins. If the score is tied at the end of the game, either a draw is declared or the game goes into extra time and/or a penalty shootout, depending on the format of the competition.

Is coin tossing unbiased way of settling a dispute or deciding between two or more arbitrary options?

In statistics, a fair coin is an idealized randomizing device with two states (usually named “heads” and “tails”) which are equally likely to occur. It is based on the ubiquitous coin flip used in sports and other situations where it is necessary to give two parties the same chance of winning. Depending on the occasion a specially designed chip or a simple currency coin is used, which due to unequal weight distribution might be “unfair”: one state might occur more frequently than the other, giving one party an unfair advantage. So it might be necessary to experimentally determine whether the coin is in fact “fair” – that is, if the probability of the coin falling on either side in the toss is approximately 50%. It is of course impossible to ever definitively rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping, and it is always possible for an unfair (or “biased”) coin to happen to turn up exactly 10 heads in 20 flips. As such, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process given only a limited sample of Bernoulli trials.

Experimental and theoretical analysis of coin tossing has shown that the outcome is predictable, to some degree at least, if the initial conditions of the toss (position, velocity and angular momentum) are known. Coin tossing may be modeled as a problem in Lagrangian mechanics. The important aspects are the tumbling motion of the coin, the precession (wobbling) of its axis, and whether the coin bounces at the end of its trajectory.

The outcome of coin flipping has been studied by Persi Diaconis and his collaborators. They have demonstrated that a mechanical coin flipper which imparts the same initial conditions for every toss has a highly predictable outcome — the phase space is fairly regular.

Moreover, they have demonstrated both mathematically and experimentally that the underlying physics of coin tosses appears to have a slight bias for a caught coin to be caught the same way up as it was thrown, with a probability of around 0.51. Stage magicians and gamblers, with practice, are able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.

Since the images on the two sides of actual coins are made of raised metal, the toss is likely to slightly favor one face or the other. This is particularly true if the coin is allowed to roll on one edge upon landing; coin spinning is much more likely to be biased than flipping, and conjurers trim the edges of coins so that when spun they usually land on a particular face.

There you have it.

It seems the football organisers will never learn. Do you remember the 8 BEST RUNNERS UP hocus pocus? Qualification rules were introduced while the competition was already in progress and then here again we have COSAFA introducing the coin toss rule two days before a semi final match?

To conspire means “to join in a secret agreement to do an unlawful or wrongful act or to use such means to accomplish a lawful end.”

P/S

My post was based on Group Standings reported on kickoff.com.
However, looking at the results of the matches I found out that the standings are not correct:

Malawi 5 Mauritius 0
Malawi 3 Botswana 2
Malawi 0 Zimbabwe 0
Zimbabwe 3 Botswana 2
Zimbabwe 2 – Mauritius 1

Both Malawi and Zimbabwe had 7 points but Malawi scored more goals than Zimbabwe and also conceded less goals than Zimbabwe.

Was it a deliberate mistake by kickoff.com? Part of the conspiracy?