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Fantasy football can be fun, but don't you just hate it when you forget to make the changes one week and any chance of victory disappears? The same with those office footy tipping contests. They are not much fun when you are so far behind that you cannot catch up whatever you do.
Which is what attracted me to the idea of probability based sports tipping.
On Newsvine we are running two of these thinking person's tipping contests - one on the NFL and the other on the English Premier League soccer. You will find details on my home page
They are games of real skill where we can have a weekly winner.
They work this way
The probabilistic competition involves the tipper entering the probability (between 0 and 1) that they believe a team will win the match. It is sometimes also referred to as the information theoretic or info competition. The father of information theory was Claude Shannon.
In a traditional tipping competition, the tipper is forced to choose one team as the outright winner. However the tipper still believes that the other team does have some chance, just not as much as the team they chose. (In closely matched games, you may even think it will be a draw.) Choosing a probability allows the tipper to express their uncertainty or confidence level in the outcome.
It can be simply proven that the highest expected score can be achieved by tipping the true probability. (Even though the true probability is never known.)
The scoring system works as follows: If the tipper assigns probability p to team A winning, then the score (in "bits") gained is:
* If A wins: 1 + log2(p)
* If A loses: 1 + log2(1 - p)
From the above we can see that the maximum gain of 1.0 is obtained by tipping 1.0 on the winning team. This however is very risky as maximum loss of -Infinity is achieved by tipping 1.0 on the losing team.
The scoring is not symmetrical and can be very non-intuitive for the beginner. The table alongside gives example tips and the scores (in bits) you would receive if your team won and if your team lost. Note that p values less than 0.5 are equivalent to tipping the other team with 1.0-p. Also, p=0.5 is equivalent to sitting on the fence - you neither gain nor lose any bits.
If there is a draw, the average of the win and loss scores are taken:
* If A draws: 1 + ½·log2(p·(1-p))
This is an upside-down "U" shaped function, which is negative for every value of p except for p=0.5. If you think a draw will occur you should tip 0.5. If correct, your reward is to lose no bits; everyone who tipped otherwise will lose bits.
