Pe Po Pr


Many analysts declare that something is possible. But possibility is very cheap and ought to be avoided if it can not be quantified in terms of probability. Whenever an analyst states that something “can” happen, then you ought to be really on your toes. Because anything you can think of can happen. It can happen that Ronaldo will become a German and win the worldcup with Germany at the age of fifty. It is highly unlikely that this will happen, but even the most unlikely cases have an extremely small chance of happening. That is why stating that something “can” happen, is cheap if you do not include a probability of it actually happening.

On top of that it is very easy to find out how probable you think something is that according to you estimations can happen. You only have to figure out what kind of bets you would accept and which bets you would refuse. Let’s take as an example the following possibility: The Netherlands can win the World Cup within the next twenty years.

If you state it like that, it has very little meaning. San Marino, currently ranked last, can also win the World Cup within the next twenty years. As you can see: without concrete probabilities these kinds of statements say very little. So let’s see what kind of probability you give to the Netherlands winning the World Cup in the next twenty years. In the following table look up which bet you will take and which bet you won’t take. That is the point where your probability estimation for this event lies:

You win this amount when the Netherlands become World Champion in the next twenty years You lose this amount when the Netherlands did not become a World Champion in the next twenty years Your probability
90 euro 10 euro 10%
80 euro 20 euro 20%
70 euro 30 euro 30%
60 euro 40 euro 40%
50 euro 50 euro 50%
40 euro 60 euro 60%
30 euro 70 euro 70%
20 euro 80 euro 80%
10 euro 90 euro 90%

You see that the more you are willing to lose, the higher you estimate that the probability is.

So instead of saying that something “can” happen, every analyst ought to state what he thinks the probability is of that actually happening. Without those probabilities, the analyst is not saying anything meaningful by stating that something “can” happen.

Once analysts start adding concrete probabilities, we can then go to the next step and calculate the prediction error these analysts have in their analyses. The precision error is the gap between the prediction and how reality turned out. Say that you thought that there was a 40% chance of the Netherlands becoming World Champion in the next twenty years. If the Netherlands actually did become World Champion in that period your prediction error was 60%. This is calculated by subtracting your probability estimation of 40% from the 100% of it happening for real. If the Netherlands did not become World Champion then your prediction error was 40%, which is calculated by subtracting 0% for the fact that the Netherlands did not become World Champion of your 40% probability estimation.

This way you can keep track of how well analysts are doing. So you can value reports from analysts with a very small prediction error over the reports from analysts with a much bigger prediction error.