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Say you predicted that Brazil would have beaten Germany 2-1, by how large a percentage were you wrong?

As Brazil scored 1 out of 2 goals, you could say that part of your prediction was 50% right. However, as Germany scored 7 times the number of goals, that's less accurate. On top of this, the combination of the two scores has me perplexed and any help would be much appreciated.

To summarise, how accurate is your prediction given the following:

Predicted Score: Brazil 2-1 Germany
Actual Score: Brazil 1-7 Germany
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  • $\begingroup$ On a more mathematical basis, a percentage describes the number of possible "good" outcomes divided by the number of total possible outcomes. To define "how large" you were wrong, you need to define "good" and most importantly "outcome", and then give weights to each outcome. This can be done in many different ways, and choosing one is up to what you want your percentage to represent. $\endgroup$ – Patrick Da Silva Jul 12 '14 at 21:38
  • $\begingroup$ ... Secondly, thanks for the more mathematical answer. I am trying to calculate how close the "correct score" prediction was to the ultimate actual score. If that can be expressed in percentage terms... (ed ajf) $\endgroup$ – Dan Jul 12 '14 at 21:47
  • $\begingroup$ My answer was essentially "mathematics alone canot tell you the answer". You have to decide what you want this percentage to mean. Do you want it to explain how badly the number of goals of Brazil was wrong? How the goal difference Brazil-Germany was wrong? (i.e in the 2-1 B/G it is +1, in the 1-7 it is -6), do you want the quadratic error as in statistics? There's no preferred option. Personally I'd like to say that since the predicted score was Brazil +1 and the actual score was Brazil -6, I'd like to say that this was 600% wrong, but then again, it's personal. $\endgroup$ – Patrick Da Silva Jul 12 '14 at 21:59
  • $\begingroup$ I suspect many people would agree that a prediction of 1000-1 for Germany is closer than one of 1-0 for Brazil. $\endgroup$ – Théophile Jul 12 '14 at 22:53
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It is common for a lot of people to assume that mathematics by itself has the answer to questions regarding "real life". While mathematics certainly does help in some cases (like telling us there is no way to cross the seven bridges of Königsberg exactly once), mathematics offers no general truth about the real world of human affairs.

It is only by defining (in mathematical terms) exactly what you mean by "how accurate", "how much wrong" etc., that you can use the tools of mathematics to answer your question.

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  • $\begingroup$ Great answer! It gets to the core of the problem. The next step would be suggesting a way to formalise the intuitive notion of how much wrong $\endgroup$ – Ant Jul 12 '14 at 23:00
  • $\begingroup$ @Ant Thank you. I will give it some thought, but I suspect there is no general consensus on the matter, and it might be more educational to let the OP think about how to formulate those terms in a precise (mathematical) way. $\endgroup$ – naslundx Jul 12 '14 at 23:07
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It is impossible to assign a percentage score to the prediction. Speaking as a mathematician, I would have to score it as "almost as bad a prediction as possible". Your claim that "part of [the] prediction was 50% right" is nonsense.

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You cannot measure your model's predictive power that way. You should measure it in the long run, for example, you calculate the probability of all correct scores for any given match, for many matches, and then you could use brier score to see how well you did. check it

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