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A guy told me that he can predict which player I would choose from Greece's Euro 2004 Champion football team. Assume my choice was random.

He then goes ahead and names all the players of the team.

He claims that he aced the prediction, since he achieved a perfect score - no chance that he would have missed my random choice when said all possible choices!

What metric did he optimized?

  • Accuracy
  • Precision
  • AUC
  • Recall

Related: https://towardsdatascience.com/the-5-classification-evaluation-metrics-you-must-know-aa97784ff226

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    $\begingroup$ What arguments do you have for or against each of your choices? $\endgroup$
    – Dave
    Jul 5, 2021 at 4:19
  • $\begingroup$ Is this supposed to be a quiz question for us? Not sure if SE is the right place for that. $\endgroup$
    – Jonathan
    Jul 5, 2021 at 13:55
  • $\begingroup$ @Sammy I was asked this question in an online test. If you think Cross Validated is better suited, then let me know and I'll migrate it. $\endgroup$
    – gsamaras
    Jul 5, 2021 at 14:02
  • $\begingroup$ I don’t mean which arguments are given in favor or against the four choices; I mean for you to argue for or against them. $\endgroup$
    – Dave
    Jul 5, 2021 at 16:02
  • $\begingroup$ @Dave I would say recall because the guy wants to make sure that he named the player I chose. Is that what you are asking please? $\endgroup$
    – gsamaras
    Jul 5, 2021 at 16:37

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The prediction algorithm resulted in only positives, and no negatives, i.e. it predicted that every member of the roster was a member of the target class, with the target class being "your pick".

Of the positive results predicted by the algorithm, there was 1 true positive and N-1 false positives, from a roster of size N.

  • In that case, the recall True Positive / (True Positive + False Negative) = 1 is maximized.
  • In the absence of negative predictions, the precision and accuracy are equal: True Positive / (True Positive + False Positive) = 1/N
  • The meaning of the AUC is ambiguous, in an absence of the ordering of the predictions.
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