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# fallacious comparison

## Question

Someone attempts to compare Zidane to Cruyff, in terms of the honours they bear with their national teams in the World Cup-finals (from now on symbolized WC).

Initially, he considers the first WC in which each of them participated. Cruyff was a runner-up with Holland in the 1974 WC, whereas Zidane was champion with France in the 1998 WC. Thus, in the first place Zidane prevails over Cruyff in one honour.

Bearing this in mind, he then observes that Zidane was a runner-up with France in the 2006 WC, whereas Cruyff didn't participate any more in WC-finals. Consequently, it seems to him now that Zidane bears on the whole two more honours than Cruyff, as to their WC participations. This, though, is fallacious. Both players were runners-up once (Cruyff in the 1974 WC, Zidane in the 2006 WC). Thus, Zidane bears only one more honour in comparison to Cruyff as to their participations in WC-finals-, since he won the 1998 WC with his national team.

On the whole, if we correlate the 1974 and 2006 WC, and consider in isolation the 1998 WC, we draw a conclusion which is different from the conclusion we arrive to, correlating the 1974 and the 1998 WC, and considering in isolation the 2006 WC.

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All I know is the headbutt was cool.

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What the above case shows- I think- is the fact that there are cases where there is a mismatch between a set of data and the splitting of this set into parts. Specific correspodences between the parts of the whole (the set) lead to conclusions who differ from each other, as well as from the whole, and can lead to misleading conclusions. Recall the famous Simpson's paradox, where-albeit in a quite different level- the reverse is observed:it is the whole data that lead to misleading conclusions, whereas the analysis in depth reveal the truth

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