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I often see similar statements on football (soccer) websites.

Team A has lost 4 out of their last 5 matches against Team B. (and thus, there is a high chance Team A will lose their next match tomorrow against Team B.

But if I procede to find out the matches played, the most recent of their last 5 matches would be something like 10 years ago! So in that span of 12 years (between 2000 and 2012), the entire team would have changed, the manager has changed etc.

So is it flawed to write statements like that?


Also, if a team just plays 1 game (assuming you can only win or lose, no draw), looking at their win percentage without seeing the number of games played could be misleading as the win percentage could be 100% or 0%. But as they play more games, you get a better idea of their "actual" win ratio. Is there some sort of statistical term for that?

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I wouldn't say it's exactly flawed statistics - it's flawed reasoning. Data from 10 years ago is relevant in some areas and not in others. E.g. the fact that a state voted heavily Democratic 10 years ago is a good predictor of vote in 2012. But soccer matches? Well, probably not.

For your second question - I don't know if it has a specific name, but it's the problem that low N implies high variance. Andrew Gelman gave a great example of this in which he displayed maps of counties with the lowest rate of a particular cancer. Then he displayed counties with highest rate of same cancer. Many were adjacent to the low-rate counties, because they were all small-population counties. (In the USA counties vary hugely in population, from less than 100 to several million).

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  • $\begingroup$ Thanks, especially for your examples. I am very satisfied with the term "low N implies high variance", it was amost exactly what I was looking for. $\endgroup$
    – Richard80
    Nov 28, 2012 at 1:44
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The inferential reasoning is not very sound, as five games is not a very large sample on which to base such a statement. More data would be needed for a stable estimate. The fact that some of the games were old, played under a different manager, with different players, might not be a fatal issue if there is some other enduring difference between the teams (one team plays in the elite division and has a lucrative market, the other team are lower division minnows who play in front of a minute and penurious home crowd). In such a circumstance, a more stable and rational estimate could be obtained by pooling data from a larger set of matches between similar teams (e.g., how often have Premier League teams lost to Conference teams in the past 5 years).

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