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Peaches LeToure's avatar

Love this! I am learning to (assistant) coach my son's soccer team. We only do tournaments, which start as pool play and end in a playoff game. We recently moved up an age division from U10 to U12 because one of our players had a birthday. That player happened to be my son and my husband happens to be the head coach, so we moved the whole team up. At any rate, we are now one of the younger and smaller teams in our division.

At one of the tourneys, we got creamed yet still qualified for the playoffs. Except that no one, including us, believed that from the way we looked on the field. We did eke out 2 wins, but lost by a landslide 2 more. The total points should have qualified us, but they didn't put us in the playoffs and we didn't realize it until the way home when I actually checked the refs numbers and the total points we earned. We were cheated out of losing badly in the playoffs because we didn't understand Simpson's Paradox and didn't see it necessary to double check the numbers until later.

Moving forward, I can now absolutely strategize the pool play better to take advantage of Simpson's Paradox. I can also do a better job at making sure the refs are treating us fairly. My son and his soccer team thank you!!

Additionally, now that I know about this concept (and totally love it!), I really am seeing it everywhere. What fun!

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Elliott Sober's avatar

Another example of Simpson's Paradox can be found in evolutionary biology in connection with the concept of evolutionary altruism. Altruists donate fitness benefits to others at a fitness cost to themselves. Selfish individuals do not donate but they receive fitness benefits from altruists in the same group. So in all mixed groups, altruists are less fit than selfish individuals. However, if you look across groups it is possible that altruists are on average fitter than selfish individuals. The following simple example shows how this can happen.

Column Player

Altruistic Selfish

Row Altruistic 3,3 1,4

player Selfish 4,1 2,2

This table gives the fitnesses (= number of offspring) of asexual organisms in groups of size two.

Within mixed groups, altruists have 1 offspring and selfish individuals have 4. But within unmixed groups altruists have 3 offspring, while selfish individuals have 2. If altruists tend to live with other altruists, and selfish individuals tend to live with other selfish individuals, the average altruist in a metapopulation made of many such groups will be a bit less than 3 and

the average selfish individual will have a fitness that is a bit more than 2.

Individual selection is selection within groups; group selection is selection among groups.

In both, selection requires variation in fitness. So individual selection favors selfishness, but

group selection favors altruism.

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