Obeying a chain letter could be catastrophic

Question: Dire things could befall you, they say, if you break a chain letter. On the other hand, imagine what might happen if nobody ever broke the chain?

Answer: The letter's request is usually quite simple, "Make 5 copies and mail them to 5 friends." Sounds harmless enough so you send out the 5 letters, then these 5 people send to 25, and these to 125, then 625, 3,125, 15,625, 78,125, etc. The number would snowball until after just 15 cycles of the chain, the total would be 6,103,515,625!

Soon the number would top the population of the world (ignoring the actual myriad duplications and overlaps), meaning everyone on the planet would receive countless never-ending letters in an astronomical, mind-boggling spiral, says Don Voorhees in "The Book of Totally Useless Information."

The world's postal system would collapse, leading to the end of civilization and eventually humankind. "So the next time you get one of these letters, toss it in the garbage. You may suffer some personal misfortune, but it will be a small price to pay to save civilization."

Question: Sharp-shooting basketballer Shaq outshoots Kobe 40 percent to 25 percent for the first half of the game, then 75 percent to 70 percent for the second. Did Shaq necessarily have the better game?

Answer: You might think so unless you know about Simpson's paradox. Here are their stats, as described by Jeffrey Bennett et al. in "Statistical Reasoning for Everyday Life":

First half: Shaq 4 baskets in 10 attempts, for 40 percent

First half: Kobe 1 basket in 4 attempts, for 25 percent

Second half: Shaq 3 baskets in 4 attempts, for 75 percent

Second half: Kobe 7 baskets in 10 attempts, for 70 percent

You can see that in spite of Shaq's better shooting percentage for each half, Kobe's overall shooting was 8 of 14 for 57 percent compared to Shaq's 7 of 14 for 50 percent. So by the paradox (Edward Simpson, 1951) one player can be better for each part of a game (or season), but worse overall. It's similar for batting averages in baseball and in many other realms, such as pharmaceutical testing and voting results.

The moral: Statistics may not lie but can be deceiving unless handled with great care.