Editing 1827: Survivorship Bias

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**In some lotteries, if the jackpot gets too big -- or goes for too many drawings -- without anyone winning it, the jackpot amount gets "rolled down" and distributed across the lower prize levels.  These can have a positive return on average -- but ''only'' on the drawings where the jackpot rolls down.  People have formed investment groups to buy hundreds of thousands of tickets to exploit these; several such groups repeatedly profited from Massachusetts's {{w|Massachusetts_Lottery#Cash Winfall|Cash WinFall}} game especially.  (The Massachusetts State Lottery has an official report ([http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf PDF, 144 KB]) on how such high-volume betting affected the game.)
 
**In some lotteries, if the jackpot gets too big -- or goes for too many drawings -- without anyone winning it, the jackpot amount gets "rolled down" and distributed across the lower prize levels.  These can have a positive return on average -- but ''only'' on the drawings where the jackpot rolls down.  People have formed investment groups to buy hundreds of thousands of tickets to exploit these; several such groups repeatedly profited from Massachusetts's {{w|Massachusetts_Lottery#Cash Winfall|Cash WinFall}} game especially.  (The Massachusetts State Lottery has an official report ([http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf PDF, 144 KB]) on how such high-volume betting affected the game.)
 
*'''Examples''' of survivorship bias:
 
*'''Examples''' of survivorship bias:
βˆ’
**Diogenes was shown paintings of people who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which he replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number."  
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**Diogenes was shown paintings of people who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which Diogenes replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number."  
 
**Many people {{w|Public Health Cigarette Smoking Act|were smoking}} back in the 1930-70s, thus almost everyone above 80 either smoked cigarettes or was at least subjected to massive passive smoking during those years. Thus anyone above that age could be claimed to prove that you can live a long life while smoking. But they consist of the small group of people that survived in spite of all the smoke, where large sections of those that would have been 80 today, died from cancer or heart disease caused by smoking, long ago, maybe even before they retired. But since these people are dead and gone many years ago, they do not speak up,{{Citation needed}} and are thus the silent majority that is not heard, which is the problem with survivorship bias.
 
**Many people {{w|Public Health Cigarette Smoking Act|were smoking}} back in the 1930-70s, thus almost everyone above 80 either smoked cigarettes or was at least subjected to massive passive smoking during those years. Thus anyone above that age could be claimed to prove that you can live a long life while smoking. But they consist of the small group of people that survived in spite of all the smoke, where large sections of those that would have been 80 today, died from cancer or heart disease caused by smoking, long ago, maybe even before they retired. But since these people are dead and gone many years ago, they do not speak up,{{Citation needed}} and are thus the silent majority that is not heard, which is the problem with survivorship bias.
 
**During World War II, there was a study of the damage done to aircraft, and the recommendation was to add armor to the areas that showed the most damage. The statistician {{w|Abraham Wald}} noticed that the study didn't take into account aircraft that ''didn't'' return: the holes in the returning aircraft thus represented areas where a bomber could take damage and still return home safely.
 
**During World War II, there was a study of the damage done to aircraft, and the recommendation was to add armor to the areas that showed the most damage. The statistician {{w|Abraham Wald}} noticed that the study didn't take into account aircraft that ''didn't'' return: the holes in the returning aircraft thus represented areas where a bomber could take damage and still return home safely.

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