The Law of Truly Large Numbers

The Law of Truly Large Numbers
With a large enough sample, any outrageous thing is likely to happen. The point is that truly rare events, say events that occur only once in a million [as the mathematician Littlewood (1953) required for an event to be surprising] are bound to be plentiful in a population of 250 million people. If a coincidence occurs to one person in a million each day, then we expect 250 occurrences a day and close to 100,000 such occurrences a year.

Going from a year to a lifetime and from the population of the United States to that of the world (5 billion at this writing), we can be absolutely sure that we will see incredibly remarkable events. When such events occur, they are often noted and recorded. If they happen to us or someone we know, it is hard to escape that spooky feeling.

http://www.wired.com/wiredscience/2012/05/methods-for-studying-coincidences/


22 February 2012

Brett Lawrie or Collin Cowgirl? Nearly a quarter-century ago, Bill James addressed this very point in the 1987 edition of his Abstract:

Brett LawrieBrett Lawrie (Photo credit: Keith Allison)English: Baseball sabermetrician and Boston Re...Image via Wikipedia2012 Bill James Handbook - Back Cover2012 Bill James Handbook - Back Cover (Photo credit: Scott Ableman)BOSTON, MA - SEPTEMBER 14: Catcher Jason Varit...Image by Getty Images via @daylifeBrett LawrieBrett Lawrie (Photo credit: Keith Allison)Brett LawrieImage via Wikipedia

Suppose that you have a 20-year-old player and a 21-year-old player of the same ability as hitters; let’s say that each hits about .265 with ten home runs. How much difference is there in the expected career home run totals for the two players?”

As best I can estimate, the 20-year-old player can be expected to hit about 61% more home runs in his career. That’s right—61%.

Click here for the WHY and how it matters in Roto.
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February 24, 2012 at 6:47 AM

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