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/


11 January 2011

Fantasy Baseball and the Theory of the Arbitrary (Part 2)

You might ask to look at projections for the forthcoming 2011 season. Here are those, from two different reputable sources:

    * Player A, Projection #1: 23 HR, 82 RBI, 86 R, 18 SB, ..287 AVG
    * Player A, Projection #2: 22 HR, 75 RBI, 76 R, 16 SB, .280 AVG
    * Player B, Projection #1: 18 HR, 77 RBI, 81 R, 25 SB, .280 AVG
    * Player B, Projection #2: 20 HR, 82 RBI, 82 R, 28 SB, .275 AVG

What to make of these lines? Well, they are pretty close. On a value calculator, Player B’s edge in speed probably outweighs Player A’s slight edge in power. Regardless, is there anything in the projections that scream that one player should be tabbed with the 39th pick and the other with the 64th pick? No, of course not.

We still don’t have enough information to form a reasonable assessment or to understand what’s driving these valuations by others. Perhaps one player is on the heels of his career while the other is on the upswing. Maybe one team is surrounded by lots of talented teammates and the other shoulders the burden of winning himself. So here’s a qualitative assessment of the context for each of these players:

    * Player A is young and plays for a team that had fewer wins last year than the Kansas City Royals. The team is in the midst of rebuilding and this player has been mentioned as a trade candidate.
    * Player B isn’t young, but isn’t yet 30 yet, and plays for a team that had about as many wins last season as the Boston Red Sox. The team is competitive and has signed free agent superstars this off-season. This player has also made the All Star team twice in his career.
Click Here For The Identities Of These 2 Players.

 ...let’s start out this year by questioning our assumptions and realizing the degree to which arbitrariness gets factored into price. There are things we can and can’t control in fantasy sports competitions. Nobody has an oracle that predict with 100 percent accuracy what’s going to happen in the following year. But on the other hand, if you embrace the Theory of the Arbitrary, you can at times come upon instances where the crowd has reached its pricing point thanks to some elusive, intangible factor.


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