Re: A Sober Hypothesis!
 

[ QUOTE ]
What I guess I'm saying is that things do not "regress" back to the mean,

[/ QUOTE ]
Right. Coins, dice, cards etc. have no memory.

Was that what you were trying to say in the original post? I read it the opposite way.

Due and more due ....
 

[ QUOTE ]
Of course, that "expectation" includes trials already performed! The truth is that for the k-1 remaining trials, the result of the 1st trial means nothing.


[/ QUOTE ]
I stand by my original analysis. The proposition assumes a law of the conservation of luck -- that the trial outcome is being drawn from a depleted pool.

Re: It\'s the Law
 

OK. First define ".5!"

Micawber
 

[ QUOTE ]
Let's say you play a game with your friend where you toss a coin and win $1 every time Heads comes up.
<font color="white"> . </font>
Then let's suppose you get extremely lucky and win 20 times in a row.
<font color="white"> . </font>
My (revised) hypothesis is that if you play this game every day until the day you die, there will be a non-zero probability that the mean will be centered around 20, and NOT zero. What I guess I'm saying is that things do not "regress" back to the mean, since you are as likely to go on another 20 game hot streak than you are to go on a 20 game loss (even over time).

[/ QUOTE ]

Careful.

Your statement that the outcome of a series of independent trials has no effect on the outcomes of other independent trials is so true, it's literally a tautology.

But regression to the mean is a real phenomenon in our world - it does happen, all the time too. A 30-year old professional basketball player who shoots a lifetime of .70 in free throws and in yesterday's game goes 0 for 10, is expected to "regress" to his mean (of "7 for 10") any day now. Can you see why?

Moreover, can you see why sports players' "hot streaks" (or "slumps") is a statistical illusion?