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Standard Deviation . What is it ?

Using a  mathematical model  (formula) can someone  beat the market ?

The answer is: no
Definitely not 
Only the optimistic  think they can .

What a mathematical model can do, is predict risk of a given event ,with certain accuracy

Premiums and policies  are based on this principle ,   using a  mathematical model they can predict the risk when given the right information 
Insurance companies do not know when an accident will happen or when a person will die they only know the probability of happening 

Same with stocks
if a model is used to reduce risk then it becomes an extremely valuable tool.

Now ,let's talk about History 
Carl Friedrich Gauss , German Mathematician ( 1777-1855) is the creator of the so called distribution curve, known as the probability curve or the Bell curve
Bell curve is a standard procedure for defining probabilities  
The curve  has the shape of a bell, it is symmetrical and in the horizontal axis measures standard deviations 1 ,  2  ,  3      -1  , -2  , -3  

Std. dev. is one  a  very useful and rather simple mathematical concepts but good explanations are hard to find  

To be honest Std. Dev. is a more difficult concept , but that does not mean it has to be ignored 

Perhaps  a good start  is by asking What is a deviation ?
Simply put is a distance being  measured from a point

And Standard ? 
It means "normal" ," usual" , and  it refers to PROBABILITY 

One Standard Deviation   the USUAL is a 68%  Probable
Two Standard Deviations the USUAL
 is a 95 % Probable 

In stocks  IV is the value for  One  Standard Deviation , in one year , as time frame 

The best way to explain is with examples and the simpler the better

Let's use 3  stocks with different  IV  

          GOOG        ATM     IV     @    47.57 %
          JNJ             ATM     IV      @   10.78 %
          CAT            ATM     IV      @   27.80 %

What do these stocks have in common ?

The SAME probability which is  68% 

And the difference ?

Each one  has  DIFFERENT  distance 

GOOG  is  68 % PROBABLE   that in a year
will move  in a 47.57 % , range ( up or down

JNJ  is  68% PROBABLE   that in a year
will move  in a 
10.78% , range ( up or down )
CAT is 68% PROBABLE  that in a year 
 will move in a  27.80 %, range ( up or down) 

What about if I want to know the 68% probable move for one day ?

Easy,  do this  IV x 0.0523
How did  I get  0.0523 ?
Easy    0.0523  =   Square Root ( 1 / 365 ) 

GOOG's    ATM   IV  =  47.57 %One std. dev.   for  one day is   47.57% x 0.0523 =  2.48 %

This is useful specially when planning  on putting  a trade  based on  earnings released one day before options expiration