Size Matters

This is a summary of a general study of opening gap behavior by gap size.  In this study no commission or slippage is taken into account.
The good news is that 70% of all gaps close on the same day.  Let's see how the distribution is.
The study is based on data from 9/12/1997 to 9/10/2010 which is about 13 years.
In the following three graphs, the X Axis it the gap size.  Positive numbers are up gaps and negative numbers are down gaps.  Gap size 1 refers to any gap above zero(close of prior day) up to 1.  Gap size 2 is any gap above 1 up to 2 and so forth.  Similarly gap size -1 is any gap under zero down to -1.  The following three graphs study gap sizes from -20 to + 20.
The following graph shows the number of gaps (Y axis)  VS Gap size. 

As expected, majority of gaps are small.  The peak is around zero area.  I have eliminated the zero point from graph because it is not considered a gap.  There is a dip at gap size 1 which I do not have any explanation for at this time.

Now let's see what percentages of gaps of different sizes get filled :

This graph is not symmetric and it appears that extreme down gaps (longs) do a bit better than similar up gaps (shorts).
About 80% of all gaps between -3 to +3 get filled and fill percentage for gaps between -1 to + 1 is about 90%.  However, the profit for small gaps are less than larger gaps.
So I did another study combining the expected profit and probability of obtaining that profit.  The result is shown in the following graph.  The Profit Expectancy in the Y axis can be used for comparing only and does not reflect the statistical "expected profit".

 As you see, the profit expectancy of small gaps are worse than larger gaps.  The bad news is that slippage and commission has more negative impact  on smaller gaps than larger gaps.  So in reality the small gaps are worse that what it shows in this graph.
It also appears that the extreme down gaps (longs) are more profitable than extreme up gaps(shorts).