Calculate whether datapoints are part of a larger distribution
One way addressing your question is to ask if your two datasets(regular points and irregular points) come from the same distribution?
The kolmogorov-smirnof test is a common tool for putting a number on the 'likelihood' of two datasets being from the same distribution.
python scipy has an implementation of this test.

Be aware that this test is more sensitive to differences around the means of each distribution, than to differences around the edges. From the looks of the graph in the question, its not an issue in your case, so the test should work.

This is a very concise explanation of the test