Notice the progression in the three parables Jesus tells in Luke 15.
First, there are one hundred sheep, and one of them gets lost.
Next, there are ten coins,and one of them gets lost.
Then comes two sons, and one of them gets lost.
We go from a 99% rate of righteousness, to 90%, to 50%. And by the end of the parable of the prodigal son, that 50% rate drops to zero.
"This man welcomes sinners and eats with them" is a psalm of joy and praise -- not to mention deep personal relief -- whether the psalmist realizes it or not.