I seen a ladder safety book by osha having explanation regarding 4:1 height to base ratio from this book i understand this ratio is for keeping ladder in a safe angle of 75 degree and to prevent accidental slips while climbing .this is explained in page number 11 of this book it also give explanation how to achive this ratio
Achieving a 4:1 set-up angle
A non-self-supporting ladder should have a
set-up angle of about 75 degrees — a 4:1 ratio of the ladder’s working length to set-back
distance.
Here’s how to achieve it: Stand at the base of
the ladder with your toes touching the rails.
Extend your arms straight out in front of you.
If the tips of your fingers just touch the rung nearest your shoulder level, the angle of your
ladder has a 4:1 ratio