The message . com
from "Mathew Newton" contains these words:

In practice you often don't have the space for the correct angle, in
which case you tend to hug the ladder rather more

Sure... but I don't have the formula for that! ;-)

I presume the optimum angle is based on consideration on lateral
stability as well as vertical stability but if the ladder is steeper
than optimum you are only really at risk of toppling over backwards near
the bottom of the ladder as that event will only occur if your centre of
gravity is further away from the vertical wall than the foot of the
ladder. However, particularly low down there is precious little
frictional force at the top to prevent the ladder slipping sideways
should the footing not be exactly level or you twist sideways as you
climb. A stand-off in this respect will usually help lateral stability
but if space is limited increasing the angle of the ladder to give room
for the stand-off may be counter productive.

--
Roger Chapman