Analysis published many years ago by Pye of Britain’s Building Research Establishment quotes the probability of a slip (not a fall or injury) as varying with the coefficient of friction (COF) between the shoe and floor as follows:
COF Risk, 1 in …
(These are Pye’s values for a pedestrian making a left turn, which had the highest risk compared to right turn or walking straight.)
Thus at a COF of 0.27 the risk is 1 in 20 and at 0.40 the risk is one in a million. These figures are not to be considered gospel, but they may be the best available. They indicate that a small improvement in COF can greatly reduce the risk of slip. As a rough rule of thumb, each increase of 0.10 in DCOF reduces the risk of slip by a factor of 4,320.
The COF is the actual value between the floor and the shoe of the pedestrian, and is not to be confused with the COF measured by a slip meter using a surrogate (such as a standard hard or soft rubber) to represent the shoe heel.
What is an acceptable risk of an injury? It’s not defined, but the risk a pedestrian is willing to accept while strolling through a mall is likely much smaller than a motorcycle racing driver is willing to take to compete in a race. The risk in the mall needs to be very, very small.