Safety Performance Function (SPF) is a mathematical representation that relates the number of crashes to different site characteristics. The most common site characteristic used in SPF is Annual Average Daily Traffic (AADT).

A typical SPF format for an intersection is listed below.

N=e^a * AADTmajor^b * AADTminor^c

where:

N- Predicted Average Crash Frequency

e - Euler's Number - a mathematical constant 

AADTmajor - Annual Average Daily Traffic (AADT) on major approach

AADTmajor - Annual Average Daily Traffic (AADT) on minor approach

a,b,c - coefficient values

A typical SPF format for a segment is listed below.

N=e^a * AADT^b * L

where:

N- Predicted Average Crash Frequency

e - Euler's Number - a mathematical constant 

AADT- Annual Average Daily Traffic (AADT) 

L- Segment length

a,b - coefficient values

Multiple techniques have been established to develop SPF. The most common technique includes Negative Binomial Likelihood Function. 

The Poisson distribution restricts the mean and variance to be equal. Often, with crash data, the variance is greater than the mean leading frequently to overdispersion. Therefore an overdispersion parameter is reported along with the function and coefficient values.