With a path intrusion incident, it is almost always the case that the collision would have been avoided if the pedestrian had not run out, or if the vehicle on the minor road had stopped, or so on. However should the other party be thought to have been travelling at an excessive speed, often the reconstructionist is asked to make a calculation of what whether the collision would, at some alternative speed say equal to the speed limit, still have occurred. In that way causation is addressed.
The paper distinguishes between those hazards which are distance limited and those which are time limited, giving definitions of the two types. Distance limited hazards are deterministic, but time limited hazards have a probabilistic basis. This difference has important implications for causation.
For a hazard at a fixed distance, there is a well known formula for calculating whether the collision would have been avoided at a slower alternative speed. However a time limited hazard often has no clear cut boundary between avoided/not avoided. According to the warning time during which the hazard develops, the alternative speed of the vehicle may mean that a collision would certainly be avoided, the alternative speed may have no effect, or the effect of the alternative speed may be in between. A method is given for estimating the effect of a slower speed.
A further type of path intrusion is where the pedestrian, or driver on a minor road, has seen the oncoming vehicle but gauged that there was time to cross in front of it. This also is considered, with its implications for causation.
Traffic lights, where one must not go over on red, have similarities and differences with path intrusion incidents. The paper gives a formula for the maximum speed at which a traffic light might be approached if drivers made the best choices, with a discussion of the difference between the unrealistic result of this calculation and a realistic maximum.