Lightning processes are statistical processes. It is hardly possible to study such processes by considering a lightning strike to the line with specific parameters (current, front) or by considering a specific lightning wave coming from the line to the switchgear. To calculate the probability, I normally use ATP/EMTP, which has been changed for the convenience of statistical calculations. Let us have an example.

Visually, the three phases (A,B,C) of the overhead line (OHL) do not differ from each other. However, from the point of view of transient processes, these phases are not the same. In case of lightning strike to the tower top or the shield wire, the probability of back flashover from grounded crossarm to the phase wire may differ many times among three phases. And it can only be seen if we take into account the statistical nature of the lightning.

In case of lightning strike to the tower top or the shield wire, the probability of flashover of the insulation of phases A,B,C depends on:
➡️ the statistics on lightning current parameters;
➡️ the design of the tower (height, number of circuits etc.);
➡️ number of shield wires (0,1,2) and their location;
➡️ the grounding impedance of the tower;
➡️ many other factors.

For example, what does the probability of flashover P=0.01 mean? This means that out of 100 lightning strikes at the point in question, the flashover will occur in one case (P*100strikes=1).

For the shown OHL 110 kV, in case of lightning strike to the tower top or the shield wire, by using EMTP, we can see that the highest probability of flashover is:
✅ At impedances R<15 ohms, for the upper phase;
✅ At impedances R>15 ohms, for the lower phases.

This allows us to draw at least the following conclusions.
1️⃣ If we know from operation which phases of the OHL are more likely to cause short circuits during a thunderstorm, then we can assess the average condition of the grounding of OHL’s towers. Even without inspecting the line.
2️⃣ If the personnel examine the specific tower and see traces of flashovers and burns on the lower insulators and wire, then this tower is poorly grounded.
3️⃣ The different number of insulation’s flashovers means that the resources of different phases of the circuit breaker can be used differently. And the service of phases may require different intensities.
4️⃣ A larger number of back flashovers for a particular phase means that more steep-front waves form on the OHL’s phase wire, and such waves pose an increased danger to the winding insulation of power transformers installed in the switchgear connected to the OHL. If such a winding is damaged, then we know that its aging due to waves was not the last reason to discuss.

Statistical calculations are very important for estimating the number of line outages, the probability of damage to switchgear equipment, the selection of surge arresters, etc. etc. etc.