The efficiency of the 3 lightning arresters around the rocket may be checked using the rolling sphere method.
You need a scaled model of the arresters, the rocket and the umbilical tower. A sphere with a radius of 20, 30, 45 or 60 m is rolled all over the model. A smaller radius is used for critical and sensitive facilities, a larger for uncritical and robust facilities.
The arresters are efficient if the rolling sphere only touches the arresters and never the rocket or the tower. If not, there is a certain probability for hits of the rocket or the launch tower.
If the distance between the aresters is too large, the rolling sphere may touch the tower without touching the arresters.
See
https://www.nasa.gov/feature/lightning-towers-stand-tall-at-nasa-kennedy-s-launch-pad-39b
Several years ago, while working on a contract as Kennedy’s Advanced
Technology and Development Laboratory technical lead, Mata used
software he designed to run simulations for a new lightning protection
system at the pad. During design, he positioned the towers using this
software and was able to obtain full coverage of the mobile launcher
by using three lightning towers, rather than the single tower that was
part of the previous pad infrastructure during the space shuttle era
and only partially protected the orbiter.
“He did a tremendous amount of field work to ensure we had the most
robust system while still saving a significant amount of money for
NASA,” Perez-Morales said.
At nearly 600 feet, the taller towers are positioned to provide more
protection to flight hardware. The height of the towers is a function
of the height of the mobile launcher and the SLS rocket when at the
pad.
Mata’s design is based on a rolling sphere theory. While the old
system used during the Apollo and shuttle programs featured a
45-degree cone of protection, which left a portion of the hardware
exposed, Mata’s design completely protects all hardware – including
the mobile launcher – under catenary wires. Supported by long
insulation masts at the top of the towers, the wires run to the ground
almost diagonally, steering the lightning current away from the
rocket.
https://www.nasa.gov/pdf/160648main_RP-06-39_05-030-E%20KSC%20Pad%20B%20Catenary%20Capability%20Analysis%20Report%20Final%207-21-06.pdf
https://file.scirp.org/pdf/EPE_2013051415384450.pdf
https://hibp.ecse.rpi.edu/~connor/education/Surge/Presentations/Joe%20Crispino%20-%20Surge%20Presentation.pdf
https://nasaeclips.arc.nasa.gov/video/realworld/real-world-lightning-protection-for-launch-complex-39-archived
https://images.nasa.gov/album/Lightning_Strikes_at_Pad_39B
https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/iet-smt.2018.5002
See how NASA is using a rolling spheres lightning protection system to
expand the cone of safety currently used on Launch Complex 39. Find
out how the towers and catenary wires create an easier path for the
lightning to get to the ground.
Some more editing to be done later.