Friend and I had this discussion, and came to no conclusion:
Hiking in the mountains. Crossing a range through a pass. Peaks on either side are a good thousand feet higher. Are you at serious risk of getting hit by lighting?
More generally: If you are walking a ridge line, and see a storm developing, how far below the ridge line do you need to be to be reasonably safe?
Since asking this question I've been doing more reading. Unless the the mountain is sharply above you -- better than 45 degrees, you only have a very moderate amount of protection. 45 degrees is steeper than the angle of repose -- 37 degrees -- the angle you can stack loose rock and not have a slide.
So the 'best answer' is correct. There is no safe path.
Still: only about 15-20 people a year die from lighting strikes, mostly fishermen. So the real question becomes: How big is the whole risk?
While strikes 6-10 miles away from the base of the thunderstorm have occurred, most of the ground strikes are under or very close to the edges of the storm base.
If we take the LD50 radius of a lightning strike at 50m then it requires a storm with 133 strikes per square kilometer to land one near you. A storm with a 10 km diameter would need to deliver about 10,000 strikes. to zot a person under it's immediate footprint. That's several hours at one per second. The storms I have experienced in the mountains are both shorter than that, and seem to be limited to a few strikes per minute.
Net conclusion: Avoid the really high risk places, and enjoy the show. Overall moving toward safety is better than staying put.
I've been unable to find stats on how much higher your risk is standing vs the lightning position (squat in a ball)
Overall on a per trip basis, I would rank risks largest to smallest:
- Accident traveling to the hike
- Avalanche (low 30's per year, North America)
- Climbing accidents (low 20's per year, North America)
- Lightning (mid to high teens per year, US)
- Wildlife attack (a few per year)
This doesn't take into account the relative frequency of the activity. Fishermen have a higher rate because they are willing to fish in the rain. And there are a lot more skiers and snowmobilers at risk of avalanche than of people walking the high country, or doing technical rock climbing.