The uncertainty in how many people would be saved anyway without intervention is (as an absolute number, not a percentage) much larger for the 250000 people case. If someone claims to save 4500 people, and the uncertainty is greater than 4500, I may be skeptical that they can save anyone at all.
Imagine it as medical trials instead. If I claim I can cure 4500 out of 250000 people it may be that I can’t cure anyone at all and I’m just counting the spontaneous remissions as “cures”. If I claim I can cure 4500 out of 11000 people, it’s very unlikely that they would have all recovered spontaneously.
The uncertainty in how many people would be saved anyway without intervention is (as an absolute number, not a percentage) much larger for the 250000 people case. If someone claims to save 4500 people, and the uncertainty is greater than 4500, I may be skeptical that they can save anyone at all.
Imagine it as medical trials instead. If I claim I can cure 4500 out of 250000 people it may be that I can’t cure anyone at all and I’m just counting the spontaneous remissions as “cures”. If I claim I can cure 4500 out of 11000 people, it’s very unlikely that they would have all recovered spontaneously.