[AnimalMuppet]

But of those billions of other planets, as they get further and further away, the probability of an asteroid from them finding Earth goes down. So does the probability of life on the asteroid surviving the trip.

I think that the number of planets within a distance R is O(R^2), but the probability of an asteroid from such a planet reaching us is O(1/R^2). But if the probability of life on the asteroid surviving the trip decreases with a longer trip, the net effect is probably that the further-away planets contribute little to the probability of life reaching us in this way.

[JoeAltmaier]

The panspermia idea is, that it started somewhere and somewhen, and has been planet hopping ever since. We only need one nearby life-bearing planet to seed earth; it got seeded from further away and so on.

Similar to how ancient Romans wore silk but didn't have trade with China. It only took each trader to trade with their neighbor, and silk could travel thousands of miles.

[AnimalMuppet]

OK, but at that point, the "billions of planets out there" argument doesn't work. You're left with the probability of it transferring from a nearby planet.

[JoeAltmaier]

Right, and the inevitability of it being present in a nearby planet went way up. Because once it started somewhere (and there are billions of 'somewheres') it would spread like a virus and infect every possible receptive environment.

The statistics is hard. No simple counting of planets is enough. All the vectors have to be accounted for.

[AnimalMuppet]

No, the inevitability of it being present in a nearby planet went way up if the probability of it moving from one planet to another planet is decently high - and not otherwise.

[JoeAltmaier]

Probability is over time. With enough time (billions of years?), the total probability approaches 1.0.

[AnimalMuppet]

No, it doesn't. If the probability per year is 10^-15, then the probability over 10 billion years (10^10) is still 10^-5. (I mean, yes, over a quadrillion years the probability approaches 1.0, but I don't think that helps your position.)

You keep trying to say "but big numbers of planets, and big amounts of time" to make this idea reasonable. But it doesn't work. You have to deal with how low the probability actually is of it happening from one planet in one year. If that's low enough, you can't salvage it just by saying "billions of years and billions of planets".