You're nit-picking the numbers I directly admitted I was making up on the spot for sake of illustrating the broader, and more salient point that the percentage of methodological errors during the original and replication studies have a multiplicative effect on the overall reproducibility rate.
I don't think so. Saying that only 1/4 of replications are, on average, useful because of methodological flaws is an extreme claim. Given the costs associated with reproductions, if anything even close to 3/4 of them are on average untrustworthy it completely changes the game in terms of spending resources on reproduction, which in turn frees original investigators to care even less about reproducibility from the start.
On the other hand, if probabilities of methodological flaws are low for reproductions, then the multiplicative effects of the original method and the reproduction method are dominated by the original method, in such a way that more replications means multiplying probabilities together on the replication side, which (if flaw rates are less than 50%) goes to zero pretty quickly.
Meaning that consistency among reproductions is strong evidence regarding the validity of the original, and so the replications are worth the cost.
There's a significant qualitative difference between cases where replications are likely to be flawed vs. cases where they aren't. Cases where different replications are likely to have correlated flaws (even when flaws overall are unlikely) would also be problematic, because different replications might not give you additional information.
I think it matters to be very clear about all this, and not give any impressions that could be easily misconstrued to cast doubt on the utility of replications. Making some back of the envelope estimates using a 50% flaw rate strikes me as a dangerous way to talk about it (unless we have evidence that the flaw rate really is that high).
You're still picking on the actual, specific number, and ignoring (or otherwise completely missing) the part where I specifically said, "for sake of a convenient number". I chose 50% because it makes the math easy. Period. Full stop. End of its value or contribution to the discussion.
I have exactly zero idea what the actual ratios are. But the actual ratios absolutely do not matter for the purposes of illustrating how the methodological errors compound.
The most salient detail about the way methodological errors compound is that by engaging in more replications, you can beat down the rate of spurious results in the replications. It's of little importance that it is multiplicative with the flaw rate of the original, because the flaw rate of a set of independent replications will go to zero super fast in the size of the replications.
If the flaw rate is >= 50% and the number of replications is low, it presents a case where it's of little social value to do replications, depending on their cost (which is usually high).
From your original comment, the way a naive reader will view it is that replications often don't work, because you primed them with a number you just pulled out of nowhere (50%). That will matter much more than the other detail about it being multiplicative, which doesn't really matter much at all no matter what the flaw rates are, because it all hinges on the flaw rates of the replications and how many replications you do anyway.
I know that you did not mean to misrepresent it with the 50% number. I'm just harping on this because by happening to use a number like 50% it has the potential to distract and do more harm than good, regardless of anything else in your comment or even whether or not the 50% had anything to do with your main point.
