The way this is presented is going to be interpreted incorrectly. It is incorrect to compare percentages or probabilities like this.

Here is a different example to try and illustrate the problem:

Is 10% larger than 5%?

It is not possible to answer this question if the basis on which the percentages are calculated are different.

What if I said the 10% was 10% of whatever you last spent money on, but the 5% was 5% of Google's annual revenue. Which is larger?

The same thing is happening in the above - it isn't okay to calculate the probabilities in two situations and then try to cross compare them for size.

Sadly this error seems to be cropping up quite a lot! Matt Parker (Stand-up Maths) has an example of this and related to a recent election: https://www.youtube.com/watch?v=aokNwKx7gM8. His explanation is likely better than mine.

> The average transmission risk in the household is further elevated when intense physical distancing is enforced

How is this possible? Distancing _elevates_ within-household risk?

> How is this possible? Distancing _elevates_ within-household risk?

One obvious mechanism: Enforced distancing makes it less likely you get COVID from a source outside of the household, which (since infection usually provides some period of immunity) thereby increases the risk you get it in the household, on average.

Ah I see, I misinterpreted this as referring to within-household distancing (separate rooms, masking, etc). Thanks!

yes, that's the explanation given in the paper--the more restrictive the public measures, the more likely spread occurs at home.

This is also misleading. The paper does not intend to mean that "lockdowns will cause you to get infected by the people you live with". Which is what you seem to have written.

Restrictive measures do not increase your absolute risk at home. The paper was talking about the relative risk between two scenarios - which allows for misunderstandings. The last sentence which was omitted in your quote was:

"These lines of evidence support that SARS-CoV-2 transmission is facilitated by close proximity, confined environment, and high frequency of contacts."

What the paper ought to have said was, when more restrictive measures are in place, it then becomes important to focus and step up measures for the people you interact with most - because those people in this new and different scenario now become the most likely people for which you will catch an infection.

The people you interact with have not suddenly become more risky in an absolute sense, but they become a more important risk factor when situations change.

Trying to draw conclusions between the relative risks between two different scenarios is not the same as absolute risk. This is the trap!

[edits: for clarity]

Perversely, it sounds like transmission occurring primarily at home suggests the government is doing a decent job at managing the problem.

no, it's really the government pushing infections to the periphery, so that it gets credit for visible action rather than meaningful effect (i.e., lowering death rates permanently without throwing half the population into severe distress). that's exactly the empty effort we should hold against politicians, especially when so much harm has blindly been brought to bear along with it.

it's unrealistic to expect families to social distance from each other for months on end for a pandemic of this severity (~0.5% fatality rate heavily skewed to the aged, as opposed to the 1918 flu with ~10-20% fatality rate across the age spectrum).

so the most impactful, and realistic, action to materially lower infection/death rates is to alter our behaviors around private social gatherings only (distance or mask indoors). focusing our efforts there would be spending our collective goodwill budget wisely, as opposed to the pointless political theater around masks and restaurants. instead, all of the focus has been on curtailing public settings (easier for the government to control), where only a small minority of transmission is happening (moreover, public behaviors changed without needing government intervention). it'd be farcical if it weren't so tragic.

> only a small minority of transmission is happening [in public settings]

Well, wouldn't that be because public settings are more controlled, as you said?

It seems strange to suggest wearing a mask at home, in private, but not in public. Or did I misread?

no, the only policy we needed is to either distance or wear masks when visiting in private with those outside your household, not at home with family (which no one would do) or in most public settings (which are already very low risk because exposure in space and time is vanishingly low). that would focus our attention and effort on the most impactful situations, not the ineffective shotgun approach we have now.