My homework assignment today was to figure out if COVID-19 lockdown restrictions and other countermeasures have been effective in reducing COVID-19 cases. I spent some time googling around, and what I discovered is that (a) conservative publications all have charts showing there's no correlation, while (b) academic papers all show a positive correlation. Hmmm.
The problem is that there are a million ways to measure this, and it's pretty easy to keep slogging away until you find one that fits your ideology. So for better or worse, I decided to try the simplest possible scatterplot and publish it regardless of how it turned out. On the horizontal axis I've used WalletHub's scores for how restrictive each state is. The vertical axis shows the cumulative percentage of each state's residents that have contracted COVID-19 as of June 1. Here's the result:

There are some interesting things here. For starters, the correlation is indeed positive: more restrictions generally lead to a lower case rate. But there are some high-profile exceptions. Texas and Florida both had very few restrictions, but their case rate is only slightly higher than California and New York, which both had lots of restrictions.
My conclusion is twofold. First, restrictions matter, but maybe not all that much. Second, you'd need to do some serious analysis with proper controls to really be confident in these results. In the meantime, this bloggy horseback estimate will have to do.
Want more? Here's a WalletHub analysis showing that blue states have been safer than red states. Here's a study in the Lancet showing that increased use of face masks leads to lower COVID-19 infection rates. Here's a study in PLOS One that divides states into buckets and finds that the bucket with the highest mask-wearing does better than the bucket with the lowest mask wearing. And here's a study from the Baker Institute showing that the correlation between openness and death rates has increased over time:

For what it's worth, I don't trust any of these studies, including mine. Still, the bulk of the studies do indeed seem to show a modest positive correlation between COVID-19 countermeasures and case rates. That's certainly the way to bet at the moment.