I've seen the number 337 a few times so thought I'd look into it.
https://en.wikipedia.org/wiki/List_o...States_in_2022
Adding up the monthly figures, there have been 337 shootings and it looks to me like this figure counts four or more people injured or killed.
Digging a bit further on the list, there are 24 where four or more people died (sometimes including the perpetrator and my hand count so could have an error) and this is week 27 of the year, so I guess the 1 a week stat is deliberate mass killings of 4+ people.
Interesting, perhaps, is that when I was searching for 337 mass shootings, this was also the annual figure for 2018 in the US. So in pretty much half a year, they have reached the 2018 total which suggests it's getting worse.