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Amex usually shows up after the second statement.
Was there a hard pull for the new card? That would be a more likely source of a lowered score than reduced spending
It's possible that you're in the "middle" between when your other cards reported $0 and the 2 month lag before Amex reports.
I'm guessing if you pulled your reports right now, you'd see $0 balance on your non-Amex card(s) + the HP for the Amex but no Amex reporting as a tradeline. This will remedy it's self once Amex starts reporting, and you age the HP a little.
Remember, everyone's credit is different and while some people might be able to pick up a couple of HPs with little to no effect, others may see significant changes to the FICO scores.
If you have other cards and they're all reporting a $0 balance, then a 13 point drop makes sense. There is a scoring penalty for 'no revolving credit usage' - you need to have at least one card reporting a low balance to avoid point loss. Once you allow any one of your other cards to report a balance, or when your amex finally reports with a balance, those points will be regained immediately.
@Dylan1 wrote:
There was a hard pull but 13 points?? That seems like a lot. And the reason Experian gave me was “lack of recent balances on revolving accounts”
I agree with the others. It smells like the "all cards at zero" penalty. My scores dropped between approximately five and forty-five points when I had all cards at zero. It's not a big deal if you're not in the midst of applying for important credit.