There are similar undocumented limits for how many open TCP connections you can have to an instance, which vary depending on the instance size and whether or no

There are similar undocumented limits for how many open TCP connections you can have to an instance, which vary depending on the instance size and whether or not your security group rules require connection tracking. And don't get me started on the opaqueness of the capacity of your ELB at any given point in time. I once had a fun week capped by AWS support recommending I create multiple ELBs and round-robin traffic across them.