How Does Sharding Increase Bandwidth From 15 TPS to 100,000 TPS?

I know how sharding works at a high level, but I'd like a more technical explanation – especially on how we can get to 100,000 transactions per second.

From my understanding, EIP-4844 proposes an increase to the size of blocks by an additional 2MB. Since blocks are already ~2MB, this will double the block size to ~4MB.

The additional 2MB allows space for 16 'blobs' which follow an alternate gas price model. But how does this increase TPS by such a large magnitude? If I assume each blob can do 15 TPS, this increases TPS to 15*16 = 240. Can someone help me with the maths?