asyncpg - connection vs connection pool

Question

I am going over asyncpg\'s documentation, and I am having trouble understanding why use a connection pool instead of a single connection.

In the example given, a pool is

Answer 1

Elvis Pranskevichus showed two benchmarks above. I took the first one bench_asyncpg_con and edited it, moving the con outside the loop:

async def bench_asyncpg_con_2():
    power = 2
    start = time.monotonic()
    con = await asyncpg.connect(**data)
    for i in range(1, 1000):
        await con.fetchval('select 2 ^ $1', power)

    await con.close()
    end = time.monotonic()
    print(end - start) 

And this worked much faster than bench_asyncpg_pool

I got 0.45 on this, whereas I got

1.62 on bench_asyncpg_pool and

63.18 on bench_asyncpg_con

I'm kinda newbie in using this lib and thinking that one connection con for a whole project would be a good choice. Correct me if I'm wrong. I will appreciate it