Protip: get earmuffs. The kind that construction workers use. They're about $20 on Amazon. If you combine them with earbuds, you literally can't hear a conversation right next to you.
This is the setup that pro Starcraft tournaments use so that players can't hear the announcers and crowd.
That has the exact same problem as headphones. I do not want to wear giant things on my head for 6-8 hours a day while I try to get into and stay in the flow.
(I don't have a problem with ambient conversation at, say, Starbucks, but I find myself very distracted by people talking about work stuff in the same room as me.)
I tried construction worker earmuffs for a while. The biggest problem is that I wear eyeglasses. The arms for my eyeglasses have to go through the soundproofing system to hang on to my face, which leaks sound and makes them kind of useless. I assume construction workers don't wear glasses?
They also squeezed my head which was uncomfortable after 8 - 10 hours.
Lastly, people kept trying to talk to me, which meant I had to pull them off and put them on and pull them off and put them on which was a little maddening.
Definiately not the case for league tournaments. In the spring split of EU LCS they wore 3M Peltor ear defenders over small in-ear buds for their actual sound.
More recent tournaments they seem to have integrated ear defenders with headphones with Mic's on. (Previously they had 3 headsets, the ear buds for sound, the defenders then their sponsors headsets around their necks for the mic.)
This is the setup that pro Starcraft tournaments use so that players can't hear the announcers and crowd.