The ego in fighting

Was watching UFC this weekend - Pat barry vs some guy.

Barry being the stand up fighter, ironically, was taking a bit of a beating on his feet.
Previous to the bout, it was however apparent in interviews etc, that barry has considerable belief in his own ability as a stand up fighter.

He seemed to get very frustrated throughout the bout however, and visibly annoyed with his opponent who was beating him to the punch.

this did not seem to do him any favours in terms of clarity of mind - which one may consider to be crucial in a bout.

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I saw another bout a while back, and one guy was taking the most tremendous beating on his feet (mma).

But his composure was remarkable.

Then, his opponent made a brief mistake - which said fighter used as an opportunity to take him to the ground and submit him.

The fact that he had been overcome the majority of the bout did not seem to enter into his mind.

He remained entirely focused and entirely technical - not allowing his judgment to be clouded, on what one would assume would be their ego.

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Examining closer certain fighters, this seems to be the case quite a bit.

The more technically proficient the guy, the less of an ego he seems to have - or so it seems to me at least.

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So having considered the above, it would certainly seem that one is better off maintaining this clarity of mind.

How does one do this?

How does one neutralize or eliminate their own ego and thus perform at a higher level?

P.S. apologies, it sounds like a question that might be more suitable for a psychology forum or some such.