DisplayLag, the people behind the handy HDTV monitor lag database, have a nice interview with three fighting game pro players on input and online lag and how it affects their game.
Carl “Perfect Legend” White, René “KOR” Maistry, and Emmanuel “MASTER” Rodriguez all make money on their fighting game abilities, and all of them say that input lag affects them professionally. It seems that input lag inconsistency is their biggest gripe. Perfect Legend, the Mortal Kombat EVO World Champion from 2011-2012, says that lag changes everything in a match:
If you’re used to practicing in a perfect environment, and then go to a tournament that uses imperfect displays, it throws off your timing and worsens your performance. Certain moves that are advantageous lose their advantage, and guaranteed situations can quickly become impossible due to the added lag on your inputs. Having to readjust to technical differences when you should be focusing on your opponent is a real pain.
Later, all parties give very specific examples of how lag breaks their game. I feel KOR's pain when it comes to Tekken specifically:
Due to the nature of how input lag affects a match in Tekken, its hard to take any match seriously when under these conditions. You are not losing to yourself, but rather factors out of your control, defeating the purpose of competitive gaming.
The piece goes on to talk about recommended displays to reduce lag, and then speaks to display manufacturers on how they can help with this situation. Check it out.