How much worse do GMs play in their blitz and bullet games? How much of a skill drop is there when a GM plays a blitz game or a bullet game versus rapid and classical?

What I mean is, imagine if Carlsen was given 1 minute to play in, and he played against somebody who was given 1 hour to play in. What must the rating of this opponent be in order for them to be equally matched? In other words, what is the "classical rating"-equivalent of Carlsen's bullet-rating? And the same for blitz?

Obviously you cannot answer this by actually playing Carlsen against somebody who can think for longer, because Carlsen would also be able to think while his opponent is taking their time and that's not what I'm looking for.

But I suspect by analyzing the quality of the games that Carlsen plays, one could compare them to his classical games and perhaps estimate what "classical-rating" skill-level he is playing at when he plays blitz?
Handicapping


I've played in blitz tournaments where the higher rated player was handicapped 1 minute per 100 rating points with a maximum of 3 minutes deducted.

When you play with one 1 minute physical ability becomes a huge factor.  If you are not fast enough to move a piece while your opponent is reaching for his clock, and then hit your clock near immediately after your opponent, you will likely lose on time.

There is an endurance factor as well.   When you play blitz or bullet it is typically a lot of games in succession.  You might note that in the recent Côte d’Ivoire Rapid &amp; Blitz (which Magnus dominated), the quality of the blitz games dropped significantly as the day went on -- this is typical of these type of tournaments and you often see players brains just stop performing.


  Overall Strength


We don't have data on GM's playing with huge time handicaps as you proposed, but we can see their quicker games and compare them to their slower games.  Of course they have multiple FIDE ratings to represent this.  Magnus is further ahead of the world in rapid than he is in classical.

I personally think that when the players are young and in great form, they don't need much time.   When Anand was a rising star he played classical games at blitz speed.  Kamsky too played fairly quickly.  This is strategic as older GMs need to take their time and would get into time pressure.

Probably a computer program could rate the quality of the games to get a non-opinion based answer to your question.  My personal opinion is that if classical was level 10, rapid would be 7-8, blitz 5-6, and bullet under a 4.

Then it would be interesting to compare these against IM or Master games.  My guess is that GM games at Rapid are still better than IM classical games.