Bullet vs blitz vs rapid time controls in engine matches

[royb]

For many years now, engine developers and their support team(s) have seemed to favor what I would consider short time controls for engine matches. An obvious benefit of this is that you can get a match of many more games in the same n hours vs when you use a slower time control.

I'm wondering if anyone has studied the accuracy of the estimated computer elo performed after the match results are tallied. If you run a match with 10K games at a time control of 1 minute + 1 second increment per move ... is that providing a better estimate of the two engine strengths relative to each other than a match with 1K games at a time control of, say, 5 minutes + 5 seconds increment per move?

Generally speaking of course more games is preferred and that makes the error bars closer together - but is that true when the greater number of games played comes due to shortening the time control? And what if we use even shorter time controls - perhaps .1 minutes + .1 second increment?