Hello Ulf,
I was almost certain that you would also have something to say about it.
Okay, so the diameter is larger than the stock intake, now consistently 80mm, and the hose from the airbox to the T4 fitting is even 100mm. However, I believe the significantly improved performance comes from the more streamlined airflow path that the air now has to the compressor inlet, and the better supply of cold air. I have to mention that my original airbox was open at the bottom because the engine is in a Golf 3, and the left engine mount is in the way, so driving with the hood open all the time isn't ideal. In addition, the intake path is much shorter. "There's also a certain mass 'x' in the intake pipes that needs to be accelerated initially. If this mass is smaller due to the shorter pipes, it allows for faster response and, at least, makes the turbocharger's intake work easier. I don't have any obstacles like a mass airflow sensor (MAF) anymore anyway."
I think this is also because, due to the increased performance and the resulting increased air demand, the effect is greater in my case than in a standard vehicle. In any case, this should not be taken as a recommendation to immediately purchase a BMC airbox.