I think its more down to throttle position (like some BMW M Cars), 10% throttle registers 30% in sport mode, 50% throttle, 100% throttle position etc. I could be wrong but the reason I say this is because most of the time this button for sport mode stuff, doesn't relate to quicker times but a perception of improved performance.
Clarkson on the GTI PP. Published 14 March 2014 Sunday Times
I took the car to Top Gear’s test track, put it in Normal and asked the Stig to do a lap. He did it in 1 minute 29.6 seconds. I then put it in Sport. This time he did a lap in 1 minute 29.6 seconds. So then I put it in Comfort, which softens everything up. He did it in 1 minute 29.5 seconds.