Back of an envelope calculation (using the Hull Trains timings via Erewash/Toton on 27 Dec) says it's not as much as a 10 min saving...:
Hull-London on 27th (
http://www.realtimetrains.co.uk/train/N49640/2013/12/27/advanced)
Chesterfield pass 1217
Trent South pass 1243
Total 26mins
allowances +3
net 23 mins
Although to be fair this appears to use the HL goods lines near Toton, so maybe nearer 20 mins?
Today's 1329 from Sheffield
Chesterfield dep 1341
Trent South 1409
Total 28 mins
minus the 2mins stop at Derby for an equivalent 26 mins
Allowances +1.5
net 24.5 mins?
As ever, if anyone's got a better envelope...
And the other thing is the commercial advantage of serving Derby - could Sheffield and Chesterfield fill a train direct to London without Derby's contribution? And you'd need another service to keep Derby at 2 an hour towards Leicester/London.