If you run early on in Q3 with somewhat older tires, and then come in late on Q3 for newer tires, you are more likely to get a longer first stint come race day, which helps strategy wise over competition close to you.
What link is there between doing a run on older medium tyres and having a longer stint on race day? Only the tyres you set your fastest lap on are relevant for the race if you have new sets spare, as Vettel did.
Vettel set his fastest time on the soft tyres. He did this at the start of Q3.
Had Vettel done a run on old mediums at the start of Q3, he would have ran a set of new softs afterwards anyway in order to get pole position. Had he opted to start on mediums, he would have ran a new set instead of, not in addition to the new softs. At no point is the used set of mediums relevant unless he was setting a 'banker' lap. But why set a banker lap on an old set of tyres if a) it's not going to be good enough for pole and b) you will have a worn set of tyres at the start of the race which will result in a poor first stint.
I can fully understand him using an old set for Q2 because the car was fast enough to get through, and it wasn't worth wasting a new set.
They used older tires so they could switch over much later in the session, even Alonso makes note of such issues with soft tires.
Again you are not making it clear why using older tyres at the start of Q3 is an advantage. With the huge pace advantage and the relatively low track evolution that happens within 10 minutes, why wait to set a time on the new set?
I never said a used said would have been a tenth slower, I'm saying if Vettel made his final lap on them they would have been slower. The only mention of a tenth I remember is him being faster than Webber by that margin or two tenths. Everything else I suggest indicates that he wouldn't have made his final quali lap on used tires but rather newer tires toward the end, which is what he and others did. I know very well of the margin lost, though it differs from track to track obviously and setting to setting, so you can't give it a constant wear rate like you've just done.
Webber made his fastest Q3 lap on a new set of medium tyres IIRC. Vettel would have easily matched him on a new set of mediums too. Vettel decided at the start of Q3 to set a lap on the new softs as this was his strategy for the race. Are you suggesting he might have attempted a run on new mediums at the end of Q3 (After already using the new softs), and this would have hurt his race strategy because he had used 2 new sets?
Saidur_Ali isn't the only one who can't understand what you are talking about, because you don't seem to be making a whole lot of sense. I feel like there is some key information or detail that you are leaving out (Possibly how tyres can be put through a heat cycle and conditioned for a race in order to improve durability?).