First few times I thought it was coincidence but now I'm puzzled. I'm baking two pizzas, one after another, made from the same dough and with the same ingredients. Every time, the second pizza base is much better: thinner crust, more elastic, you know, closer to perfect pizza.  I have two pans and I tried them in a different order, same result. Only difference is that the second pizza gets 15 minutes more dough raising, but raising 3 hours or 3 hours and 15 minutes shouldn't make such a difference.  Any idea what is happening? 
I think it might be the humidity inside the oven that's making the difference. After cooking one pizza, the oven is filled with the steam given off by the cooking dough, sauce, etc.  The humid air in your oven is probably heating the pizza up faster and more evenly (which is what you want for pizza).   Try putting a pan of hot water in your oven for a few minutes before you cook the first pizza and see if that makes the difference.  