FWSY pizza dough problem

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We do pizza night every Friday and last week I tried the same day pizza dough from flour water salt yeast. 70% hydration, which is higher than my usual pizza dough. Anyway, when I put the pizzas in the oven(one at a time) they puffed up...a lot. I expected the crust to puff up but the whole thing did. I docked the middle area of the,second pizza but got the same puffiness. I didn't roll them out quite as thin as I like because my wife likes a little thicker crust. Will rolling it thinner help set the crust before it can rise so much or will I just have a bigger puffy pizza?

"dock" means pricking with a fork. Sorry about that.

I think the next best thing is to post the recipe and if you changed anything then post that too.

The recipe is

 

1000g flour (I used KA ap)

700g water

20g salt

2g instant yeast

The only difference is the recipe said it made 5 pizzas but I divided it into 4 for bigger pizzas

If you stuck to the recipe exactly the only thing I can think of is you didn't shape it flat enough if it's puffing up too much. So it's a technical issue as supposed to a recipe issue. Making larger pizza doughs could have contributed to this making it more difficult to shape well.

I probably should have looked at the picture lol. It puffed up similarly to what the website showed. I guess that's just what Ken Forkish intended? I've never had a pizza dough puff up to that extent though, even my wife didn't like it, too much dough according to her. Maybe rolling it out an extra couple of inches may help.

Sounds like it wasn't stretched thin enough. Also, if you can get some 00 flour (one of the Caputo brand flours is recommended), it might help. But mostly, this happens if it is not thin enough or not enough toppings (but normally the former). This should be a thin crust pizza and the one at sauce magazine is not what it should look like. These are Neapolitan style thin crust pizzas. So try it again but get it thin like you like.

Do you mean roll it out then chill it? I can if there's room in the fridge. Not for a long time though since it's late when I get home already.