First-pitch strikes

Yes, this is about Tim Lincecum -- but my purpose is to get others to broaden it out.

I have mentioned here that Tim is a better pitcher when he gets strike one.  I would assume that would be the case with virtually all pitchers. But by how much?

Last season batters didn't hit quite as well against Tim when he got the first pitch over, but the huge difference was that his walk rate was only about a quarter as high when that first pitch was a strike.

In last night's strange game, the far bigger difference was in hits rather than walks.  The 12 times Tim's first pitch was a strike, batters went only 1-for-8 against him (a single) with two walks and a sacrifice.  The seven times Tim's first pitch missed, batters went a healthy 3-for-5 (including two doubles) with two walks.

My question is, how much difference DOES throwing that first pitch strike make?  Anyone know of any overall stats or have any experience with a particular pitcher?