Here's how I go about calculating the amount of water I need for a brew day.
Looks like you have 19.25lbs of grain there so let's multiply by 1.5 qts H20/ lbs of grain which equals 28.875 qts H20. Divide that by 4 qts/gal = 7.22 gal H20 for the mash. Grain absorption of water is supposed to be equal to it's weight so divide 19.25 by the weight of H20 (8.3lbs/gal) = 2.32gal lost to grain absorption. 7.22gal - 2.32gal should net close to 4.9gal for the first runnings. So I would expect to sparge with say a touch more than 6gal to get to my 11gal preboil volume.
Once upon a time I was cruising though Palmer's "How to Brew" and stumbled across the chapter on efficiency and basically it talks about how to extract the most amount of sugars from the grain bill. If you shoot for a 50/50 split between the first runnings and the sparge you will see your efficiency numbers climb. So I started crunching the numbers, with the formula above, for 1.5, 1.75, 2.0 qts of H2O/lb of grains for each recipe I make and eventually I would find a volume of water that gave me a pretty even split or 50/50 between 1st runnings and the sparge.
For your recipe I would use more like 7.82gal of H2O to mash in and expect to get about 5.5gal first runnings. Then I would sparge with another 5.5gal to reach the 11gal preboil volume ( ;
