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Bonestar

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After the transfer my boil kettle has 1.25 gallons of wort left in the bottom.

Knowing this... I make my calculations as follows.

I boil 8 gallons
I loose 1.5 gallons to boil off.
I loose 1.25 gallons to the kettle.
I end up with roughly 5 gallons in my carboy.

I adjust my Beer Smith settings for all this but I continue to miss my target OG. However, when I go back and change my batch size to 6.25 (My actual post boil volume) I nail the OG. Should I be setting my batch size for my post boil volume to properly calculate my ingredients?
 
Batch size is how much volume is in your kettle at flame out. If you lose volume in your kettle or CFC or hoses that is still wort, it just didn't make it to the fermenter. You have to account for all that because there are sugars and IBUs in the lost wort.

The bigger problem is that 1.25 gallons in the kettle seems like too much loss. I would look at redesigning your pick up tube.
 
It is a 10 gallon Polarware Kettle with a torpedo screen. Got it from Northern Brewer. I personally think that the hole was drilled too high but not by much. What do you suggest I do to fix the tube?
 
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