You choose how long a bar you want to use based on your available room, my example was 15" link bar. Then you decide how much actual lift you want at the axle, I choose to have 13" of lift. Now you look at your bag an see how much stroke it has, I said it has 7" of stroke.
Now, from right triangle geometry, the angle at the pivot point is shared so the tangent of this angle is the same for each lift to distance ratio.
So (13/15)=(7/?). The question mark is the distance from the pivot point to the bag. So you divide 13 by 15 and get .866667, then divide 7 by .866667 to get ~8". Whoever told you to start at halfway when deciding on placement has made things a lot more difficult than it has to be. You choose the amount of lift you want and the length of the canti bar because that is the least amount of math to get the placement.
There are other ways, but there is no reason start from the center of the bar.
Now the type of lever setup I'm talking about has the fulcrum on one end of the bar. If you place the fulcrum in the middle of the bar then things are different.
So you need to decide on that as well.