This was certainly a puzzler. Let’s look at it mathematically, rather than going with how things feel as we look at the lane in the stance. We know the 4 pin is on about the 32nd board, the 7 pin is on about the 37th board, and we would like the ball to hit them both. As you probably know, it’s 60 feet from the foul line to the center of the head pin. The pins are on 12 inch center-to-center triangles. Therefore, to hit both the 4 and 7 pins, I would want the ball to be on about the 34th board 61.73 feet down the lane.
The ball path will be a bit longer (61.79). Let’s make a triangle of these points. Draw a line connecting the laydown point at the foul line (8) to the objective (the 34th board at 61.73 feet down the lane). From that point, draw a line parallel to the ditch to the 34th board at the foul line. Finally, draw a line from the 34th board at the foul line to the 8th board at the foul line.
If I draw a line from where I want to be at the pin deck (34th board at 61.73 feet) to where I want to be at the arrows (10th board) and then continue that line so I can define my laydown point at the foul line and where I would be on the approach, the numbers are different than either one of us thought.
Foul line = 2.3 board
5 feet = 4.87 board
10 feet = 7.43 board
15 feet = 10 board
20 feet = 12.57 board
25 feet = 15.13 board
30 feet = 17.70 board
35 feet = 20.26 board
40 feet = 22.83 board
45 feet = 25.40 board
50 feet = 27.96 board
55 feet = 30.53 board
60 feet = 33.09 board
61.73 feet = 34 board
Continuing the line back from the foul line indicates this:
5 feet behind the foul line = inside of slide foot needs to be on 6.7 board/ball would be on -0.26
10 feet behind the foul line = inside of slide foot needs to be on 4.2 board/ball would be on -2.83
12 feet behind the foul line (first row of dots) = inside of slide foot needs to be on 3.1 board/ball would be on -3.86
15 feet behind the foul line (second row of dots) = inside of slide foot needs to be on 1.6 board/ball would need to be on the -5.40 board
So, if you wanted the ball to be on the 10th board at 15 feet going toward the 34th board at 61.73 feet and you stood on the first row of dots, you would need to stand on about the 3rd board, which with a 7 board displacement, would put the ball over the negative 3.86 board.
If we wish to slide on 15 and have the laydown point be at the 8th board at the foul line as in my original suggestion, the objective at the arrows must change. It will need to be about 14 (14.32 to be exact) in order for the ball to be on the 34th board 61.73 feet down the lane. For the ball to go from the 8th board at the foul line to the 34th board at the pin deck, the ball will need to cross 26 boards in that 61.79 feet or about .42 boards per foot. So the ball path would be:
Foul line = 8th board
5 feet = 10.10 board
10 feet = 12.21 board
15 feet = 14.31 board
20 feet = 16.42 board
25 feet = 18.52 board
30 feet = 20.63 board
35 feet = 22.73 board
40 feet = 24.84 board
45 feet = 26.94 board
50 feet = 29.04 board
55 feet = 31.15 board
60 feet = 33.25 board
61.73 feet = 34 board
Like in the example above, if I continue the line back through the foul line and on to the approach, with a ball displacement of seven boards, I would get these positions:
5 feet behind the foul line = inside of slide foot needs to be on 12.9/ball would be on 5.90
10 feet behind the foul line = inside of slide foot needs to be on 10.8/ball would be on 3.79
12 feet behind the foul line = inside of slide foot needs to be on 9.9/ball would be on 2.95
15 feet behind the foul line = inside of slide foot needs to be on 8.7/ball would be on 1.69
In this instance, if you stood on the first row of dots, you would need to start from about the 3rd board. Both of these examples, of course, include feet, hips, and shoulders facing the objective and a sliding farther left at the foul line than the board on which you started.
It's been an interesting discussion. As you can see, the math shows that the facts are quite different than our perceptions. Some people stand in front of the 4/7 and play down the boards to make the spare and others are much more cross lane shooters like the example of laying the ball down near the 2nd board. The bottom line is that you do whatever is comfortable for you to make the spare.