Here is a simple geometric explanation:

With the sheet taught, lift the boom, pulling the 4:1 blocks 1" further apart. This pulls 4" of the red line into the 4:1 system, moving the floating block 4", and pulling 8" of the black line into the end of the boom. However, since the end of the boom moved 1" away, this pulls 9" of line through the main sheet cleat.

So, it's 9:1, with the "extra 1" coming from the boom movement as you sheet.

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Here's another simple geometric explanation:

Imagine you had a conventional 8:1 rigged upside down like this:

     BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB Boom
       /O
      /4 4
     / 4 4
       4 4
        O

and then you take the line at the end and run it through the bottom set of blocks like this:

     BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB Boom
        O
       5 4
       5 4
        O______

Suddenly, it is 9:1. It's no different for the cascaded system. That's where the "extra 1" comes from.