But the distance from the luff cringle to the deck is being shortened, so must be counted. Consider if you just had a line going from the gooseneck, up to the luff cringle, and down to the deck. For every inch the luff moves down you would take in two inches of line, ergo a 2:1 system.
A 3:1 system would require the line to start at the leach cringle.
Edit to add: the direction that the final line is pulled in makes no difference in this case. If you stood at the mast and pulled downwards on the line directly below the luff cringle you would have a 3:1 system rigged to advantage, which is functionally the same as a 4:1 system. Consider that the turning block at the base of the mast does not change the length of line pulled for a given movement of the sail.
Edit 2: why would pulling upwards be different to pulling backwards?
I still think it's a 3:1 purchase.
In the standard single line set up, there are only 3 lines being shortened - the line from the boom end up to the leech cringle, the line from the leech cringle back down to the boom end and finally the line from the boom front end up to the luff cringle. The line coming back down from the luff cringle is just the pulling in line and, in any diagrams I've seen, isn't counted as part of the purchase system.
For those who think it's 4:1 ask yourself how it could be reduced to 3:1 - what intervening step could be eliminated.
I think if, at the luff, the line after going up to the luff cringle came back down to a block on the boom and was then taken in by being pulled upwards then that would give you a 4:1 purchase.
