Thanks to all for your comments (and noticing the typo), and especially to Dnddungeoneer for the pdf, it's just awesome ! I'll link it in front page.
Perhaps I shall have said that the math is not here to prevent the cool. Just to help the DM figure out how well (or how badly) the PC may handle any given challenge. Sometime it is worth figuring it out in advance.
Dont see how this is any easier or quicker than adding up the monster XP and referring to a chart?
Of course everyone is entitled to use their preferred system to build encounters, from the official rules to plain DM intuition, I respect that. So if you are happy with official rules, good for you.
I think it is however easier to remember a table with simple numbers and almost logical progression, forget the parties sizes factors, and cure the "lich and 3 rats" issue. This is of course a matter of taste… Just give it a try
Now to answer specific questions : yes, NPC should be treated according to their CR, not their level. If you look at the NPC mage of 9th level casting ability in the Basic Rules, she is quoted as a CR6. Well, CR6 is PEL 13, but a level 9 PC is PEL 9, so I assume that the table are not meant to be used for PvP. A deadly encounter doesn't mean that the monsters are exactly of the same strength as the PCs. Experience will tell exactly what "deadly" means. And perhaps the DMG will come with a formula to assess CR to PCs. For the moment, I limited myself to the material available in the Basic Rules.
A single giant is much, much easier to take down than an equivalent number of goblins, and is far less likely to KO one or more party members.
Let's take this one as an example, and let's assume a party of 4.
A hill giant is CR 5 - 1800 XP (*) - PEL 11
A goblin is CR 1/4 - 50 XP - PEL 1
How many goblins do I need to get a challenge equivalent of a Hill giant ?
My method: 11 (this is straightforward)
Official method: the number of goblins will be 1800 / 50 / fudge factor. But fudge factor depends on the number of gobelin. So N = 36 / f(N). Now we can only resort to gut feeling go guess the initial range of N
Let's try a party of 7-10. Encounter multiplier is x2.5, so the number of goblins will be 36 / 2.5 = 14; Oops.
Let's try a party of 11-14 then. Number of gobelin is then 12 !
You can see how simple is my approximate method with respect to the official one. It brings the same answer, up to the advertised accuracy of 10%. And my gut feeling is that against a dozen of goblins, the real challenge will be much more affected by the encounter condition (ambush, …) than by one goblin missing the show.
Even if I don't have time to address all comments, I really welcome feedback, including (and especially) from real tabletop situations.