still confused about lawn fertilizers

I'm still trying to get my head around this

so, looking at fertilizers, we have the 3 major components, namely N-P-K

N is for greening the leaves
P is to encourage root growth
K is t encourage flower growth

so, for an autumn/winter lawn feed, we don't need much nitrogen and we don't need much/any K, but we need loads of P

this is what I have learned so far .... so if this is true, why do some autumn lawn feeds (such as EverGreen Autumn Lawn Builder) state in their adverts:

SCOTTS AUTUMN LAWN BUILDER 100m2

EverGreen Autumn Lawn Builder prepares the lawn for Winter by strengthening the roots. Provides better greening next Spring. Slow release formula - no surge growth. No scorch fertiliser - no need to water in. Apply using a handheld spreader or alternatively, for larger lawns the job can be made much easier by applying using an EverGreen or Scotts Spreader. For use on lawns only. NPK 15-0-26.

p=0??? with a high K???

or am I missing something? ... are fertilizer companies conning us, or am I dumb?

I think that I will try nothing more than superphospate on my own front lawn and see if it makes any difference (

I also bought 4 boxes of B&Q salad crop fertilizer today with an N-P-K of 4-8-16 with sodium, iron, selenium, molybenium, boron, zinc, copper, cobalt and calcium (£1 per box of 750 grams) ... I will try this on my own back lawn as an autumn feed and see the difference between the superphosphate on the front lawn, and the salad crop fertilizer on the back lawn next spring

:wallbang:

 

Hmmmm.

I know nothing on the subject, but a squint round the interweb brings up links like :

N.P.K. Explained: A Summary
Which says that K also is good for roots

Explanation of NPK and fertilizers
And this one that says that K is also good for 'general plant health'

So dunno ... is it not quite as "rigid" as one thing = one benefit, and some of these components help the plant generally ... ?

 

Some more
Explanation of NPK and fertilizers