Fertilizer question

Method for converting an N-P-K value to an actual composition
The factors for converting from P2O5 and K2O values to their respective P and K elemental values are as follows:

• P2O5 consists of 56.4% oxygen and 43.6% elemental phosphorus. The percentage (mass fraction) of elemental phosphorus is 43.6% so P = 0.436 x P2O5

• K2O consists of 17% oxygen and 83% elemental potassium. The percentage (mass fraction) of elemental potassium is 83% so K = 0.83 x K2O

• Nitrogen values represent actual nitrogen content so these numbers do not need to be converted.

Using these conversion factors we can determine that an 18−51−20 fertilizer contains by weight:

• 18% elemental (N)
• 22% elemental (P), and
• 16% elemental (K)

 

a typical example of the lawn fertilizers:

Scotts lawn builder Autumn Lawn food which is recommended during Autumn / winter has an N-P-K ratio of 16-0-16

http://www.lovethegarden.com/files/sc-lb-lawn-food-autumn-label.pdf

there is 0% P so, this does not feed the rootgrowth, and is high in N and K?

then, there is Scotts Prewinter with an N-P-K of 14-5-21 plus 2Mg0
Landscapes-Direct.com | Providing landscape design & build supplies to landscaping specialists across the UK.

then we have Lebanon country club fertilizer which is recommended to be used until october ... has an N-P-K of 8-4-24
Lebanon Country Club 8-4-24 - Lebanon Country Club - Pitchcare Shop

then we have Premier Autumn / Winter lawn fertilizer with an N-P-K of 3-6-8 plus 4%Fe
Premier 3+6+8+4%Fe Autumn & Winter Mini Gran 25kg - Premier Range Fertiliser - Pitchcare Shop

loads more and none makes sense as they all differ greatly?

so, my theory is that the lawn roots need strengthening during winter .... the lawn will not need nitrogen or K, (unless I am missing something?) so I may aswell go to poundland and buy 900 grams boxes of superhosphate for a pound each and use this over winter as it's also slow release and has an N-P-K of 0-17-0 .... £5-£6 worth of superphosphate will be enough for an average sized lawn

then in spring, use phostrogen (which is very cheap and which I know does wonders to the lawn) and if there are any moss/weeds, use something appropriate at the time